Properties

Label 684.3.m.a.353.8
Level $684$
Weight $3$
Character 684.353
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 353.8
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.55262 - 1.57611i) q^{3} +9.08186i q^{5} +(3.71777 - 6.43936i) q^{7} +(4.03172 + 8.04644i) q^{9} +O(q^{10})\) \(q+(-2.55262 - 1.57611i) q^{3} +9.08186i q^{5} +(3.71777 - 6.43936i) q^{7} +(4.03172 + 8.04644i) q^{9} +(-3.75893 - 2.17022i) q^{11} +(5.81239 - 10.0674i) q^{13} +(14.3141 - 23.1825i) q^{15} +(18.6676 + 10.7777i) q^{17} +(-9.10009 - 16.6790i) q^{19} +(-19.6392 + 10.5776i) q^{21} +(-3.34831 - 1.93315i) q^{23} -57.4802 q^{25} +(2.39066 - 26.8940i) q^{27} +50.7205i q^{29} +(17.5657 + 30.4248i) q^{31} +(6.17460 + 11.4642i) q^{33} +(58.4814 + 33.7642i) q^{35} +22.6583 q^{37} +(-30.7041 + 16.5371i) q^{39} +39.2048i q^{41} +(3.94146 + 6.82682i) q^{43} +(-73.0766 + 36.6156i) q^{45} -66.6664i q^{47} +(-3.14360 - 5.44487i) q^{49} +(-30.6643 - 56.9337i) q^{51} +(10.7574 - 6.21080i) q^{53} +(19.7096 - 34.1381i) q^{55} +(-3.05893 + 56.9179i) q^{57} +113.530i q^{59} +100.522 q^{61} +(66.8030 + 3.95306i) q^{63} +(91.4303 + 52.7873i) q^{65} +(-36.7385 + 63.6330i) q^{67} +(5.50009 + 10.2119i) q^{69} +(-2.86289 - 1.65289i) q^{71} +(17.9246 - 31.0463i) q^{73} +(146.725 + 90.5953i) q^{75} +(-27.9496 + 16.1367i) q^{77} +(63.5801 + 110.124i) q^{79} +(-48.4904 + 64.8821i) q^{81} +(-76.8076 - 44.3449i) q^{83} +(-97.8819 + 169.536i) q^{85} +(79.9413 - 129.470i) q^{87} +(78.4512 - 45.2938i) q^{89} +(-43.2183 - 74.8562i) q^{91} +(3.11427 - 105.348i) q^{93} +(151.476 - 82.6457i) q^{95} +(29.8352 + 51.6761i) q^{97} +(2.30757 - 38.9957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −2.55262 1.57611i −0.850873 0.525372i
\(4\) 0 0
\(5\) 9.08186i 1.81637i 0.418567 + 0.908186i \(0.362532\pi\)
−0.418567 + 0.908186i \(0.637468\pi\)
\(6\) 0 0
\(7\) 3.71777 6.43936i 0.531110 0.919909i −0.468231 0.883606i \(-0.655109\pi\)
0.999341 0.0363030i \(-0.0115581\pi\)
\(8\) 0 0
\(9\) 4.03172 + 8.04644i 0.447969 + 0.894049i
\(10\) 0 0
\(11\) −3.75893 2.17022i −0.341721 0.197293i 0.319312 0.947650i \(-0.396548\pi\)
−0.661033 + 0.750357i \(0.729882\pi\)
\(12\) 0 0
\(13\) 5.81239 10.0674i 0.447107 0.774412i −0.551089 0.834446i \(-0.685788\pi\)
0.998196 + 0.0600340i \(0.0191209\pi\)
\(14\) 0 0
\(15\) 14.3141 23.1825i 0.954270 1.54550i
\(16\) 0 0
\(17\) 18.6676 + 10.7777i 1.09809 + 0.633985i 0.935720 0.352745i \(-0.114752\pi\)
0.162374 + 0.986729i \(0.448085\pi\)
\(18\) 0 0
\(19\) −9.10009 16.6790i −0.478952 0.877841i
\(20\) 0 0
\(21\) −19.6392 + 10.5776i −0.935201 + 0.503696i
\(22\) 0 0
\(23\) −3.34831 1.93315i −0.145579 0.0840498i 0.425441 0.904986i \(-0.360119\pi\)
−0.571020 + 0.820936i \(0.693452\pi\)
\(24\) 0 0
\(25\) −57.4802 −2.29921
\(26\) 0 0
\(27\) 2.39066 26.8940i 0.0885428 0.996072i
\(28\) 0 0
\(29\) 50.7205i 1.74898i 0.485042 + 0.874491i \(0.338804\pi\)
−0.485042 + 0.874491i \(0.661196\pi\)
\(30\) 0 0
\(31\) 17.5657 + 30.4248i 0.566637 + 0.981444i 0.996895 + 0.0787382i \(0.0250891\pi\)
−0.430258 + 0.902706i \(0.641578\pi\)
\(32\) 0 0
\(33\) 6.17460 + 11.4642i 0.187109 + 0.347401i
\(34\) 0 0
\(35\) 58.4814 + 33.7642i 1.67090 + 0.964693i
\(36\) 0 0
\(37\) 22.6583 0.612388 0.306194 0.951969i \(-0.400944\pi\)
0.306194 + 0.951969i \(0.400944\pi\)
\(38\) 0 0
\(39\) −30.7041 + 16.5371i −0.787286 + 0.424029i
\(40\) 0 0
\(41\) 39.2048i 0.956214i 0.878301 + 0.478107i \(0.158677\pi\)
−0.878301 + 0.478107i \(0.841323\pi\)
\(42\) 0 0
\(43\) 3.94146 + 6.82682i 0.0916619 + 0.158763i 0.908211 0.418514i \(-0.137449\pi\)
−0.816549 + 0.577277i \(0.804115\pi\)
\(44\) 0 0
\(45\) −73.0766 + 36.6156i −1.62393 + 0.813679i
\(46\) 0 0
\(47\) 66.6664i 1.41843i −0.704990 0.709217i \(-0.749049\pi\)
0.704990 0.709217i \(-0.250951\pi\)
\(48\) 0 0
\(49\) −3.14360 5.44487i −0.0641551 0.111120i
\(50\) 0 0
\(51\) −30.6643 56.9337i −0.601261 1.11635i
\(52\) 0 0
\(53\) 10.7574 6.21080i 0.202970 0.117185i −0.395070 0.918651i \(-0.629280\pi\)
0.598040 + 0.801466i \(0.295946\pi\)
\(54\) 0 0
\(55\) 19.7096 34.1381i 0.358357 0.620692i
\(56\) 0 0
\(57\) −3.05893 + 56.9179i −0.0536654 + 0.998559i
\(58\) 0 0
\(59\) 113.530i 1.92424i 0.272626 + 0.962120i \(0.412108\pi\)
−0.272626 + 0.962120i \(0.587892\pi\)
\(60\) 0 0
\(61\) 100.522 1.64791 0.823955 0.566656i \(-0.191763\pi\)
0.823955 + 0.566656i \(0.191763\pi\)
\(62\) 0 0
\(63\) 66.8030 + 3.95306i 1.06036 + 0.0627469i
\(64\) 0 0
\(65\) 91.4303 + 52.7873i 1.40662 + 0.812113i
\(66\) 0 0
\(67\) −36.7385 + 63.6330i −0.548336 + 0.949746i 0.450053 + 0.893002i \(0.351405\pi\)
−0.998389 + 0.0567438i \(0.981928\pi\)
\(68\) 0 0
\(69\) 5.50009 + 10.2119i 0.0797115 + 0.147999i
\(70\) 0 0
\(71\) −2.86289 1.65289i −0.0403224 0.0232802i 0.479703 0.877431i \(-0.340744\pi\)
−0.520026 + 0.854151i \(0.674078\pi\)
\(72\) 0 0
\(73\) 17.9246 31.0463i 0.245542 0.425292i −0.716742 0.697339i \(-0.754367\pi\)
0.962284 + 0.272047i \(0.0877007\pi\)
\(74\) 0 0
\(75\) 146.725 + 90.5953i 1.95633 + 1.20794i
\(76\) 0 0
\(77\) −27.9496 + 16.1367i −0.362982 + 0.209568i
\(78\) 0 0
\(79\) 63.5801 + 110.124i 0.804812 + 1.39397i 0.916418 + 0.400222i \(0.131067\pi\)
−0.111607 + 0.993752i \(0.535600\pi\)
\(80\) 0 0
\(81\) −48.4904 + 64.8821i −0.598647 + 0.801013i
\(82\) 0 0
\(83\) −76.8076 44.3449i −0.925393 0.534276i −0.0400412 0.999198i \(-0.512749\pi\)
−0.885351 + 0.464922i \(0.846082\pi\)
\(84\) 0 0
\(85\) −97.8819 + 169.536i −1.15155 + 1.99455i
\(86\) 0 0
\(87\) 79.9413 129.470i 0.918865 1.48816i
\(88\) 0 0
\(89\) 78.4512 45.2938i 0.881474 0.508919i 0.0103298 0.999947i \(-0.496712\pi\)
0.871144 + 0.491027i \(0.163379\pi\)
\(90\) 0 0
\(91\) −43.2183 74.8562i −0.474926 0.822596i
\(92\) 0 0
\(93\) 3.11427 105.348i 0.0334867 1.13278i
\(94\) 0 0
\(95\) 151.476 82.6457i 1.59449 0.869955i
\(96\) 0 0
\(97\) 29.8352 + 51.6761i 0.307579 + 0.532743i 0.977832 0.209390i \(-0.0671477\pi\)
−0.670253 + 0.742133i \(0.733814\pi\)
\(98\) 0 0
\(99\) 2.30757 38.9957i 0.0233087 0.393896i
\(100\) 0 0
\(101\) 160.036i 1.58452i 0.610185 + 0.792259i \(0.291095\pi\)
−0.610185 + 0.792259i \(0.708905\pi\)
\(102\) 0 0
\(103\) −16.7614 29.0316i −0.162732 0.281860i 0.773116 0.634265i \(-0.218697\pi\)
−0.935848 + 0.352405i \(0.885364\pi\)
\(104\) 0 0
\(105\) −96.0644 178.361i −0.914899 1.69867i
\(106\) 0 0
\(107\) 113.499i 1.06073i 0.847768 + 0.530367i \(0.177946\pi\)
−0.847768 + 0.530367i \(0.822054\pi\)
\(108\) 0 0
\(109\) −27.9996 + 48.4968i −0.256877 + 0.444925i −0.965404 0.260760i \(-0.916027\pi\)
0.708526 + 0.705684i \(0.249360\pi\)
\(110\) 0 0
\(111\) −57.8381 35.7121i −0.521064 0.321731i
\(112\) 0 0
\(113\) 27.7838 16.0410i 0.245874 0.141955i −0.372000 0.928233i \(-0.621328\pi\)
0.617874 + 0.786278i \(0.287994\pi\)
\(114\) 0 0
\(115\) 17.5566 30.4089i 0.152666 0.264425i
\(116\) 0 0
\(117\) 104.440 + 6.18024i 0.892653 + 0.0528226i
\(118\) 0 0
\(119\) 138.804 80.1383i 1.16642 0.673431i
\(120\) 0 0
\(121\) −51.0803 88.4737i −0.422151 0.731187i
\(122\) 0 0
\(123\) 61.7912 100.075i 0.502368 0.813617i
\(124\) 0 0
\(125\) 294.980i 2.35984i
\(126\) 0 0
\(127\) 113.530 + 196.639i 0.893934 + 1.54834i 0.835119 + 0.550070i \(0.185399\pi\)
0.0588151 + 0.998269i \(0.481268\pi\)
\(128\) 0 0
\(129\) 0.698790 23.6385i 0.00541698 0.183244i
\(130\) 0 0
\(131\) 80.7881i 0.616703i 0.951272 + 0.308352i \(0.0997773\pi\)
−0.951272 + 0.308352i \(0.900223\pi\)
\(132\) 0 0
\(133\) −141.234 3.40980i −1.06191 0.0256376i
\(134\) 0 0
\(135\) 244.247 + 21.7116i 1.80924 + 0.160827i
\(136\) 0 0
\(137\) 200.994i 1.46711i −0.679631 0.733555i \(-0.737860\pi\)
0.679631 0.733555i \(-0.262140\pi\)
\(138\) 0 0
\(139\) −115.620 + 200.259i −0.831797 + 1.44072i 0.0648140 + 0.997897i \(0.479355\pi\)
−0.896611 + 0.442818i \(0.853979\pi\)
\(140\) 0 0
\(141\) −105.074 + 170.174i −0.745205 + 1.20691i
\(142\) 0 0
\(143\) −43.6967 + 25.2283i −0.305572 + 0.176422i
\(144\) 0 0
\(145\) −460.636 −3.17680
\(146\) 0 0
\(147\) −0.557335 + 18.8534i −0.00379139 + 0.128254i
\(148\) 0 0
\(149\) 215.584i 1.44688i −0.690390 0.723438i \(-0.742561\pi\)
0.690390 0.723438i \(-0.257439\pi\)
\(150\) 0 0
\(151\) 37.9858 65.7932i 0.251561 0.435717i −0.712395 0.701779i \(-0.752389\pi\)
0.963956 + 0.266062i \(0.0857227\pi\)
\(152\) 0 0
\(153\) −11.4598 + 193.661i −0.0749009 + 1.26576i
\(154\) 0 0
\(155\) −276.313 + 159.530i −1.78267 + 1.02922i
\(156\) 0 0
\(157\) −77.9228 −0.496324 −0.248162 0.968719i \(-0.579826\pi\)
−0.248162 + 0.968719i \(0.579826\pi\)
\(158\) 0 0
\(159\) −37.2485 1.10113i −0.234268 0.00692532i
\(160\) 0 0
\(161\) −24.8965 + 14.3740i −0.154636 + 0.0892794i
\(162\) 0 0
\(163\) 13.6477 0.0837281 0.0418641 0.999123i \(-0.486670\pi\)
0.0418641 + 0.999123i \(0.486670\pi\)
\(164\) 0 0
\(165\) −104.117 + 56.0768i −0.631010 + 0.339860i
\(166\) 0 0
\(167\) 55.3372 + 31.9490i 0.331361 + 0.191311i 0.656445 0.754374i \(-0.272059\pi\)
−0.325084 + 0.945685i \(0.605393\pi\)
\(168\) 0 0
\(169\) 16.9322 + 29.3274i 0.100190 + 0.173535i
\(170\) 0 0
\(171\) 97.5174 140.468i 0.570277 0.821453i
\(172\) 0 0
\(173\) −149.313 + 86.2059i −0.863081 + 0.498300i −0.865043 0.501698i \(-0.832709\pi\)
0.00196174 + 0.999998i \(0.499376\pi\)
\(174\) 0 0
\(175\) −213.698 + 370.136i −1.22113 + 2.11506i
\(176\) 0 0
\(177\) 178.937 289.799i 1.01094 1.63728i
\(178\) 0 0
\(179\) 58.2650i 0.325503i −0.986667 0.162751i \(-0.947963\pi\)
0.986667 0.162751i \(-0.0520369\pi\)
\(180\) 0 0
\(181\) −149.077 258.209i −0.823631 1.42657i −0.902961 0.429723i \(-0.858611\pi\)
0.0793295 0.996848i \(-0.474722\pi\)
\(182\) 0 0
\(183\) −256.596 158.435i −1.40216 0.865765i
\(184\) 0 0
\(185\) 205.780i 1.11232i
\(186\) 0 0
\(187\) −46.7801 81.0255i −0.250161 0.433291i
\(188\) 0 0
\(189\) −164.292 115.380i −0.869270 0.610475i
\(190\) 0 0
\(191\) −108.988 62.9245i −0.570620 0.329448i 0.186777 0.982402i \(-0.440196\pi\)
−0.757397 + 0.652955i \(0.773529\pi\)
\(192\) 0 0
\(193\) 77.3511 0.400783 0.200391 0.979716i \(-0.435779\pi\)
0.200391 + 0.979716i \(0.435779\pi\)
\(194\) 0 0
\(195\) −150.188 278.851i −0.770194 1.43000i
\(196\) 0 0
\(197\) 107.228i 0.544304i 0.962254 + 0.272152i \(0.0877354\pi\)
−0.962254 + 0.272152i \(0.912265\pi\)
\(198\) 0 0
\(199\) −24.3491 42.1738i −0.122357 0.211929i 0.798340 0.602207i \(-0.205712\pi\)
−0.920697 + 0.390279i \(0.872379\pi\)
\(200\) 0 0
\(201\) 194.072 104.527i 0.965534 0.520033i
\(202\) 0 0
\(203\) 326.608 + 188.567i 1.60890 + 0.928901i
\(204\) 0 0
\(205\) −356.052 −1.73684
\(206\) 0 0
\(207\) 2.05549 34.7359i 0.00992990 0.167806i
\(208\) 0 0
\(209\) −1.99045 + 82.4443i −0.00952367 + 0.394470i
\(210\) 0 0
\(211\) −9.00077 −0.0426577 −0.0213288 0.999773i \(-0.506790\pi\)
−0.0213288 + 0.999773i \(0.506790\pi\)
\(212\) 0 0
\(213\) 4.70273 + 8.73145i 0.0220785 + 0.0409927i
\(214\) 0 0
\(215\) −62.0002 + 35.7958i −0.288373 + 0.166492i
\(216\) 0 0
\(217\) 261.221 1.20379
\(218\) 0 0
\(219\) −94.6871 + 50.9981i −0.432361 + 0.232868i
\(220\) 0 0
\(221\) 217.007 125.289i 0.981931 0.566918i
\(222\) 0 0
\(223\) −116.684 202.102i −0.523246 0.906288i −0.999634 0.0270532i \(-0.991388\pi\)
0.476388 0.879235i \(-0.341946\pi\)
\(224\) 0 0
\(225\) −231.744 462.511i −1.02997 2.05560i
\(226\) 0 0
\(227\) 127.238 + 73.4611i 0.560522 + 0.323617i 0.753355 0.657614i \(-0.228434\pi\)
−0.192833 + 0.981232i \(0.561768\pi\)
\(228\) 0 0
\(229\) −109.935 190.413i −0.480065 0.831496i 0.519674 0.854365i \(-0.326053\pi\)
−0.999738 + 0.0228685i \(0.992720\pi\)
\(230\) 0 0
\(231\) 96.7781 + 2.86091i 0.418953 + 0.0123849i
\(232\) 0 0
\(233\) 87.1319 + 50.3056i 0.373956 + 0.215904i 0.675186 0.737648i \(-0.264064\pi\)
−0.301229 + 0.953552i \(0.597397\pi\)
\(234\) 0 0
\(235\) 605.455 2.57640
\(236\) 0 0
\(237\) 11.2722 381.314i 0.0475622 1.60892i
\(238\) 0 0
\(239\) 224.956 129.878i 0.941237 0.543423i 0.0508891 0.998704i \(-0.483794\pi\)
0.890348 + 0.455281i \(0.150461\pi\)
\(240\) 0 0
\(241\) 80.0410 0.332120 0.166060 0.986116i \(-0.446895\pi\)
0.166060 + 0.986116i \(0.446895\pi\)
\(242\) 0 0
\(243\) 226.039 89.1928i 0.930202 0.367048i
\(244\) 0 0
\(245\) 49.4495 28.5497i 0.201835 0.116529i
\(246\) 0 0
\(247\) −220.807 5.33092i −0.893954 0.0215827i
\(248\) 0 0
\(249\) 126.168 + 234.253i 0.506698 + 0.940776i
\(250\) 0 0
\(251\) −99.7198 + 57.5732i −0.397290 + 0.229375i −0.685314 0.728248i \(-0.740335\pi\)
0.288024 + 0.957623i \(0.407002\pi\)
\(252\) 0 0
\(253\) 8.39070 + 14.5331i 0.0331648 + 0.0574432i
\(254\) 0 0
\(255\) 517.064 278.489i 2.02770 1.09211i
\(256\) 0 0
\(257\) 283.621 + 163.749i 1.10358 + 0.637154i 0.937160 0.348900i \(-0.113445\pi\)
0.166424 + 0.986054i \(0.446778\pi\)
\(258\) 0 0
\(259\) 84.2385 145.905i 0.325245 0.563341i
\(260\) 0 0
\(261\) −408.119 + 204.491i −1.56368 + 0.783491i
\(262\) 0 0
\(263\) −59.4198 + 34.3060i −0.225931 + 0.130441i −0.608693 0.793405i \(-0.708306\pi\)
0.382763 + 0.923847i \(0.374973\pi\)
\(264\) 0 0
\(265\) 56.4056 + 97.6974i 0.212851 + 0.368670i
\(266\) 0 0
\(267\) −271.644 8.03023i −1.01739 0.0300758i
\(268\) 0 0
\(269\) 59.6954 + 34.4652i 0.221916 + 0.128123i 0.606837 0.794826i \(-0.292438\pi\)
−0.384921 + 0.922949i \(0.625771\pi\)
\(270\) 0 0
\(271\) 156.478 271.029i 0.577411 1.00011i −0.418364 0.908280i \(-0.637396\pi\)
0.995775 0.0918261i \(-0.0292704\pi\)
\(272\) 0 0
\(273\) −7.66225 + 259.196i −0.0280669 + 0.949437i
\(274\) 0 0
\(275\) 216.064 + 124.744i 0.785687 + 0.453616i
\(276\) 0 0
\(277\) 253.618 439.279i 0.915588 1.58584i 0.109549 0.993981i \(-0.465059\pi\)
0.806039 0.591863i \(-0.201607\pi\)
\(278\) 0 0
\(279\) −173.991 + 264.006i −0.623623 + 0.946258i
\(280\) 0 0
\(281\) 462.014i 1.64418i −0.569359 0.822089i \(-0.692809\pi\)
0.569359 0.822089i \(-0.307191\pi\)
\(282\) 0 0
\(283\) 52.1104 0.184136 0.0920678 0.995753i \(-0.470652\pi\)
0.0920678 + 0.995753i \(0.470652\pi\)
\(284\) 0 0
\(285\) −516.920 27.7808i −1.81375 0.0974764i
\(286\) 0 0
\(287\) 252.454 + 145.754i 0.879630 + 0.507855i
\(288\) 0 0
\(289\) 87.8193 + 152.108i 0.303873 + 0.526324i
\(290\) 0 0
\(291\) 5.28954 178.933i 0.0181771 0.614890i
\(292\) 0 0
\(293\) 209.042 120.691i 0.713455 0.411913i −0.0988841 0.995099i \(-0.531527\pi\)
0.812339 + 0.583186i \(0.198194\pi\)
\(294\) 0 0
\(295\) −1031.06 −3.49514
\(296\) 0 0
\(297\) −67.3521 + 95.9042i −0.226775 + 0.322910i
\(298\) 0 0
\(299\) −38.9234 + 22.4724i −0.130178 + 0.0751586i
\(300\) 0 0
\(301\) 58.6138 0.194730
\(302\) 0 0
\(303\) 252.236 408.512i 0.832461 1.34822i
\(304\) 0 0
\(305\) 912.931i 2.99322i
\(306\) 0 0
\(307\) −10.6736 + 18.4872i −0.0347673 + 0.0602187i −0.882885 0.469588i \(-0.844402\pi\)
0.848118 + 0.529807i \(0.177736\pi\)
\(308\) 0 0
\(309\) −2.97166 + 100.524i −0.00961702 + 0.325322i
\(310\) 0 0
\(311\) −228.456 + 131.899i −0.734587 + 0.424114i −0.820098 0.572223i \(-0.806081\pi\)
0.0855112 + 0.996337i \(0.472748\pi\)
\(312\) 0 0
\(313\) −8.08946 −0.0258449 −0.0129225 0.999917i \(-0.504113\pi\)
−0.0129225 + 0.999917i \(0.504113\pi\)
\(314\) 0 0
\(315\) −35.9011 + 606.695i −0.113972 + 1.92602i
\(316\) 0 0
\(317\) 13.8994i 0.0438466i −0.999760 0.0219233i \(-0.993021\pi\)
0.999760 0.0219233i \(-0.00697897\pi\)
\(318\) 0 0
\(319\) 110.075 190.655i 0.345061 0.597664i
\(320\) 0 0
\(321\) 178.887 289.719i 0.557280 0.902550i
\(322\) 0 0
\(323\) 9.88496 409.435i 0.0306036 1.26760i
\(324\) 0 0
\(325\) −334.097 + 578.673i −1.02799 + 1.78053i
\(326\) 0 0
\(327\) 147.909 79.6632i 0.452321 0.243618i
\(328\) 0 0
\(329\) −429.289 247.850i −1.30483 0.753344i
\(330\) 0 0
\(331\) 12.4470 21.5588i 0.0376041 0.0651322i −0.846611 0.532212i \(-0.821361\pi\)
0.884215 + 0.467080i \(0.154694\pi\)
\(332\) 0 0
\(333\) 91.3522 + 182.319i 0.274331 + 0.547504i
\(334\) 0 0
\(335\) −577.906 333.654i −1.72509 0.995982i
\(336\) 0 0
\(337\) 435.422 1.29205 0.646027 0.763315i \(-0.276429\pi\)
0.646027 + 0.763315i \(0.276429\pi\)
\(338\) 0 0
\(339\) −96.2037 2.84393i −0.283787 0.00838918i
\(340\) 0 0
\(341\) 152.486i 0.447173i
\(342\) 0 0
\(343\) 317.593 0.925926
\(344\) 0 0
\(345\) −92.7431 + 49.9511i −0.268820 + 0.144786i
\(346\) 0 0
\(347\) 295.665i 0.852060i 0.904709 + 0.426030i \(0.140088\pi\)
−0.904709 + 0.426030i \(0.859912\pi\)
\(348\) 0 0
\(349\) −331.114 + 573.506i −0.948750 + 1.64328i −0.200687 + 0.979655i \(0.564317\pi\)
−0.748063 + 0.663628i \(0.769016\pi\)
\(350\) 0 0
\(351\) −256.856 180.386i −0.731783 0.513920i
\(352\) 0 0
\(353\) 244.745 + 141.304i 0.693328 + 0.400293i 0.804858 0.593468i \(-0.202242\pi\)
−0.111529 + 0.993761i \(0.535575\pi\)
\(354\) 0 0
\(355\) 15.0113 26.0004i 0.0422855 0.0732406i
\(356\) 0 0
\(357\) −480.620 14.2079i −1.34627 0.0397980i
\(358\) 0 0
\(359\) 197.563 + 114.063i 0.550316 + 0.317725i 0.749249 0.662288i \(-0.230414\pi\)
−0.198934 + 0.980013i \(0.563748\pi\)
\(360\) 0 0
\(361\) −195.377 + 303.560i −0.541210 + 0.840888i
\(362\) 0 0
\(363\) −9.05613 + 306.348i −0.0249480 + 0.843934i
\(364\) 0 0
\(365\) 281.958 + 162.789i 0.772488 + 0.445996i
\(366\) 0 0
\(367\) 224.046 0.610479 0.305239 0.952276i \(-0.401264\pi\)
0.305239 + 0.952276i \(0.401264\pi\)
\(368\) 0 0
\(369\) −315.459 + 158.063i −0.854902 + 0.428355i
\(370\) 0 0
\(371\) 92.3613i 0.248952i
\(372\) 0 0
\(373\) −44.0874 76.3616i −0.118197 0.204723i 0.800856 0.598856i \(-0.204378\pi\)
−0.919053 + 0.394134i \(0.871045\pi\)
\(374\) 0 0
\(375\) −464.923 + 752.972i −1.23979 + 2.00793i
\(376\) 0 0
\(377\) 510.621 + 294.807i 1.35443 + 0.781982i
\(378\) 0 0
\(379\) −420.700 −1.11003 −0.555013 0.831841i \(-0.687287\pi\)
−0.555013 + 0.831841i \(0.687287\pi\)
\(380\) 0 0
\(381\) 20.1279 680.880i 0.0528291 1.78709i
\(382\) 0 0
\(383\) 264.276i 0.690016i −0.938600 0.345008i \(-0.887876\pi\)
0.938600 0.345008i \(-0.112124\pi\)
\(384\) 0 0
\(385\) −146.552 253.835i −0.380653 0.659311i
\(386\) 0 0
\(387\) −39.0407 + 59.2386i −0.100880 + 0.153071i
\(388\) 0 0
\(389\) 201.953i 0.519160i −0.965722 0.259580i \(-0.916416\pi\)
0.965722 0.259580i \(-0.0835841\pi\)
\(390\) 0 0
\(391\) −41.6699 72.1744i −0.106573 0.184589i
\(392\) 0 0
\(393\) 127.331 206.221i 0.323998 0.524736i
\(394\) 0 0
\(395\) −1000.13 + 577.426i −2.53198 + 1.46184i
\(396\) 0 0
\(397\) −190.682 + 330.271i −0.480308 + 0.831918i −0.999745 0.0225909i \(-0.992808\pi\)
0.519437 + 0.854509i \(0.326142\pi\)
\(398\) 0 0
\(399\) 355.142 + 231.305i 0.890081 + 0.579712i
\(400\) 0 0
\(401\) 632.695i 1.57779i −0.614526 0.788896i \(-0.710653\pi\)
0.614526 0.788896i \(-0.289347\pi\)
\(402\) 0 0
\(403\) 408.396 1.01339
\(404\) 0 0
\(405\) −589.250 440.383i −1.45494 1.08737i
\(406\) 0 0
\(407\) −85.1711 49.1736i −0.209266 0.120820i
\(408\) 0 0
\(409\) 105.950 183.511i 0.259047 0.448683i −0.706940 0.707274i \(-0.749925\pi\)
0.965987 + 0.258591i \(0.0832582\pi\)
\(410\) 0 0
\(411\) −316.790 + 513.061i −0.770777 + 1.24832i
\(412\) 0 0
\(413\) 731.062 + 422.079i 1.77013 + 1.02198i
\(414\) 0 0
\(415\) 402.734 697.556i 0.970443 1.68086i
\(416\) 0 0
\(417\) 610.765 328.956i 1.46466 0.788863i
\(418\) 0 0
\(419\) 14.7373 8.50858i 0.0351726 0.0203069i −0.482311 0.876000i \(-0.660202\pi\)
0.517483 + 0.855693i \(0.326869\pi\)
\(420\) 0 0
\(421\) 106.884 + 185.129i 0.253881 + 0.439735i 0.964591 0.263750i \(-0.0849594\pi\)
−0.710710 + 0.703485i \(0.751626\pi\)
\(422\) 0 0
\(423\) 536.427 268.781i 1.26815 0.635415i
\(424\) 0 0
\(425\) −1073.02 619.506i −2.52474 1.45766i
\(426\) 0 0
\(427\) 373.719 647.301i 0.875221 1.51593i
\(428\) 0 0
\(429\) 151.304 + 4.47278i 0.352690 + 0.0104261i
\(430\) 0 0
\(431\) 4.09834 2.36618i 0.00950891 0.00548997i −0.495238 0.868757i \(-0.664919\pi\)
0.504747 + 0.863267i \(0.331586\pi\)
\(432\) 0 0
\(433\) 329.460 + 570.641i 0.760877 + 1.31788i 0.942399 + 0.334491i \(0.108564\pi\)
−0.181522 + 0.983387i \(0.558102\pi\)
\(434\) 0 0
\(435\) 1175.83 + 726.016i 2.70305 + 1.66900i
\(436\) 0 0
\(437\) −1.77301 + 73.4382i −0.00405724 + 0.168051i
\(438\) 0 0
\(439\) 146.973 + 254.565i 0.334791 + 0.579874i 0.983445 0.181209i \(-0.0580011\pi\)
−0.648654 + 0.761083i \(0.724668\pi\)
\(440\) 0 0
\(441\) 31.1377 47.2470i 0.0706070 0.107136i
\(442\) 0 0
\(443\) 387.744i 0.875269i 0.899153 + 0.437634i \(0.144184\pi\)
−0.899153 + 0.437634i \(0.855816\pi\)
\(444\) 0 0
\(445\) 411.352 + 712.482i 0.924386 + 1.60108i
\(446\) 0 0
\(447\) −339.786 + 550.305i −0.760147 + 1.23111i
\(448\) 0 0
\(449\) 732.714i 1.63188i −0.578137 0.815940i \(-0.696220\pi\)
0.578137 0.815940i \(-0.303780\pi\)
\(450\) 0 0
\(451\) 85.0830 147.368i 0.188654 0.326758i
\(452\) 0 0
\(453\) −200.661 + 108.075i −0.442960 + 0.238577i
\(454\) 0 0
\(455\) 679.834 392.502i 1.49414 0.862642i
\(456\) 0 0
\(457\) 208.608 361.319i 0.456472 0.790632i −0.542300 0.840185i \(-0.682446\pi\)
0.998772 + 0.0495528i \(0.0157796\pi\)
\(458\) 0 0
\(459\) 334.484 476.279i 0.728723 1.03765i
\(460\) 0 0
\(461\) −389.307 + 224.767i −0.844484 + 0.487563i −0.858786 0.512334i \(-0.828781\pi\)
0.0143016 + 0.999898i \(0.495448\pi\)
\(462\) 0 0
\(463\) −268.570 465.176i −0.580064 1.00470i −0.995471 0.0950649i \(-0.969694\pi\)
0.415407 0.909636i \(-0.363639\pi\)
\(464\) 0 0
\(465\) 956.760 + 28.2833i 2.05755 + 0.0608243i
\(466\) 0 0
\(467\) 582.780i 1.24792i −0.781455 0.623961i \(-0.785522\pi\)
0.781455 0.623961i \(-0.214478\pi\)
\(468\) 0 0
\(469\) 273.171 + 473.145i 0.582453 + 1.00884i
\(470\) 0 0
\(471\) 198.907 + 122.815i 0.422308 + 0.260754i
\(472\) 0 0
\(473\) 34.2153i 0.0723369i
\(474\) 0 0
\(475\) 523.075 + 958.710i 1.10121 + 2.01834i
\(476\) 0 0
\(477\) 93.3458 + 61.5187i 0.195694 + 0.128970i
\(478\) 0 0
\(479\) 46.4224i 0.0969153i 0.998825 + 0.0484577i \(0.0154306\pi\)
−0.998825 + 0.0484577i \(0.984569\pi\)
\(480\) 0 0
\(481\) 131.699 228.110i 0.273803 0.474241i
\(482\) 0 0
\(483\) 86.2062 + 2.54839i 0.178481 + 0.00527617i
\(484\) 0 0
\(485\) −469.315 + 270.959i −0.967659 + 0.558678i
\(486\) 0 0
\(487\) −98.2155 −0.201674 −0.100837 0.994903i \(-0.532152\pi\)
−0.100837 + 0.994903i \(0.532152\pi\)
\(488\) 0 0
\(489\) −34.8373 21.5103i −0.0712420 0.0439884i
\(490\) 0 0
\(491\) 669.171i 1.36287i −0.731877 0.681437i \(-0.761356\pi\)
0.731877 0.681437i \(-0.238644\pi\)
\(492\) 0 0
\(493\) −546.652 + 946.829i −1.10883 + 1.92055i
\(494\) 0 0
\(495\) 354.154 + 20.9570i 0.715462 + 0.0423373i
\(496\) 0 0
\(497\) −21.2871 + 12.2901i −0.0428313 + 0.0247287i
\(498\) 0 0
\(499\) 133.576 0.267686 0.133843 0.991003i \(-0.457268\pi\)
0.133843 + 0.991003i \(0.457268\pi\)
\(500\) 0 0
\(501\) −90.8996 168.771i −0.181436 0.336869i
\(502\) 0 0
\(503\) −768.121 + 443.475i −1.52708 + 0.881659i −0.527596 + 0.849495i \(0.676907\pi\)
−0.999483 + 0.0321643i \(0.989760\pi\)
\(504\) 0 0
\(505\) −1453.43 −2.87807
\(506\) 0 0
\(507\) 3.00194 101.549i 0.00592098 0.200293i
\(508\) 0 0
\(509\) −4.94903 2.85732i −0.00972305 0.00561360i 0.495131 0.868819i \(-0.335120\pi\)
−0.504854 + 0.863205i \(0.668454\pi\)
\(510\) 0 0
\(511\) −133.279 230.846i −0.260820 0.451753i
\(512\) 0 0
\(513\) −470.319 + 204.864i −0.916801 + 0.399344i
\(514\) 0 0
\(515\) 263.661 152.225i 0.511963 0.295582i
\(516\) 0 0
\(517\) −144.681 + 250.594i −0.279847 + 0.484708i
\(518\) 0 0
\(519\) 517.010 + 15.2836i 0.996165 + 0.0294482i
\(520\) 0 0
\(521\) 399.843i 0.767453i 0.923447 + 0.383726i \(0.125359\pi\)
−0.923447 + 0.383726i \(0.874641\pi\)
\(522\) 0 0
\(523\) −199.151 344.940i −0.380786 0.659541i 0.610389 0.792102i \(-0.291013\pi\)
−0.991175 + 0.132561i \(0.957680\pi\)
\(524\) 0 0
\(525\) 1128.87 608.003i 2.15022 1.15810i
\(526\) 0 0
\(527\) 757.276i 1.43696i
\(528\) 0 0
\(529\) −257.026 445.182i −0.485871 0.841554i
\(530\) 0 0
\(531\) −913.514 + 457.722i −1.72036 + 0.862001i
\(532\) 0 0
\(533\) 394.689 + 227.874i 0.740504 + 0.427530i
\(534\) 0 0
\(535\) −1030.78 −1.92669
\(536\) 0 0
\(537\) −91.8324 + 148.728i −0.171010 + 0.276962i
\(538\) 0 0
\(539\) 27.2892i 0.0506293i
\(540\) 0 0
\(541\) 142.004 + 245.957i 0.262484 + 0.454635i 0.966901 0.255151i \(-0.0821251\pi\)
−0.704418 + 0.709786i \(0.748792\pi\)
\(542\) 0 0
\(543\) −26.4302 + 894.073i −0.0486744 + 1.64654i
\(544\) 0 0
\(545\) −440.441 254.289i −0.808149 0.466585i
\(546\) 0 0
\(547\) 688.387 1.25848 0.629239 0.777212i \(-0.283367\pi\)
0.629239 + 0.777212i \(0.283367\pi\)
\(548\) 0 0
\(549\) 405.279 + 808.848i 0.738213 + 1.47331i
\(550\) 0 0
\(551\) 845.966 461.561i 1.53533 0.837679i
\(552\) 0 0
\(553\) 945.504 1.70977
\(554\) 0 0
\(555\) 324.333 525.278i 0.584383 0.946446i
\(556\) 0 0
\(557\) −640.827 + 369.982i −1.15050 + 0.664240i −0.949008 0.315251i \(-0.897911\pi\)
−0.201489 + 0.979491i \(0.564578\pi\)
\(558\) 0 0
\(559\) 91.6373 0.163931
\(560\) 0 0
\(561\) −8.29374 + 280.558i −0.0147838 + 0.500103i
\(562\) 0 0
\(563\) 537.579 310.371i 0.954847 0.551281i 0.0602639 0.998182i \(-0.480806\pi\)
0.894583 + 0.446901i \(0.147472\pi\)
\(564\) 0 0
\(565\) 145.682 + 252.328i 0.257844 + 0.446599i
\(566\) 0 0
\(567\) 237.523 + 553.464i 0.418912 + 0.976126i
\(568\) 0 0
\(569\) 536.511 + 309.755i 0.942902 + 0.544385i 0.890869 0.454261i \(-0.150097\pi\)
0.0520329 + 0.998645i \(0.483430\pi\)
\(570\) 0 0
\(571\) −87.0815 150.830i −0.152507 0.264150i 0.779641 0.626226i \(-0.215401\pi\)
−0.932148 + 0.362076i \(0.882068\pi\)
\(572\) 0 0
\(573\) 179.030 + 332.401i 0.312443 + 0.580106i
\(574\) 0 0
\(575\) 192.461 + 111.118i 0.334715 + 0.193248i
\(576\) 0 0
\(577\) −715.882 −1.24070 −0.620348 0.784327i \(-0.713009\pi\)
−0.620348 + 0.784327i \(0.713009\pi\)
\(578\) 0 0
\(579\) −197.448 121.914i −0.341015 0.210560i
\(580\) 0 0
\(581\) −571.106 + 329.728i −0.982970 + 0.567518i
\(582\) 0 0
\(583\) −53.9152 −0.0924789
\(584\) 0 0
\(585\) −56.1281 + 948.513i −0.0959455 + 1.62139i
\(586\) 0 0
\(587\) −699.883 + 404.077i −1.19230 + 0.688377i −0.958829 0.283986i \(-0.908343\pi\)
−0.233476 + 0.972363i \(0.575010\pi\)
\(588\) 0 0
\(589\) 347.604 569.847i 0.590160 0.967482i
\(590\) 0 0
\(591\) 169.003 273.712i 0.285962 0.463134i
\(592\) 0 0
\(593\) −639.673 + 369.316i −1.07871 + 0.622792i −0.930547 0.366172i \(-0.880668\pi\)
−0.148160 + 0.988963i \(0.547335\pi\)
\(594\) 0 0
\(595\) 727.804 + 1260.59i 1.22320 + 2.11865i
\(596\) 0 0
\(597\) −4.31689 + 146.031i −0.00723098 + 0.244607i
\(598\) 0 0
\(599\) 728.812 + 420.780i 1.21671 + 0.702470i 0.964214 0.265126i \(-0.0854137\pi\)
0.252501 + 0.967597i \(0.418747\pi\)
\(600\) 0 0
\(601\) −65.8638 + 114.079i −0.109590 + 0.189816i −0.915604 0.402080i \(-0.868287\pi\)
0.806014 + 0.591896i \(0.201621\pi\)
\(602\) 0 0
\(603\) −660.138 39.0636i −1.09476 0.0647821i
\(604\) 0 0
\(605\) 803.505 463.904i 1.32811 0.766784i
\(606\) 0 0
\(607\) −399.055 691.184i −0.657422 1.13869i −0.981281 0.192583i \(-0.938313\pi\)
0.323858 0.946106i \(-0.395020\pi\)
\(608\) 0 0
\(609\) −536.501 996.111i −0.880955 1.63565i
\(610\) 0 0
\(611\) −671.155 387.491i −1.09845 0.634192i
\(612\) 0 0
\(613\) 520.371 901.308i 0.848892 1.47032i −0.0333062 0.999445i \(-0.510604\pi\)
0.882198 0.470879i \(-0.156063\pi\)
\(614\) 0 0
\(615\) 908.866 + 561.179i 1.47783 + 0.912487i
\(616\) 0 0
\(617\) −463.269 267.468i −0.750841 0.433498i 0.0751567 0.997172i \(-0.476054\pi\)
−0.825998 + 0.563673i \(0.809388\pi\)
\(618\) 0 0
\(619\) 57.3192 99.2797i 0.0925996 0.160387i −0.816005 0.578045i \(-0.803816\pi\)
0.908604 + 0.417658i \(0.137149\pi\)
\(620\) 0 0
\(621\) −59.9946 + 85.4278i −0.0966097 + 0.137565i
\(622\) 0 0
\(623\) 673.567i 1.08117i
\(624\) 0 0
\(625\) 1241.96 1.98714
\(626\) 0 0
\(627\) 135.022 207.312i 0.215347 0.330641i
\(628\) 0 0
\(629\) 422.977 + 244.206i 0.672459 + 0.388244i
\(630\) 0 0
\(631\) −319.956 554.181i −0.507063 0.878258i −0.999967 0.00817442i \(-0.997398\pi\)
0.492904 0.870084i \(-0.335935\pi\)
\(632\) 0 0
\(633\) 22.9755 + 14.1862i 0.0362963 + 0.0224111i
\(634\) 0 0
\(635\) −1785.85 + 1031.06i −2.81236 + 1.62372i
\(636\) 0 0
\(637\) −73.0873 −0.114737
\(638\) 0 0
\(639\) 1.75750 29.7001i 0.00275039 0.0464790i
\(640\) 0 0
\(641\) 252.396 145.721i 0.393754 0.227334i −0.290031 0.957017i \(-0.593666\pi\)
0.683785 + 0.729683i \(0.260332\pi\)
\(642\) 0 0
\(643\) 913.504 1.42069 0.710346 0.703853i \(-0.248539\pi\)
0.710346 + 0.703853i \(0.248539\pi\)
\(644\) 0 0
\(645\) 214.681 + 6.34631i 0.332839 + 0.00983924i
\(646\) 0 0
\(647\) 179.023i 0.276697i −0.990384 0.138349i \(-0.955821\pi\)
0.990384 0.138349i \(-0.0441795\pi\)
\(648\) 0 0
\(649\) 246.385 426.752i 0.379638 0.657553i
\(650\) 0 0
\(651\) −666.799 411.715i −1.02427 0.632435i
\(652\) 0 0
\(653\) 62.3253 35.9836i 0.0954446 0.0551050i −0.451518 0.892262i \(-0.649117\pi\)
0.546963 + 0.837157i \(0.315784\pi\)
\(654\) 0 0
\(655\) −733.706 −1.12016
\(656\) 0 0
\(657\) 322.079 + 19.0590i 0.490227 + 0.0290091i
\(658\) 0 0
\(659\) 33.4949i 0.0508269i 0.999677 + 0.0254134i \(0.00809022\pi\)
−0.999677 + 0.0254134i \(0.991910\pi\)
\(660\) 0 0
\(661\) −58.6617 + 101.605i −0.0887469 + 0.153714i −0.906982 0.421170i \(-0.861620\pi\)
0.818235 + 0.574884i \(0.194953\pi\)
\(662\) 0 0
\(663\) −751.405 22.2127i −1.13334 0.0335033i
\(664\) 0 0
\(665\) 30.9674 1282.67i 0.0465675 1.92882i
\(666\) 0 0
\(667\) 98.0501 169.828i 0.147002 0.254614i
\(668\) 0 0
\(669\) −20.6871 + 699.797i −0.0309224 + 1.04603i
\(670\) 0 0
\(671\) −377.857 218.156i −0.563125 0.325120i
\(672\) 0 0
\(673\) 194.081 336.158i 0.288382 0.499492i −0.685042 0.728504i \(-0.740216\pi\)
0.973424 + 0.229012i \(0.0735494\pi\)
\(674\) 0 0
\(675\) −137.415 + 1545.87i −0.203578 + 2.29018i
\(676\) 0 0
\(677\) −724.175 418.103i −1.06968 0.617582i −0.141588 0.989926i \(-0.545221\pi\)
−0.928095 + 0.372344i \(0.878554\pi\)
\(678\) 0 0
\(679\) 443.681 0.653433
\(680\) 0 0
\(681\) −209.008 388.061i −0.306913 0.569839i
\(682\) 0 0
\(683\) 911.489i 1.33454i 0.744817 + 0.667268i \(0.232537\pi\)
−0.744817 + 0.667268i \(0.767463\pi\)
\(684\) 0 0
\(685\) 1825.40 2.66482
\(686\) 0 0
\(687\) −19.4906 + 659.321i −0.0283705 + 0.959710i
\(688\) 0 0
\(689\) 144.399i 0.209577i
\(690\) 0 0
\(691\) 617.578 1069.68i 0.893745 1.54801i 0.0583958 0.998294i \(-0.481401\pi\)
0.835350 0.549719i \(-0.185265\pi\)
\(692\) 0 0
\(693\) −242.529 159.836i −0.349969 0.230644i
\(694\) 0 0
\(695\) −1818.73 1050.04i −2.61687 1.51085i
\(696\) 0 0
\(697\) −422.539 + 731.859i −0.606225 + 1.05001i
\(698\) 0 0
\(699\) −143.127 265.741i −0.204760 0.380173i
\(700\) 0 0
\(701\) 126.432 + 72.9953i 0.180359 + 0.104130i 0.587461 0.809252i \(-0.300127\pi\)
−0.407102 + 0.913383i \(0.633461\pi\)
\(702\) 0 0
\(703\) −206.193 377.918i −0.293304 0.537579i
\(704\) 0 0
\(705\) −1545.50 954.266i −2.19219 1.35357i
\(706\) 0 0
\(707\) 1030.53 + 594.978i 1.45761 + 0.841553i
\(708\) 0 0
\(709\) 743.280 1.04835 0.524175 0.851611i \(-0.324374\pi\)
0.524175 + 0.851611i \(0.324374\pi\)
\(710\) 0 0
\(711\) −629.769 + 955.583i −0.885750 + 1.34400i
\(712\) 0 0
\(713\) 135.829i 0.190503i
\(714\) 0 0
\(715\) −229.120 396.848i −0.320448 0.555032i
\(716\) 0 0
\(717\) −778.929 23.0264i −1.08637 0.0321149i
\(718\) 0 0
\(719\) 299.714 + 173.040i 0.416848 + 0.240667i 0.693728 0.720237i \(-0.255967\pi\)
−0.276880 + 0.960905i \(0.589300\pi\)
\(720\) 0 0
\(721\) −249.260 −0.345714
\(722\) 0 0
\(723\) −204.314 126.154i −0.282592 0.174487i
\(724\) 0 0
\(725\) 2915.42i 4.02127i
\(726\) 0 0
\(727\) −471.068 815.913i −0.647961 1.12230i −0.983609 0.180314i \(-0.942289\pi\)
0.335648 0.941987i \(-0.391045\pi\)
\(728\) 0 0
\(729\) −717.570 128.588i −0.984320 0.176390i
\(730\) 0 0
\(731\) 169.920i 0.232449i
\(732\) 0 0
\(733\) −35.7338 61.8927i −0.0487500 0.0844376i 0.840621 0.541624i \(-0.182190\pi\)
−0.889371 + 0.457187i \(0.848857\pi\)
\(734\) 0 0
\(735\) −171.223 5.06163i −0.232957 0.00688658i
\(736\) 0 0
\(737\) 276.195 159.461i 0.374756 0.216365i
\(738\) 0 0
\(739\) 0.461491 0.799326i 0.000624481 0.00108163i −0.865713 0.500541i \(-0.833135\pi\)
0.866337 + 0.499459i \(0.166468\pi\)
\(740\) 0 0
\(741\) 555.233 + 361.624i 0.749302 + 0.488022i
\(742\) 0 0
\(743\) 373.582i 0.502802i −0.967883 0.251401i \(-0.919109\pi\)
0.967883 0.251401i \(-0.0808912\pi\)
\(744\) 0 0
\(745\) 1957.91 2.62806
\(746\) 0 0
\(747\) 47.1514 796.814i 0.0631210 1.06669i
\(748\) 0 0
\(749\) 730.858 + 421.961i 0.975779 + 0.563366i
\(750\) 0 0
\(751\) −182.718 + 316.476i −0.243299 + 0.421406i −0.961652 0.274272i \(-0.911563\pi\)
0.718353 + 0.695679i \(0.244896\pi\)
\(752\) 0 0
\(753\) 345.289 + 10.2073i 0.458551 + 0.0135555i
\(754\) 0 0
\(755\) 597.525 + 344.981i 0.791424 + 0.456929i
\(756\) 0 0
\(757\) −678.845 + 1175.79i −0.896757 + 1.55323i −0.0651422 + 0.997876i \(0.520750\pi\)
−0.831615 + 0.555353i \(0.812583\pi\)
\(758\) 0 0
\(759\) 1.48760 50.3222i 0.00195995 0.0663007i
\(760\) 0 0
\(761\) −795.277 + 459.153i −1.04504 + 0.603355i −0.921257 0.388954i \(-0.872836\pi\)
−0.123784 + 0.992309i \(0.539503\pi\)
\(762\) 0 0
\(763\) 208.192 + 360.600i 0.272860 + 0.472608i
\(764\) 0 0
\(765\) −1758.80 104.077i −2.29908 0.136048i
\(766\) 0 0
\(767\) 1142.95 + 659.882i 1.49016 + 0.860342i
\(768\) 0 0
\(769\) 31.3693 54.3333i 0.0407924 0.0706545i −0.844908 0.534911i \(-0.820345\pi\)
0.885701 + 0.464257i \(0.153678\pi\)
\(770\) 0 0
\(771\) −465.890 865.007i −0.604267 1.12193i
\(772\) 0 0
\(773\) −761.999 + 439.940i −0.985769 + 0.569134i −0.904007 0.427518i \(-0.859388\pi\)
−0.0817619 + 0.996652i \(0.526055\pi\)
\(774\) 0 0
\(775\) −1009.68 1748.82i −1.30282 2.25654i
\(776\) 0 0
\(777\) −444.992 + 239.671i −0.572705 + 0.308457i
\(778\) 0 0
\(779\) 653.896 356.767i 0.839404 0.457981i
\(780\) 0 0
\(781\) 7.17428 + 12.4262i 0.00918601 + 0.0159106i
\(782\) 0 0
\(783\) 1364.07 + 121.255i 1.74211 + 0.154860i
\(784\) 0 0
\(785\) 707.684i 0.901508i
\(786\) 0 0
\(787\) −390.537 676.431i −0.496236 0.859505i 0.503755 0.863847i \(-0.331951\pi\)
−0.999991 + 0.00434131i \(0.998618\pi\)
\(788\) 0 0
\(789\) 205.746 + 6.08219i 0.260769 + 0.00770873i
\(790\) 0 0
\(791\) 238.546i 0.301576i
\(792\) 0 0
\(793\) 584.276 1012.00i 0.736792 1.27616i
\(794\) 0 0
\(795\) 10.0003 338.286i 0.0125790 0.425517i
\(796\) 0 0
\(797\) 105.463