Properties

Label 684.3.s.a.445.18
Level $684$
Weight $3$
Character 684.445
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.s (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 445.18
Character \(\chi\) \(=\) 684.445
Dual form 684.3.s.a.601.18

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.455700 + 2.96519i) q^{3} +(1.91242 + 3.31241i) q^{5} +(-3.97487 - 6.88467i) q^{7} +(-8.58467 - 2.70247i) q^{9} +O(q^{10})\) \(q+(-0.455700 + 2.96519i) q^{3} +(1.91242 + 3.31241i) q^{5} +(-3.97487 - 6.88467i) q^{7} +(-8.58467 - 2.70247i) q^{9} +(2.64440 + 4.58024i) q^{11} -14.2808i q^{13} +(-10.6934 + 4.16122i) q^{15} +(6.41269 - 11.1071i) q^{17} +(2.65616 - 18.8134i) q^{19} +(22.2257 - 8.64888i) q^{21} -18.5774 q^{23} +(5.18529 - 8.98119i) q^{25} +(11.9254 - 24.2237i) q^{27} +(24.1574 + 13.9473i) q^{29} +(-22.1365 - 12.7805i) q^{31} +(-14.7863 + 5.75394i) q^{33} +(15.2032 - 26.3328i) q^{35} -12.6278i q^{37} +(42.3453 + 6.50777i) q^{39} +(-29.4375 + 16.9957i) q^{41} +26.6270 q^{43} +(-7.46582 - 33.6042i) q^{45} +(-5.03379 + 8.71877i) q^{47} +(-7.09914 + 12.2961i) q^{49} +(30.0124 + 24.0763i) q^{51} +(26.8513 - 15.5026i) q^{53} +(-10.1144 + 17.5187i) q^{55} +(54.5749 + 16.4493i) q^{57} +(23.0876 - 13.3296i) q^{59} +(14.9942 - 25.9707i) q^{61} +(15.5173 + 69.8446i) q^{63} +(47.3040 - 27.3110i) q^{65} +48.5515i q^{67} +(8.46574 - 55.0856i) q^{69} +(38.6617 + 22.3213i) q^{71} +(-18.2629 + 31.6322i) q^{73} +(24.2680 + 19.4681i) q^{75} +(21.0223 - 36.4117i) q^{77} -2.68433i q^{79} +(66.3933 + 46.3997i) q^{81} +(-65.5498 - 113.536i) q^{83} +49.0551 q^{85} +(-52.3649 + 65.2755i) q^{87} +(133.364 - 76.9979i) q^{89} +(-98.3188 + 56.7644i) q^{91} +(47.9843 - 59.8148i) q^{93} +(67.3975 - 27.1809i) q^{95} -101.085i q^{97} +(-10.3234 - 46.4663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - q^{7} + 4 q^{9} + O(q^{10}) \) \( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −0.455700 + 2.96519i −0.151900 + 0.988396i
\(4\) 0 0
\(5\) 1.91242 + 3.31241i 0.382484 + 0.662482i 0.991417 0.130740i \(-0.0417353\pi\)
−0.608932 + 0.793222i \(0.708402\pi\)
\(6\) 0 0
\(7\) −3.97487 6.88467i −0.567838 0.983525i −0.996779 0.0801922i \(-0.974447\pi\)
0.428941 0.903332i \(-0.358887\pi\)
\(8\) 0 0
\(9\) −8.58467 2.70247i −0.953853 0.300275i
\(10\) 0 0
\(11\) 2.64440 + 4.58024i 0.240400 + 0.416386i 0.960828 0.277144i \(-0.0893879\pi\)
−0.720428 + 0.693530i \(0.756055\pi\)
\(12\) 0 0
\(13\) 14.2808i 1.09852i −0.835650 0.549262i \(-0.814909\pi\)
0.835650 0.549262i \(-0.185091\pi\)
\(14\) 0 0
\(15\) −10.6934 + 4.16122i −0.712894 + 0.277415i
\(16\) 0 0
\(17\) 6.41269 11.1071i 0.377217 0.653359i −0.613439 0.789742i \(-0.710214\pi\)
0.990656 + 0.136383i \(0.0435477\pi\)
\(18\) 0 0
\(19\) 2.65616 18.8134i 0.139798 0.990180i
\(20\) 0 0
\(21\) 22.2257 8.64888i 1.05837 0.411851i
\(22\) 0 0
\(23\) −18.5774 −0.807715 −0.403857 0.914822i \(-0.632331\pi\)
−0.403857 + 0.914822i \(0.632331\pi\)
\(24\) 0 0
\(25\) 5.18529 8.98119i 0.207412 0.359247i
\(26\) 0 0
\(27\) 11.9254 24.2237i 0.441680 0.897172i
\(28\) 0 0
\(29\) 24.1574 + 13.9473i 0.833014 + 0.480941i 0.854884 0.518820i \(-0.173628\pi\)
−0.0218694 + 0.999761i \(0.506962\pi\)
\(30\) 0 0
\(31\) −22.1365 12.7805i −0.714081 0.412275i 0.0984892 0.995138i \(-0.468599\pi\)
−0.812570 + 0.582863i \(0.801932\pi\)
\(32\) 0 0
\(33\) −14.7863 + 5.75394i −0.448071 + 0.174362i
\(34\) 0 0
\(35\) 15.2032 26.3328i 0.434378 0.752365i
\(36\) 0 0
\(37\) 12.6278i 0.341292i −0.985332 0.170646i \(-0.945415\pi\)
0.985332 0.170646i \(-0.0545855\pi\)
\(38\) 0 0
\(39\) 42.3453 + 6.50777i 1.08578 + 0.166866i
\(40\) 0 0
\(41\) −29.4375 + 16.9957i −0.717988 + 0.414530i −0.814012 0.580849i \(-0.802721\pi\)
0.0960240 + 0.995379i \(0.469387\pi\)
\(42\) 0 0
\(43\) 26.6270 0.619232 0.309616 0.950862i \(-0.399800\pi\)
0.309616 + 0.950862i \(0.399800\pi\)
\(44\) 0 0
\(45\) −7.46582 33.6042i −0.165907 0.746761i
\(46\) 0 0
\(47\) −5.03379 + 8.71877i −0.107102 + 0.185506i −0.914595 0.404371i \(-0.867490\pi\)
0.807493 + 0.589877i \(0.200824\pi\)
\(48\) 0 0
\(49\) −7.09914 + 12.2961i −0.144880 + 0.250940i
\(50\) 0 0
\(51\) 30.0124 + 24.0763i 0.588478 + 0.472085i
\(52\) 0 0
\(53\) 26.8513 15.5026i 0.506628 0.292502i −0.224818 0.974401i \(-0.572179\pi\)
0.731446 + 0.681899i \(0.238846\pi\)
\(54\) 0 0
\(55\) −10.1144 + 17.5187i −0.183899 + 0.318522i
\(56\) 0 0
\(57\) 54.5749 + 16.4493i 0.957455 + 0.288584i
\(58\) 0 0
\(59\) 23.0876 13.3296i 0.391315 0.225926i −0.291415 0.956597i \(-0.594126\pi\)
0.682730 + 0.730671i \(0.260793\pi\)
\(60\) 0 0
\(61\) 14.9942 25.9707i 0.245806 0.425749i −0.716552 0.697534i \(-0.754281\pi\)
0.962358 + 0.271785i \(0.0876140\pi\)
\(62\) 0 0
\(63\) 15.5173 + 69.8446i 0.246306 + 1.10865i
\(64\) 0 0
\(65\) 47.3040 27.3110i 0.727753 0.420168i
\(66\) 0 0
\(67\) 48.5515i 0.724649i 0.932052 + 0.362324i \(0.118017\pi\)
−0.932052 + 0.362324i \(0.881983\pi\)
\(68\) 0 0
\(69\) 8.46574 55.0856i 0.122692 0.798342i
\(70\) 0 0
\(71\) 38.6617 + 22.3213i 0.544531 + 0.314385i 0.746913 0.664922i \(-0.231535\pi\)
−0.202382 + 0.979307i \(0.564868\pi\)
\(72\) 0 0
\(73\) −18.2629 + 31.6322i −0.250176 + 0.433318i −0.963574 0.267441i \(-0.913822\pi\)
0.713398 + 0.700759i \(0.247155\pi\)
\(74\) 0 0
\(75\) 24.2680 + 19.4681i 0.323573 + 0.259574i
\(76\) 0 0
\(77\) 21.0223 36.4117i 0.273017 0.472879i
\(78\) 0 0
\(79\) 2.68433i 0.0339789i −0.999856 0.0169894i \(-0.994592\pi\)
0.999856 0.0169894i \(-0.00540817\pi\)
\(80\) 0 0
\(81\) 66.3933 + 46.3997i 0.819670 + 0.572836i
\(82\) 0 0
\(83\) −65.5498 113.536i −0.789757 1.36790i −0.926116 0.377239i \(-0.876874\pi\)
0.136359 0.990659i \(-0.456460\pi\)
\(84\) 0 0
\(85\) 49.0551 0.577118
\(86\) 0 0
\(87\) −52.3649 + 65.2755i −0.601895 + 0.750293i
\(88\) 0 0
\(89\) 133.364 76.9979i 1.49847 0.865145i 0.498476 0.866903i \(-0.333893\pi\)
0.999998 + 0.00175855i \(0.000559765\pi\)
\(90\) 0 0
\(91\) −98.3188 + 56.7644i −1.08043 + 0.623784i
\(92\) 0 0
\(93\) 47.9843 59.8148i 0.515960 0.643170i
\(94\) 0 0
\(95\) 67.3975 27.1809i 0.709447 0.286115i
\(96\) 0 0
\(97\) 101.085i 1.04212i −0.853521 0.521058i \(-0.825537\pi\)
0.853521 0.521058i \(-0.174463\pi\)
\(98\) 0 0
\(99\) −10.3234 46.4663i −0.104277 0.469357i
\(100\) 0 0
\(101\) −3.74464 + 6.48591i −0.0370757 + 0.0642169i −0.883968 0.467548i \(-0.845138\pi\)
0.846892 + 0.531765i \(0.178471\pi\)
\(102\) 0 0
\(103\) −57.6457 33.2818i −0.559667 0.323124i 0.193345 0.981131i \(-0.438066\pi\)
−0.753012 + 0.658007i \(0.771400\pi\)
\(104\) 0 0
\(105\) 71.1535 + 57.0803i 0.677653 + 0.543622i
\(106\) 0 0
\(107\) 99.4176i 0.929137i −0.885537 0.464568i \(-0.846210\pi\)
0.885537 0.464568i \(-0.153790\pi\)
\(108\) 0 0
\(109\) 74.6730 + 43.1125i 0.685073 + 0.395527i 0.801764 0.597641i \(-0.203895\pi\)
−0.116691 + 0.993168i \(0.537229\pi\)
\(110\) 0 0
\(111\) 37.4438 + 5.75450i 0.337332 + 0.0518423i
\(112\) 0 0
\(113\) −128.680 74.2935i −1.13876 0.657464i −0.192638 0.981270i \(-0.561704\pi\)
−0.946124 + 0.323806i \(0.895038\pi\)
\(114\) 0 0
\(115\) −35.5279 61.5361i −0.308938 0.535097i
\(116\) 0 0
\(117\) −38.5935 + 122.596i −0.329859 + 1.04783i
\(118\) 0 0
\(119\) −101.958 −0.856793
\(120\) 0 0
\(121\) 46.5142 80.5650i 0.384415 0.665827i
\(122\) 0 0
\(123\) −36.9809 95.0326i −0.300658 0.772623i
\(124\) 0 0
\(125\) 135.287 1.08230
\(126\) 0 0
\(127\) 18.7261 10.8115i 0.147450 0.0851300i −0.424460 0.905447i \(-0.639536\pi\)
0.571910 + 0.820317i \(0.306203\pi\)
\(128\) 0 0
\(129\) −12.1339 + 78.9540i −0.0940613 + 0.612046i
\(130\) 0 0
\(131\) −16.9934 29.4334i −0.129721 0.224683i 0.793848 0.608117i \(-0.208075\pi\)
−0.923568 + 0.383434i \(0.874741\pi\)
\(132\) 0 0
\(133\) −140.082 + 56.4941i −1.05325 + 0.424768i
\(134\) 0 0
\(135\) 103.045 6.82410i 0.763297 0.0505489i
\(136\) 0 0
\(137\) −5.49958 + 9.52556i −0.0401429 + 0.0695296i −0.885399 0.464832i \(-0.846115\pi\)
0.845256 + 0.534362i \(0.179448\pi\)
\(138\) 0 0
\(139\) −206.386 −1.48479 −0.742394 0.669963i \(-0.766310\pi\)
−0.742394 + 0.669963i \(0.766310\pi\)
\(140\) 0 0
\(141\) −23.5589 18.8993i −0.167084 0.134037i
\(142\) 0 0
\(143\) 65.4096 37.7643i 0.457410 0.264086i
\(144\) 0 0
\(145\) 106.692i 0.735809i
\(146\) 0 0
\(147\) −33.2251 26.6536i −0.226021 0.181317i
\(148\) 0 0
\(149\) −31.0391 53.7613i −0.208316 0.360814i 0.742868 0.669438i \(-0.233465\pi\)
−0.951184 + 0.308624i \(0.900132\pi\)
\(150\) 0 0
\(151\) −181.343 + 104.699i −1.20095 + 0.693369i −0.960766 0.277359i \(-0.910541\pi\)
−0.240184 + 0.970727i \(0.577208\pi\)
\(152\) 0 0
\(153\) −85.0675 + 78.0208i −0.555997 + 0.509940i
\(154\) 0 0
\(155\) 97.7670i 0.630755i
\(156\) 0 0
\(157\) 94.4399 + 163.575i 0.601528 + 1.04188i 0.992590 + 0.121512i \(0.0387744\pi\)
−0.391062 + 0.920364i \(0.627892\pi\)
\(158\) 0 0
\(159\) 33.7320 + 86.6836i 0.212151 + 0.545180i
\(160\) 0 0
\(161\) 73.8428 + 127.900i 0.458651 + 0.794407i
\(162\) 0 0
\(163\) −319.340 −1.95914 −0.979571 0.201099i \(-0.935549\pi\)
−0.979571 + 0.201099i \(0.935549\pi\)
\(164\) 0 0
\(165\) −47.3371 37.9745i −0.286892 0.230148i
\(166\) 0 0
\(167\) 251.049i 1.50329i 0.659569 + 0.751644i \(0.270739\pi\)
−0.659569 + 0.751644i \(0.729261\pi\)
\(168\) 0 0
\(169\) −34.9419 −0.206757
\(170\) 0 0
\(171\) −73.6450 + 154.329i −0.430672 + 0.902508i
\(172\) 0 0
\(173\) 114.034i 0.659158i −0.944128 0.329579i \(-0.893093\pi\)
0.944128 0.329579i \(-0.106907\pi\)
\(174\) 0 0
\(175\) −82.4433 −0.471105
\(176\) 0 0
\(177\) 29.0038 + 74.5333i 0.163863 + 0.421092i
\(178\) 0 0
\(179\) 108.778i 0.607700i −0.952720 0.303850i \(-0.901728\pi\)
0.952720 0.303850i \(-0.0982721\pi\)
\(180\) 0 0
\(181\) 85.6045 49.4238i 0.472953 0.273060i −0.244522 0.969644i \(-0.578631\pi\)
0.717475 + 0.696584i \(0.245298\pi\)
\(182\) 0 0
\(183\) 70.1751 + 56.2954i 0.383470 + 0.307625i
\(184\) 0 0
\(185\) 41.8285 24.1497i 0.226100 0.130539i
\(186\) 0 0
\(187\) 67.8310 0.362733
\(188\) 0 0
\(189\) −214.174 + 14.1835i −1.13319 + 0.0750451i
\(190\) 0 0
\(191\) −41.6268 72.0997i −0.217941 0.377485i 0.736237 0.676724i \(-0.236601\pi\)
−0.954178 + 0.299238i \(0.903267\pi\)
\(192\) 0 0
\(193\) 83.2933 48.0894i 0.431571 0.249168i −0.268444 0.963295i \(-0.586510\pi\)
0.700016 + 0.714127i \(0.253176\pi\)
\(194\) 0 0
\(195\) 59.4257 + 152.711i 0.304747 + 0.783132i
\(196\) 0 0
\(197\) 174.092 0.883713 0.441857 0.897086i \(-0.354320\pi\)
0.441857 + 0.897086i \(0.354320\pi\)
\(198\) 0 0
\(199\) 58.0248 + 100.502i 0.291582 + 0.505035i 0.974184 0.225756i \(-0.0724851\pi\)
−0.682602 + 0.730790i \(0.739152\pi\)
\(200\) 0 0
\(201\) −143.964 22.1249i −0.716240 0.110074i
\(202\) 0 0
\(203\) 221.754i 1.09239i
\(204\) 0 0
\(205\) −112.594 65.0060i −0.549238 0.317103i
\(206\) 0 0
\(207\) 159.481 + 50.2050i 0.770441 + 0.242536i
\(208\) 0 0
\(209\) 93.1940 37.5845i 0.445904 0.179830i
\(210\) 0 0
\(211\) 56.3953 32.5598i 0.267276 0.154312i −0.360373 0.932808i \(-0.617351\pi\)
0.627649 + 0.778496i \(0.284017\pi\)
\(212\) 0 0
\(213\) −83.8050 + 104.467i −0.393451 + 0.490457i
\(214\) 0 0
\(215\) 50.9220 + 88.1995i 0.236846 + 0.410230i
\(216\) 0 0
\(217\) 203.204i 0.936422i
\(218\) 0 0
\(219\) −85.4731 68.5676i −0.390288 0.313094i
\(220\) 0 0
\(221\) −158.619 91.5785i −0.717731 0.414382i
\(222\) 0 0
\(223\) 276.954i 1.24194i −0.783832 0.620972i \(-0.786738\pi\)
0.783832 0.620972i \(-0.213262\pi\)
\(224\) 0 0
\(225\) −68.7854 + 63.0875i −0.305713 + 0.280389i
\(226\) 0 0
\(227\) −312.633 + 180.499i −1.37724 + 0.795148i −0.991826 0.127597i \(-0.959273\pi\)
−0.385411 + 0.922745i \(0.625940\pi\)
\(228\) 0 0
\(229\) 48.8659 84.6381i 0.213388 0.369599i −0.739385 0.673283i \(-0.764883\pi\)
0.952773 + 0.303684i \(0.0982168\pi\)
\(230\) 0 0
\(231\) 98.3877 + 78.9279i 0.425921 + 0.341679i
\(232\) 0 0
\(233\) −108.162 + 187.342i −0.464216 + 0.804045i −0.999166 0.0408387i \(-0.986997\pi\)
0.534950 + 0.844884i \(0.320330\pi\)
\(234\) 0 0
\(235\) −38.5069 −0.163859
\(236\) 0 0
\(237\) 7.95955 + 1.22325i 0.0335846 + 0.00516139i
\(238\) 0 0
\(239\) −95.2811 + 165.032i −0.398666 + 0.690509i −0.993562 0.113294i \(-0.963860\pi\)
0.594896 + 0.803803i \(0.297193\pi\)
\(240\) 0 0
\(241\) −339.264 195.874i −1.40773 0.812756i −0.412565 0.910928i \(-0.635367\pi\)
−0.995169 + 0.0981726i \(0.968700\pi\)
\(242\) 0 0
\(243\) −167.839 + 175.724i −0.690696 + 0.723145i
\(244\) 0 0
\(245\) −54.3062 −0.221658
\(246\) 0 0
\(247\) −268.671 37.9321i −1.08774 0.153571i
\(248\) 0 0
\(249\) 366.525 142.629i 1.47199 0.572808i
\(250\) 0 0
\(251\) −86.5365 149.886i −0.344767 0.597154i 0.640545 0.767921i \(-0.278709\pi\)
−0.985311 + 0.170767i \(0.945375\pi\)
\(252\) 0 0
\(253\) −49.1263 85.0892i −0.194175 0.336321i
\(254\) 0 0
\(255\) −22.3544 + 145.457i −0.0876643 + 0.570421i
\(256\) 0 0
\(257\) 271.345i 1.05582i −0.849301 0.527909i \(-0.822976\pi\)
0.849301 0.527909i \(-0.177024\pi\)
\(258\) 0 0
\(259\) −86.9384 + 50.1939i −0.335669 + 0.193799i
\(260\) 0 0
\(261\) −169.691 185.018i −0.650159 0.708880i
\(262\) 0 0
\(263\) 329.887 1.25432 0.627162 0.778889i \(-0.284216\pi\)
0.627162 + 0.778889i \(0.284216\pi\)
\(264\) 0 0
\(265\) 102.702 + 59.2950i 0.387554 + 0.223755i
\(266\) 0 0
\(267\) 167.539 + 430.538i 0.627487 + 1.61250i
\(268\) 0 0
\(269\) 114.156 + 65.9081i 0.424373 + 0.245012i 0.696946 0.717123i \(-0.254542\pi\)
−0.272574 + 0.962135i \(0.587875\pi\)
\(270\) 0 0
\(271\) −229.959 + 398.301i −0.848558 + 1.46975i 0.0339369 + 0.999424i \(0.489195\pi\)
−0.882495 + 0.470322i \(0.844138\pi\)
\(272\) 0 0
\(273\) −123.513 317.401i −0.452429 1.16264i
\(274\) 0 0
\(275\) 54.8480 0.199447
\(276\) 0 0
\(277\) −143.132 247.912i −0.516722 0.894989i −0.999811 0.0194182i \(-0.993819\pi\)
0.483089 0.875571i \(-0.339515\pi\)
\(278\) 0 0
\(279\) 155.496 + 169.540i 0.557333 + 0.607670i
\(280\) 0 0
\(281\) 114.991 + 66.3903i 0.409222 + 0.236264i 0.690455 0.723375i \(-0.257410\pi\)
−0.281234 + 0.959639i \(0.590744\pi\)
\(282\) 0 0
\(283\) 166.098 + 287.691i 0.586920 + 1.01658i 0.994633 + 0.103465i \(0.0329930\pi\)
−0.407713 + 0.913110i \(0.633674\pi\)
\(284\) 0 0
\(285\) 49.8835 + 212.232i 0.175030 + 0.744675i
\(286\) 0 0
\(287\) 234.020 + 135.112i 0.815401 + 0.470772i
\(288\) 0 0
\(289\) 62.2548 + 107.828i 0.215415 + 0.373109i
\(290\) 0 0
\(291\) 299.737 + 46.0646i 1.03002 + 0.158297i
\(292\) 0 0
\(293\) 113.130 + 65.3157i 0.386110 + 0.222921i 0.680473 0.732773i \(-0.261774\pi\)
−0.294363 + 0.955694i \(0.595108\pi\)
\(294\) 0 0
\(295\) 88.3063 + 50.9837i 0.299343 + 0.172826i
\(296\) 0 0
\(297\) 142.486 9.43604i 0.479750 0.0317712i
\(298\) 0 0
\(299\) 265.301i 0.887295i
\(300\) 0 0
\(301\) −105.839 183.318i −0.351623 0.609030i
\(302\) 0 0
\(303\) −17.5255 14.0592i −0.0578400 0.0464000i
\(304\) 0 0
\(305\) 114.701 0.376068
\(306\) 0 0
\(307\) −220.685 127.413i −0.718844 0.415025i 0.0954831 0.995431i \(-0.469560\pi\)
−0.814327 + 0.580406i \(0.802894\pi\)
\(308\) 0 0
\(309\) 124.956 155.764i 0.404388 0.504090i
\(310\) 0 0
\(311\) −55.6250 + 96.3453i −0.178858 + 0.309792i −0.941490 0.337042i \(-0.890574\pi\)
0.762631 + 0.646833i \(0.223907\pi\)
\(312\) 0 0
\(313\) −181.922 + 315.098i −0.581221 + 1.00670i 0.414114 + 0.910225i \(0.364091\pi\)
−0.995335 + 0.0964793i \(0.969242\pi\)
\(314\) 0 0
\(315\) −201.679 + 184.972i −0.640249 + 0.587213i
\(316\) 0 0
\(317\) −271.069 156.502i −0.855107 0.493696i 0.00726361 0.999974i \(-0.497688\pi\)
−0.862371 + 0.506277i \(0.831021\pi\)
\(318\) 0 0
\(319\) 147.529i 0.462474i
\(320\) 0 0
\(321\) 294.792 + 45.3046i 0.918355 + 0.141136i
\(322\) 0 0
\(323\) −191.930 150.147i −0.594209 0.464851i
\(324\) 0 0
\(325\) −128.259 74.0502i −0.394642 0.227847i
\(326\) 0 0
\(327\) −161.865 + 201.773i −0.495000 + 0.617043i
\(328\) 0 0
\(329\) 80.0345 0.243266
\(330\) 0 0
\(331\) 165.604 95.6114i 0.500313 0.288856i −0.228530 0.973537i \(-0.573392\pi\)
0.728843 + 0.684681i \(0.240058\pi\)
\(332\) 0 0
\(333\) −34.1263 + 108.406i −0.102481 + 0.325543i
\(334\) 0 0
\(335\) −160.822 + 92.8509i −0.480067 + 0.277167i
\(336\) 0 0
\(337\) 458.782 264.878i 1.36137 0.785989i 0.371566 0.928407i \(-0.378821\pi\)
0.989807 + 0.142418i \(0.0454877\pi\)
\(338\) 0 0
\(339\) 278.934 347.705i 0.822813 1.02568i
\(340\) 0 0
\(341\) 135.187i 0.396444i
\(342\) 0 0
\(343\) −276.664 −0.806602
\(344\) 0 0
\(345\) 198.656 77.3048i 0.575815 0.224072i
\(346\) 0 0
\(347\) 31.6748 + 54.8624i 0.0912818 + 0.158105i 0.908051 0.418860i \(-0.137570\pi\)
−0.816769 + 0.576965i \(0.804237\pi\)
\(348\) 0 0
\(349\) 171.227 + 296.574i 0.490623 + 0.849783i 0.999942 0.0107945i \(-0.00343607\pi\)
−0.509319 + 0.860578i \(0.670103\pi\)
\(350\) 0 0
\(351\) −345.934 170.304i −0.985566 0.485197i
\(352\) 0 0
\(353\) −101.118 175.141i −0.286453 0.496150i 0.686508 0.727122i \(-0.259143\pi\)
−0.972960 + 0.230972i \(0.925809\pi\)
\(354\) 0 0
\(355\) 170.751i 0.480989i
\(356\) 0 0
\(357\) 46.4624 302.326i 0.130147 0.846851i
\(358\) 0 0
\(359\) −14.2795 + 24.7328i −0.0397757 + 0.0688936i −0.885228 0.465158i \(-0.845998\pi\)
0.845452 + 0.534051i \(0.179331\pi\)
\(360\) 0 0
\(361\) −346.890 99.9427i −0.960913 0.276850i
\(362\) 0 0
\(363\) 217.694 + 174.637i 0.599708 + 0.481094i
\(364\) 0 0
\(365\) −139.705 −0.382754
\(366\) 0 0
\(367\) 219.299 379.836i 0.597544 1.03498i −0.395639 0.918406i \(-0.629477\pi\)
0.993182 0.116570i \(-0.0371900\pi\)
\(368\) 0 0
\(369\) 298.642 66.3489i 0.809327 0.179807i
\(370\) 0 0
\(371\) −213.461 123.242i −0.575365 0.332187i
\(372\) 0 0
\(373\) −209.926 121.201i −0.562805 0.324936i 0.191466 0.981499i \(-0.438676\pi\)
−0.754271 + 0.656564i \(0.772009\pi\)
\(374\) 0 0
\(375\) −61.6502 + 401.151i −0.164401 + 1.06974i
\(376\) 0 0
\(377\) 199.179 344.988i 0.528326 0.915087i
\(378\) 0 0
\(379\) 93.9089i 0.247781i 0.992296 + 0.123890i \(0.0395371\pi\)
−0.992296 + 0.123890i \(0.960463\pi\)
\(380\) 0 0
\(381\) 23.5247 + 60.4532i 0.0617446 + 0.158670i
\(382\) 0 0
\(383\) 509.030 293.889i 1.32906 0.767334i 0.343906 0.939004i \(-0.388250\pi\)
0.985154 + 0.171670i \(0.0549164\pi\)
\(384\) 0 0
\(385\) 160.814 0.417699
\(386\) 0 0
\(387\) −228.584 71.9586i −0.590656 0.185940i
\(388\) 0 0
\(389\) −121.984 + 211.283i −0.313584 + 0.543143i −0.979135 0.203209i \(-0.934863\pi\)
0.665552 + 0.746352i \(0.268196\pi\)
\(390\) 0 0
\(391\) −119.131 + 206.342i −0.304684 + 0.527728i
\(392\) 0 0
\(393\) 95.0195 36.9758i 0.241780 0.0940860i
\(394\) 0 0
\(395\) 8.89161 5.13357i 0.0225104 0.0129964i
\(396\) 0 0
\(397\) 187.117 324.096i 0.471327 0.816362i −0.528135 0.849160i \(-0.677109\pi\)
0.999462 + 0.0327984i \(0.0104419\pi\)
\(398\) 0 0
\(399\) −103.680 441.114i −0.259850 1.10555i
\(400\) 0 0
\(401\) −618.010 + 356.808i −1.54117 + 0.889796i −0.542407 + 0.840116i \(0.682487\pi\)
−0.998765 + 0.0496804i \(0.984180\pi\)
\(402\) 0 0
\(403\) −182.516 + 316.128i −0.452894 + 0.784436i
\(404\) 0 0
\(405\) −26.7229 + 308.658i −0.0659825 + 0.762118i
\(406\) 0 0
\(407\) 57.8385 33.3930i 0.142109 0.0820468i
\(408\) 0 0
\(409\) 254.901i 0.623230i −0.950208 0.311615i \(-0.899130\pi\)
0.950208 0.311615i \(-0.100870\pi\)
\(410\) 0 0
\(411\) −25.7389 20.6481i −0.0626251 0.0502387i
\(412\) 0 0
\(413\) −183.540 105.967i −0.444407 0.256578i
\(414\) 0 0
\(415\) 250.718 434.256i 0.604139 1.04640i
\(416\) 0 0
\(417\) 94.0499 611.972i 0.225539 1.46756i
\(418\) 0 0
\(419\) 40.7422 70.5676i 0.0972369 0.168419i −0.813303 0.581840i \(-0.802333\pi\)
0.910540 + 0.413421i \(0.135666\pi\)
\(420\) 0 0
\(421\) 555.712i 1.31998i 0.751274 + 0.659991i \(0.229440\pi\)
−0.751274 + 0.659991i \(0.770560\pi\)
\(422\) 0 0
\(423\) 66.7757 61.2442i 0.157862 0.144785i
\(424\) 0 0
\(425\) −66.5033 115.187i −0.156478 0.271029i
\(426\) 0 0
\(427\) −238.399 −0.558313
\(428\) 0 0
\(429\) 82.1710 + 211.161i 0.191541 + 0.492217i
\(430\) 0 0
\(431\) −44.0582 + 25.4370i −0.102223 + 0.0590186i −0.550240 0.835007i \(-0.685464\pi\)
0.448017 + 0.894025i \(0.352130\pi\)
\(432\) 0 0
\(433\) 587.106 338.966i 1.35590 0.782832i 0.366835 0.930286i \(-0.380441\pi\)
0.989069 + 0.147454i \(0.0471079\pi\)
\(434\) 0 0
\(435\) −316.363 48.6197i −0.727271 0.111769i
\(436\) 0 0
\(437\) −49.3446 + 349.505i −0.112917 + 0.799783i
\(438\) 0 0
\(439\) 281.489i 0.641204i 0.947214 + 0.320602i \(0.103885\pi\)
−0.947214 + 0.320602i \(0.896115\pi\)
\(440\) 0 0
\(441\) 94.1736 86.3725i 0.213545 0.195856i
\(442\) 0 0
\(443\) 432.905 749.814i 0.977213 1.69258i 0.304784 0.952421i \(-0.401416\pi\)
0.672429 0.740161i \(-0.265251\pi\)
\(444\) 0 0
\(445\) 510.097 + 294.505i 1.14629 + 0.661809i
\(446\) 0 0
\(447\) 173.557 67.5377i 0.388270 0.151091i
\(448\) 0 0
\(449\) 615.442i 1.37070i −0.728216 0.685348i \(-0.759650\pi\)
0.728216 0.685348i \(-0.240350\pi\)
\(450\) 0 0
\(451\) −155.689 89.8872i −0.345209 0.199307i
\(452\) 0 0
\(453\) −227.813 585.429i −0.502899 1.29234i
\(454\) 0 0
\(455\) −376.054 217.115i −0.826492 0.477175i
\(456\) 0 0
\(457\) 333.190 + 577.102i 0.729081 + 1.26280i 0.957272 + 0.289189i \(0.0933855\pi\)
−0.228191 + 0.973616i \(0.573281\pi\)
\(458\) 0 0
\(459\) −192.581 287.795i −0.419566 0.627005i
\(460\) 0 0
\(461\) −404.973 −0.878466 −0.439233 0.898373i \(-0.644750\pi\)
−0.439233 + 0.898373i \(0.644750\pi\)
\(462\) 0 0
\(463\) 366.950 635.577i 0.792549 1.37274i −0.131835 0.991272i \(-0.542087\pi\)
0.924384 0.381464i \(-0.124580\pi\)
\(464\) 0 0
\(465\) 289.897 + 44.5524i 0.623435 + 0.0958116i
\(466\) 0 0
\(467\) 840.548 1.79989 0.899944 0.436006i \(-0.143607\pi\)
0.899944 + 0.436006i \(0.143607\pi\)
\(468\) 0 0
\(469\) 334.261 192.986i 0.712710 0.411483i
\(470\) 0 0
\(471\) −528.066 + 205.491i −1.12116 + 0.436286i
\(472\) 0 0
\(473\) 70.4125 + 121.958i 0.148864 + 0.257839i
\(474\) 0 0
\(475\) −155.194 121.408i −0.326724 0.255597i
\(476\) 0 0
\(477\) −272.405 + 60.5199i −0.571079 + 0.126876i
\(478\) 0 0
\(479\) 283.207 490.530i 0.591247 1.02407i −0.402817 0.915280i \(-0.631969\pi\)
0.994065 0.108790i \(-0.0346976\pi\)
\(480\) 0 0
\(481\) −180.336 −0.374918
\(482\) 0 0
\(483\) −412.896 + 160.674i −0.854858 + 0.332658i
\(484\) 0 0
\(485\) 334.836 193.318i 0.690383 0.398593i
\(486\) 0 0
\(487\) 374.070i 0.768111i −0.923310 0.384056i \(-0.874527\pi\)
0.923310 0.384056i \(-0.125473\pi\)
\(488\) 0 0
\(489\) 145.523 946.903i 0.297594 1.93641i
\(490\) 0 0
\(491\) 341.737 + 591.907i 0.696003 + 1.20551i 0.969841 + 0.243737i \(0.0783732\pi\)
−0.273839 + 0.961776i \(0.588293\pi\)
\(492\) 0 0
\(493\) 309.828 178.879i 0.628454 0.362838i
\(494\) 0 0
\(495\) 134.173 123.058i 0.271056 0.248603i
\(496\) 0 0
\(497\) 354.897i 0.714079i
\(498\) 0 0
\(499\) 107.071 + 185.452i 0.214570 + 0.371647i 0.953140 0.302531i \(-0.0978315\pi\)
−0.738569 + 0.674178i \(0.764498\pi\)
\(500\) 0 0
\(501\) −744.408 114.403i −1.48584 0.228350i
\(502\) 0 0
\(503\) 234.118 + 405.504i 0.465443 + 0.806171i 0.999221 0.0394537i \(-0.0125618\pi\)
−0.533779 + 0.845624i \(0.679228\pi\)
\(504\) 0 0
\(505\) −28.6453 −0.0567234
\(506\) 0 0
\(507\) 15.9230 103.609i 0.0314064 0.204358i
\(508\) 0 0
\(509\) 882.494i 1.73378i 0.498500 + 0.866890i \(0.333884\pi\)
−0.498500 + 0.866890i \(0.666116\pi\)
\(510\) 0 0
\(511\) 290.370 0.568239
\(512\) 0 0
\(513\) −424.054 288.699i −0.826616 0.562766i
\(514\) 0 0
\(515\) 254.595i 0.494360i
\(516\) 0 0
\(517\) −53.2455 −0.102989
\(518\) 0 0
\(519\) 338.133 + 51.9654i 0.651509 + 0.100126i
\(520\) 0 0
\(521\) 309.176i 0.593429i 0.954966 + 0.296714i \(0.0958909\pi\)
−0.954966 + 0.296714i \(0.904109\pi\)
\(522\) 0 0
\(523\) 580.689 335.261i 1.11030 0.641035i 0.171396 0.985202i \(-0.445172\pi\)
0.938908 + 0.344168i \(0.111839\pi\)
\(524\) 0 0
\(525\) 37.5694 244.460i 0.0715608 0.465638i
\(526\) 0 0
\(527\) −283.909 + 163.915i −0.538727 + 0.311034i
\(528\) 0 0
\(529\) −183.879 −0.347597
\(530\) 0 0
\(531\) −234.222 + 52.0369i −0.441096 + 0.0979979i
\(532\) 0 0
\(533\) 242.713 + 420.392i 0.455372 + 0.788727i
\(534\) 0 0
\(535\) 329.312 190.128i 0.615536 0.355380i
\(536\) 0 0
\(537\) 322.548 + 49.5702i 0.600648 + 0.0923096i
\(538\) 0 0
\(539\) −75.0920 −0.139317
\(540\) 0 0
\(541\) 448.760 + 777.276i 0.829502 + 1.43674i 0.898430 + 0.439117i \(0.144709\pi\)
−0.0689281 + 0.997622i \(0.521958\pi\)
\(542\) 0 0
\(543\) 107.541 + 276.356i 0.198049 + 0.508943i
\(544\) 0 0
\(545\) 329.797i 0.605132i
\(546\) 0 0
\(547\) 64.6950 + 37.3517i 0.118272 + 0.0682846i 0.557969 0.829862i \(-0.311581\pi\)
−0.439697 + 0.898146i \(0.644914\pi\)
\(548\) 0 0
\(549\) −198.905 + 182.428i −0.362304 + 0.332292i
\(550\) 0 0
\(551\) 326.562 417.437i 0.592672 0.757600i
\(552\) 0 0
\(553\) −18.4807 + 10.6699i −0.0334191 + 0.0192945i
\(554\) 0 0
\(555\) 52.5471 + 135.034i 0.0946795 + 0.243305i
\(556\) 0 0
\(557\) 458.732 + 794.547i 0.823577 + 1.42648i 0.903002 + 0.429636i \(0.141358\pi\)
−0.0794258 + 0.996841i \(0.525309\pi\)
\(558\) 0 0
\(559\) 380.255i 0.680242i
\(560\) 0 0
\(561\) −30.9106 + 201.132i −0.0550991 + 0.358523i
\(562\) 0 0
\(563\) −206.762 119.374i −0.367251 0.212033i 0.305006 0.952351i \(-0.401342\pi\)
−0.672257 + 0.740318i \(0.734675\pi\)
\(564\) 0 0
\(565\) 568.322i 1.00588i
\(566\) 0 0
\(567\) 55.5421 641.529i 0.0979579 1.13144i
\(568\) 0 0
\(569\) −321.105 + 185.390i −0.564333 + 0.325818i −0.754883 0.655860i \(-0.772306\pi\)
0.190550 + 0.981678i \(0.438973\pi\)
\(570\) 0 0
\(571\) −187.660 + 325.036i −0.328651 + 0.569240i −0.982244 0.187606i \(-0.939927\pi\)
0.653593 + 0.756846i \(0.273261\pi\)
\(572\) 0 0
\(573\) 232.758 90.5753i 0.406210 0.158072i
\(574\) 0 0
\(575\) −96.3294 + 166.847i −0.167529 + 0.290169i
\(576\) 0 0
\(577\) 646.755 1.12089 0.560446 0.828191i \(-0.310630\pi\)
0.560446 + 0.828191i \(0.310630\pi\)
\(578\) 0 0
\(579\) 104.637 + 268.895i 0.180721 + 0.464412i
\(580\) 0 0
\(581\) −521.103 + 902.578i −0.896908 + 1.55349i
\(582\) 0 0
\(583\) 142.011 + 81.9903i 0.243587 + 0.140635i
\(584\) 0 0
\(585\) −479.896 + 106.618i −0.820335 + 0.182253i
\(586\) 0 0
\(587\) 816.083 1.39026 0.695130 0.718884i \(-0.255347\pi\)
0.695130 + 0.718884i \(0.255347\pi\)
\(588\) 0 0
\(589\) −299.243 + 382.517i −0.508053 + 0.649434i
\(590\) 0 0
\(591\) −79.3335 + 516.214i −0.134236 + 0.873459i
\(592\) 0 0
\(593\) 329.386 + 570.514i 0.555457 + 0.962080i 0.997868 + 0.0652676i \(0.0207901\pi\)
−0.442410 + 0.896813i \(0.645877\pi\)
\(594\) 0 0
\(595\) −194.987 337.728i −0.327710 0.567610i
\(596\) 0 0
\(597\) −324.449 + 126.256i −0.543465 + 0.211484i
\(598\) 0 0
\(599\) 831.970i 1.38893i 0.719526 + 0.694466i \(0.244359\pi\)
−0.719526 + 0.694466i \(0.755641\pi\)
\(600\) 0 0
\(601\) 1026.61 592.713i 1.70817 0.986212i 0.771342 0.636421i \(-0.219586\pi\)
0.936828 0.349791i \(-0.113747\pi\)
\(602\) 0 0
\(603\) 131.209 416.799i 0.217594 0.691208i
\(604\) 0 0
\(605\) 355.819 0.588131
\(606\) 0 0
\(607\) −120.556 69.6030i −0.198609 0.114667i 0.397397 0.917647i \(-0.369913\pi\)
−0.596007 + 0.802979i \(0.703247\pi\)
\(608\) 0 0
\(609\) 657.544 + 101.054i 1.07971 + 0.165934i
\(610\) 0 0
\(611\) 124.511 + 71.8866i 0.203783 + 0.117654i
\(612\) 0 0
\(613\) 111.885 193.790i 0.182520 0.316134i −0.760218 0.649668i \(-0.774908\pi\)
0.942738 + 0.333534i \(0.108241\pi\)
\(614\) 0 0
\(615\) 244.064 304.238i 0.396852 0.494697i
\(616\) 0 0
\(617\) 16.8135 0.0272504 0.0136252 0.999907i \(-0.495663\pi\)
0.0136252 + 0.999907i \(0.495663\pi\)
\(618\) 0 0
\(619\) 288.780 + 500.182i 0.466527 + 0.808048i 0.999269 0.0382294i \(-0.0121718\pi\)
−0.532742 + 0.846278i \(0.678838\pi\)
\(620\) 0 0
\(621\) −221.543 + 450.013i −0.356752 + 0.724659i
\(622\) 0 0
\(623\) −1060.21 612.113i −1.70178 0.982524i
\(624\) 0 0
\(625\) 129.093 + 223.596i 0.206549 + 0.357754i
\(626\) 0 0
\(627\) 68.9765 + 293.465i 0.110010 + 0.468046i
\(628\) 0 0
\(629\) −140.258 80.9783i −0.222986 0.128741i
\(630\) 0 0
\(631\) 482.513 + 835.738i 0.764680 + 1.32447i 0.940415 + 0.340028i \(0.110437\pi\)
−0.175735 + 0.984438i \(0.556230\pi\)
\(632\) 0 0
\(633\) 70.8467 + 182.060i 0.111922 + 0.287615i
\(634\) 0 0
\(635\) 71.6244 + 41.3523i 0.112794 + 0.0651218i
\(636\) 0 0
\(637\) 175.598 + 101.382i 0.275664 + 0.159155i
\(638\) 0 0
\(639\) −271.575 296.103i −0.425000 0.463386i
\(640\) 0 0
\(641\) 476.248i 0.742976i −0.928438 0.371488i \(-0.878848\pi\)
0.928438 0.371488i \(-0.121152\pi\)
\(642\) 0 0
\(643\) −326.068 564.766i −0.507104 0.878330i −0.999966 0.00822274i \(-0.997383\pi\)
0.492862 0.870107i \(-0.335951\pi\)
\(644\) 0 0
\(645\) −284.733 + 110.801i −0.441447 + 0.171784i
\(646\) 0 0
\(647\) −55.1929 −0.0853059 −0.0426529 0.999090i \(-0.513581\pi\)
−0.0426529 + 0.999090i \(0.513581\pi\)
\(648\) 0 0
\(649\) 122.106 + 70.4978i 0.188144 + 0.108625i
\(650\) 0 0
\(651\) −602.537 92.5998i −0.925555 0.142242i
\(652\) 0 0
\(653\) −616.599 + 1067.98i −0.944256 + 1.63550i −0.187022 + 0.982356i \(0.559884\pi\)
−0.757234 + 0.653144i \(0.773450\pi\)
\(654\) 0 0
\(655\) 64.9971 112.578i 0.0992322 0.171875i
\(656\) 0 0
\(657\) 242.266 222.197i 0.368746 0.338200i
\(658\) 0 0
\(659\) −1046.04 603.931i −1.58731 0.916436i −0.993748 0.111650i \(-0.964387\pi\)
−0.593565 0.804786i \(-0.702280\pi\)
\(660\) 0 0
\(661\) 934.971i 1.41448i −0.706974 0.707240i \(-0.749940\pi\)
0.706974 0.707240i \(-0.250060\pi\)
\(662\) 0 0
\(663\) 343.830 428.602i 0.518597 0.646458i
\(664\) 0 0
\(665\) −455.028 355.969i −0.684252 0.535292i
\(666\) 0 0
\(667\) −448.783 259.105i −0.672838 0.388463i
\(668\) 0 0
\(669\) 821.220 + 126.208i 1.22753 + 0.188651i
\(670\) 0 0
\(671\) 158.603 0.236368
\(672\) 0 0
\(673\) −371.470 + 214.468i −0.551961 + 0.318675i −0.749913 0.661537i \(-0.769904\pi\)
0.197952 + 0.980212i \(0.436571\pi\)
\(674\) 0 0
\(675\) −155.721 232.711i −0.230697 0.344757i
\(676\) 0 0
\(677\) −754.793 + 435.780i −1.11491 + 0.643693i −0.940096 0.340909i \(-0.889265\pi\)
−0.174813 + 0.984602i \(0.555932\pi\)
\(678\) 0 0
\(679\) −695.939 + 401.801i −1.02495 + 0.591753i
\(680\) 0 0
\(681\) −392.745 1009.27i −0.576719 1.48204i
\(682\) 0 0
\(683\) 20.0977i 0.0294257i 0.999892 + 0.0147128i \(0.00468341\pi\)
−0.999892 + 0.0147128i \(0.995317\pi\)
\(684\) 0 0
\(685\) −42.0701 −0.0614162
\(686\) 0 0
\(687\) 228.700 + 183.466i 0.332896 + 0.267054i
\(688\) 0 0
\(689\) −221.390 383.458i −0.321321 0.556543i
\(690\) 0 0
\(691\) 330.331 + 572.150i 0.478048 + 0.828004i 0.999683 0.0251651i \(-0.00801113\pi\)
−0.521635 + 0.853169i \(0.674678\pi\)
\(692\) 0 0
\(693\) −278.871 + 255.771i −0.402412 + 0.369077i
\(694\) 0 0
\(695\) −394.696 683.634i −0.567908 0.983646i
\(696\) 0 0
\(697\) 435.954i 0.625472i
\(698\) 0 0
\(699\) −506.216 406.093i −0.724200 0.580963i
\(700\) 0 0
\(701\) −102.728 + 177.930i −0.146545 + 0.253823i −0.929948 0.367690i \(-0.880149\pi\)
0.783403 + 0.621514i \(0.213482\pi\)
\(702\) 0 0
\(703\) −237.572 33.5414i −0.337941 0.0477119i
\(704\) 0 0
\(705\) 17.5476 114.180i 0.0248902 0.161958i
\(706\) 0 0
\(707\) 59.5378 0.0842119
\(708\) 0 0
\(709\) 68.1450 118.031i 0.0961143 0.166475i −0.813959 0.580923i \(-0.802692\pi\)
0.910073 + 0.414448i \(0.136025\pi\)
\(710\) 0 0
\(711\) −7.25433 + 23.0441i −0.0102030 + 0.0324109i
\(712\) 0 0
\(713\) 411.240 + 237.429i 0.576774 + 0.333000i
\(714\) 0 0
\(715\) 250.182 + 144.442i 0.349904 + 0.202017i
\(716\) 0 0
\(717\) −445.930 357.731i −0.621939 0.498928i
\(718\) 0 0
\(719\) −59.4121 + 102.905i −0.0826316 + 0.143122i −0.904380 0.426729i \(-0.859666\pi\)
0.821748 + 0.569851i \(0.192999\pi\)
\(720\) 0 0
\(721\) 529.163i 0.733929i
\(722\) 0 0
\(723\) 735.406 916.721i 1.01716 1.26794i
\(724\) 0 0
\(725\) 250.526 144.641i 0.345554 0.199505i
\(726\) 0 0
\(727\) −367.189 −0.505074 −0.252537 0.967587i \(-0.581265\pi\)
−0.252537 + 0.967587i \(0.581265\pi\)
\(728\) 0 0
\(729\) −444.571 577.752i −0.609837 0.792527i
\(730\) 0 0
\(731\) 170.750 295.749i 0.233585 0.404581i
\(732\) 0 0
\(733\) −8.02715 + 13.9034i −0.0109511 + 0.0189678i −0.871449 0.490486i \(-0.836819\pi\)
0.860498 + 0.509454i \(0.170153\pi\)
\(734\) 0 0
\(735\) 24.7473 161.028i 0.0336698 0.219086i
\(736\) 0 0
\(737\) −222.378 + 128.390i −0.301733 + 0.174206i
\(738\) 0 0
\(739\) −290.683 + 503.478i −0.393347 + 0.681296i −0.992889 0.119047i \(-0.962016\pi\)
0.599542 + 0.800343i \(0.295349\pi\)
\(740\) 0 0
\(741\) 234.909 779.375i 0.317016 1.05179i
\(742\) 0 0
\(743\) −673.469 + 388.827i −0.906418 + 0.523321i −0.879277 0.476311i \(-0.841974\pi\)
−0.0271413 + 0.999632i \(0.508640\pi\)
\(744\) 0 0
\(745\) 118.720 205.628i 0.159355 0.276011i
\(746\) 0 0
\(747\) 255.897 + 1151.81i 0.342566 + 1.54192i
\(748\) 0 0
\(749\) −684.458 + 395.172i −0.913829 + 0.527599i
\(750\) 0 0
\(751\) 746.926i 0.994575i 0.867586 + 0.497287i \(0.165671\pi\)
−0.867586 + 0.497287i \(0.834329\pi\)
\(752\) 0 0
\(753\) 483.874 188.294i 0.642594 0.250058i
\(754\) 0 0
\(755\) −693.610 400.456i −0.918689 0.530405i
\(756\) 0 0
\(757\) 271.640 470.495i 0.358838 0.621526i −0.628929 0.777463i \(-0.716506\pi\)
0.987767 + 0.155937i \(0.0498397\pi\)
\(758\) 0 0
\(759\) 274.692 106.893i 0.361913 0.140835i
\(760\) 0 0
\(761\) −240.238 + 416.105i −0.315688 + 0.546787i −0.979583 0.201038i \(-0.935569\pi\)
0.663896 + 0.747825i \(0.268902\pi\)
\(762\) 0 0
\(763\) 685.465i 0.898382i
\(764\) 0 0
\(765\) −421.122 132.570i −0.550486 0.173294i
\(766\) 0 0
\(767\) −190.358 329.709i −0.248185 0.429869i
\(768\) 0 0
\(769\) 572.420 0.744369 0.372184 0.928159i \(-0.378609\pi\)
0.372184 + 0.928159i \(0.378609\pi\)
\(770\) 0 0
\(771\) 804.590 + 123.652i 1.04357 + 0.160379i
\(772\) 0 0
\(773\) 159.458 92.0633i 0.206285 0.119099i −0.393299 0.919411i \(-0.628666\pi\)
0.599584 + 0.800312i \(0.295333\pi\)
\(774\) 0 0
\(775\) −229.568 + 132.541i −0.296217 + 0.171021i
\(776\) 0 0
\(777\) −109.216 280.662i −0.140562 0.361212i
\(778\) 0 0
\(779\) 241.558 + 598.963i 0.310087 + 0.768887i
\(780\) 0 0
\(781\) 236.106i 0.302313i
\(782\) 0 0
\(783\) 625.940 418.854i 0.799413 0.534935i
\(784\) 0 0
\(785\) −361.218 + 625.647i −0.460150 + 0.797003i
\(786\) 0 0
\(787\) −320.809 185.219i −0.407635 0.235348i 0.282138 0.959374i \(-0.408956\pi\)
−0.689773 + 0.724026i \(0.742290\pi\)
\(788\) 0 0
\(789\) −150.330 + 978.178i −0.190532 + 1.23977i
\(790\) 0 0
\(791\) 1181.23i 1.49333i
\(792\) 0 0
\(793\) −370.883 214.129i −0.467696 0.270024i
\(794\) 0 0
\(795\) −222.622 + 277.510i −0.280028 + 0.349069i
\(796\) 0 0
\(797\) 917.008 + 529.435i 1.15057 +