Properties

Label 690.3.b.a.599.3
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.3
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-2.90508 - 0.748659i) q^{3} +2.00000 q^{4} +(-4.90392 - 0.975491i) q^{5} +(4.10841 + 1.05876i) q^{6} -3.09484i q^{7} -2.82843 q^{8} +(7.87902 + 4.34983i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-2.90508 - 0.748659i) q^{3} +2.00000 q^{4} +(-4.90392 - 0.975491i) q^{5} +(4.10841 + 1.05876i) q^{6} -3.09484i q^{7} -2.82843 q^{8} +(7.87902 + 4.34983i) q^{9} +(6.93519 + 1.37955i) q^{10} -10.9962i q^{11} +(-5.81017 - 1.49732i) q^{12} +23.5927i q^{13} +4.37677i q^{14} +(13.5160 + 6.50524i) q^{15} +4.00000 q^{16} -14.9626 q^{17} +(-11.1426 - 6.15159i) q^{18} -24.8534 q^{19} +(-9.80784 - 1.95098i) q^{20} +(-2.31698 + 8.99077i) q^{21} +15.5509i q^{22} +4.79583 q^{23} +(8.21682 + 2.11753i) q^{24} +(23.0968 + 9.56746i) q^{25} -33.3651i q^{26} +(-19.6327 - 18.5353i) q^{27} -6.18968i q^{28} +42.9868i q^{29} +(-19.1145 - 9.19980i) q^{30} -31.1614 q^{31} -5.65685 q^{32} +(-8.23238 + 31.9448i) q^{33} +21.1603 q^{34} +(-3.01899 + 15.1768i) q^{35} +(15.7580 + 8.69967i) q^{36} -48.5503i q^{37} +35.1480 q^{38} +(17.6629 - 68.5387i) q^{39} +(13.8704 + 2.75910i) q^{40} +31.4396i q^{41} +(3.27670 - 12.7149i) q^{42} -37.4985i q^{43} -21.9923i q^{44} +(-34.3949 - 29.0171i) q^{45} -6.78233 q^{46} +50.4805 q^{47} +(-11.6203 - 2.99464i) q^{48} +39.4220 q^{49} +(-32.6639 - 13.5304i) q^{50} +(43.4675 + 11.2019i) q^{51} +47.1854i q^{52} +37.0253 q^{53} +(27.7648 + 26.2129i) q^{54} +(-10.7267 + 53.9243i) q^{55} +8.75353i q^{56} +(72.2013 + 18.6067i) q^{57} -60.7925i q^{58} +35.4084i q^{59} +(27.0320 + 13.0105i) q^{60} -17.9790 q^{61} +44.0688 q^{62} +(13.4620 - 24.3843i) q^{63} +8.00000 q^{64} +(23.0145 - 115.697i) q^{65} +(11.6423 - 45.1768i) q^{66} +68.1965i q^{67} -29.9251 q^{68} +(-13.9323 - 3.59044i) q^{69} +(4.26949 - 21.4633i) q^{70} -99.8069i q^{71} +(-22.2852 - 12.3032i) q^{72} -39.3878i q^{73} +68.6605i q^{74} +(-59.9355 - 45.0859i) q^{75} -49.7068 q^{76} -34.0314 q^{77} +(-24.9791 + 96.9284i) q^{78} +30.7676 q^{79} +(-19.6157 - 3.90196i) q^{80} +(43.1579 + 68.5448i) q^{81} -44.4623i q^{82} +110.238 q^{83} +(-4.63396 + 17.9815i) q^{84} +(73.3752 + 14.5958i) q^{85} +53.0308i q^{86} +(32.1824 - 124.880i) q^{87} +31.1019i q^{88} -146.036i q^{89} +(48.6417 + 41.0364i) q^{90} +73.0156 q^{91} +9.59166 q^{92} +(90.5264 + 23.3292i) q^{93} -71.3903 q^{94} +(121.879 + 24.2443i) q^{95} +(16.4336 + 4.23505i) q^{96} -118.760i q^{97} -55.7511 q^{98} +(47.8315 - 86.6391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −2.90508 0.748659i −0.968361 0.249553i
\(4\) 2.00000 0.500000
\(5\) −4.90392 0.975491i −0.980784 0.195098i
\(6\) 4.10841 + 1.05876i 0.684735 + 0.176461i
\(7\) 3.09484i 0.442120i −0.975260 0.221060i \(-0.929048\pi\)
0.975260 0.221060i \(-0.0709517\pi\)
\(8\) −2.82843 −0.353553
\(9\) 7.87902 + 4.34983i 0.875447 + 0.483315i
\(10\) 6.93519 + 1.37955i 0.693519 + 0.137955i
\(11\) 10.9962i 0.999652i −0.866126 0.499826i \(-0.833397\pi\)
0.866126 0.499826i \(-0.166603\pi\)
\(12\) −5.81017 1.49732i −0.484181 0.124776i
\(13\) 23.5927i 1.81482i 0.420244 + 0.907411i \(0.361945\pi\)
−0.420244 + 0.907411i \(0.638055\pi\)
\(14\) 4.37677i 0.312626i
\(15\) 13.5160 + 6.50524i 0.901066 + 0.433683i
\(16\) 4.00000 0.250000
\(17\) −14.9626 −0.880150 −0.440075 0.897961i \(-0.645048\pi\)
−0.440075 + 0.897961i \(0.645048\pi\)
\(18\) −11.1426 6.15159i −0.619034 0.341755i
\(19\) −24.8534 −1.30807 −0.654037 0.756462i \(-0.726926\pi\)
−0.654037 + 0.756462i \(0.726926\pi\)
\(20\) −9.80784 1.95098i −0.490392 0.0975491i
\(21\) −2.31698 + 8.99077i −0.110332 + 0.428132i
\(22\) 15.5509i 0.706861i
\(23\) 4.79583 0.208514
\(24\) 8.21682 + 2.11753i 0.342367 + 0.0882303i
\(25\) 23.0968 + 9.56746i 0.923873 + 0.382698i
\(26\) 33.3651i 1.28327i
\(27\) −19.6327 18.5353i −0.727136 0.686494i
\(28\) 6.18968i 0.221060i
\(29\) 42.9868i 1.48230i 0.671338 + 0.741152i \(0.265720\pi\)
−0.671338 + 0.741152i \(0.734280\pi\)
\(30\) −19.1145 9.19980i −0.637150 0.306660i
\(31\) −31.1614 −1.00521 −0.502603 0.864517i \(-0.667624\pi\)
−0.502603 + 0.864517i \(0.667624\pi\)
\(32\) −5.65685 −0.176777
\(33\) −8.23238 + 31.9448i −0.249466 + 0.968024i
\(34\) 21.1603 0.622360
\(35\) −3.01899 + 15.1768i −0.0862568 + 0.433624i
\(36\) 15.7580 + 8.69967i 0.437723 + 0.241657i
\(37\) 48.5503i 1.31217i −0.754687 0.656085i \(-0.772211\pi\)
0.754687 0.656085i \(-0.227789\pi\)
\(38\) 35.1480 0.924948
\(39\) 17.6629 68.5387i 0.452894 1.75740i
\(40\) 13.8704 + 2.75910i 0.346759 + 0.0689776i
\(41\) 31.4396i 0.766819i 0.923578 + 0.383410i \(0.125250\pi\)
−0.923578 + 0.383410i \(0.874750\pi\)
\(42\) 3.27670 12.7149i 0.0780168 0.302735i
\(43\) 37.4985i 0.872057i −0.899933 0.436029i \(-0.856385\pi\)
0.899933 0.436029i \(-0.143615\pi\)
\(44\) 21.9923i 0.499826i
\(45\) −34.3949 29.0171i −0.764330 0.644825i
\(46\) −6.78233 −0.147442
\(47\) 50.4805 1.07405 0.537027 0.843565i \(-0.319547\pi\)
0.537027 + 0.843565i \(0.319547\pi\)
\(48\) −11.6203 2.99464i −0.242090 0.0623882i
\(49\) 39.4220 0.804530
\(50\) −32.6639 13.5304i −0.653277 0.270609i
\(51\) 43.4675 + 11.2019i 0.852304 + 0.219644i
\(52\) 47.1854i 0.907411i
\(53\) 37.0253 0.698590 0.349295 0.937013i \(-0.386421\pi\)
0.349295 + 0.937013i \(0.386421\pi\)
\(54\) 27.7648 + 26.2129i 0.514163 + 0.485424i
\(55\) −10.7267 + 53.9243i −0.195030 + 0.980443i
\(56\) 8.75353i 0.156313i
\(57\) 72.2013 + 18.6067i 1.26669 + 0.326434i
\(58\) 60.7925i 1.04815i
\(59\) 35.4084i 0.600143i 0.953917 + 0.300071i \(0.0970105\pi\)
−0.953917 + 0.300071i \(0.902989\pi\)
\(60\) 27.0320 + 13.0105i 0.450533 + 0.216841i
\(61\) −17.9790 −0.294737 −0.147369 0.989082i \(-0.547080\pi\)
−0.147369 + 0.989082i \(0.547080\pi\)
\(62\) 44.0688 0.710788
\(63\) 13.4620 24.3843i 0.213683 0.387053i
\(64\) 8.00000 0.125000
\(65\) 23.0145 115.697i 0.354069 1.77995i
\(66\) 11.6423 45.1768i 0.176399 0.684497i
\(67\) 68.1965i 1.01786i 0.860808 + 0.508929i \(0.169959\pi\)
−0.860808 + 0.508929i \(0.830041\pi\)
\(68\) −29.9251 −0.440075
\(69\) −13.9323 3.59044i −0.201917 0.0520354i
\(70\) 4.26949 21.4633i 0.0609928 0.306619i
\(71\) 99.8069i 1.40573i −0.711323 0.702866i \(-0.751904\pi\)
0.711323 0.702866i \(-0.248096\pi\)
\(72\) −22.2852 12.3032i −0.309517 0.170878i
\(73\) 39.3878i 0.539558i −0.962922 0.269779i \(-0.913049\pi\)
0.962922 0.269779i \(-0.0869507\pi\)
\(74\) 68.6605i 0.927845i
\(75\) −59.9355 45.0859i −0.799140 0.601145i
\(76\) −49.7068 −0.654037
\(77\) −34.0314 −0.441966
\(78\) −24.9791 + 96.9284i −0.320245 + 1.24267i
\(79\) 30.7676 0.389463 0.194732 0.980857i \(-0.437616\pi\)
0.194732 + 0.980857i \(0.437616\pi\)
\(80\) −19.6157 3.90196i −0.245196 0.0487745i
\(81\) 43.1579 + 68.5448i 0.532814 + 0.846233i
\(82\) 44.4623i 0.542223i
\(83\) 110.238 1.32817 0.664086 0.747657i \(-0.268821\pi\)
0.664086 + 0.747657i \(0.268821\pi\)
\(84\) −4.63396 + 17.9815i −0.0551662 + 0.214066i
\(85\) 73.3752 + 14.5958i 0.863237 + 0.171716i
\(86\) 53.0308i 0.616638i
\(87\) 32.1824 124.880i 0.369913 1.43540i
\(88\) 31.1019i 0.353430i
\(89\) 146.036i 1.64086i −0.571748 0.820429i \(-0.693734\pi\)
0.571748 0.820429i \(-0.306266\pi\)
\(90\) 48.6417 + 41.0364i 0.540463 + 0.455960i
\(91\) 73.0156 0.802369
\(92\) 9.59166 0.104257
\(93\) 90.5264 + 23.3292i 0.973402 + 0.250852i
\(94\) −71.3903 −0.759471
\(95\) 121.879 + 24.2443i 1.28294 + 0.255203i
\(96\) 16.4336 + 4.23505i 0.171184 + 0.0441151i
\(97\) 118.760i 1.22433i −0.790732 0.612163i \(-0.790300\pi\)
0.790732 0.612163i \(-0.209700\pi\)
\(98\) −55.7511 −0.568889
\(99\) 47.8315 86.6391i 0.483147 0.875142i
\(100\) 46.1937 + 19.1349i 0.461937 + 0.191349i
\(101\) 152.807i 1.51294i 0.654030 + 0.756469i \(0.273077\pi\)
−0.654030 + 0.756469i \(0.726923\pi\)
\(102\) −61.4723 15.8418i −0.602670 0.155312i
\(103\) 153.920i 1.49437i −0.664616 0.747185i \(-0.731405\pi\)
0.664616 0.747185i \(-0.268595\pi\)
\(104\) 66.7302i 0.641637i
\(105\) 20.1327 41.8298i 0.191740 0.398379i
\(106\) −52.3616 −0.493977
\(107\) −5.89126 −0.0550585 −0.0275292 0.999621i \(-0.508764\pi\)
−0.0275292 + 0.999621i \(0.508764\pi\)
\(108\) −39.2653 37.0706i −0.363568 0.343247i
\(109\) 93.4247 0.857107 0.428554 0.903516i \(-0.359023\pi\)
0.428554 + 0.903516i \(0.359023\pi\)
\(110\) 15.1698 76.2605i 0.137907 0.693278i
\(111\) −36.3476 + 141.043i −0.327456 + 1.27066i
\(112\) 12.3794i 0.110530i
\(113\) 158.025 1.39845 0.699226 0.714901i \(-0.253528\pi\)
0.699226 + 0.714901i \(0.253528\pi\)
\(114\) −102.108 26.3139i −0.895684 0.230824i
\(115\) −23.5184 4.67829i −0.204508 0.0406808i
\(116\) 85.9736i 0.741152i
\(117\) −102.624 + 185.887i −0.877130 + 1.58878i
\(118\) 50.0751i 0.424365i
\(119\) 46.3067i 0.389132i
\(120\) −38.2290 18.3996i −0.318575 0.153330i
\(121\) 0.0841400 0.000695372
\(122\) 25.4261 0.208411
\(123\) 23.5375 91.3346i 0.191362 0.742558i
\(124\) −62.3227 −0.502603
\(125\) −103.932 69.4488i −0.831456 0.555590i
\(126\) −19.0382 + 34.4846i −0.151097 + 0.273687i
\(127\) 202.869i 1.59739i 0.601735 + 0.798696i \(0.294477\pi\)
−0.601735 + 0.798696i \(0.705523\pi\)
\(128\) −11.3137 −0.0883883
\(129\) −28.0736 + 108.936i −0.217624 + 0.844467i
\(130\) −32.5474 + 163.620i −0.250364 + 1.25861i
\(131\) 232.701i 1.77635i −0.459510 0.888173i \(-0.651975\pi\)
0.459510 0.888173i \(-0.348025\pi\)
\(132\) −16.4648 + 63.8896i −0.124733 + 0.484012i
\(133\) 76.9174i 0.578326i
\(134\) 96.4444i 0.719735i
\(135\) 78.1960 + 110.047i 0.579229 + 0.815165i
\(136\) 42.3205 0.311180
\(137\) −28.9097 −0.211020 −0.105510 0.994418i \(-0.533647\pi\)
−0.105510 + 0.994418i \(0.533647\pi\)
\(138\) 19.7032 + 5.07765i 0.142777 + 0.0367946i
\(139\) 19.0941 0.137367 0.0686837 0.997638i \(-0.478120\pi\)
0.0686837 + 0.997638i \(0.478120\pi\)
\(140\) −6.03798 + 30.3537i −0.0431284 + 0.216812i
\(141\) −146.650 37.7927i −1.04007 0.268033i
\(142\) 141.148i 0.994002i
\(143\) 259.429 1.81419
\(144\) 31.5161 + 17.3993i 0.218862 + 0.120829i
\(145\) 41.9332 210.804i 0.289195 1.45382i
\(146\) 55.7027i 0.381525i
\(147\) −114.524 29.5136i −0.779075 0.200773i
\(148\) 97.1006i 0.656085i
\(149\) 2.09186i 0.0140394i −0.999975 0.00701968i \(-0.997766\pi\)
0.999975 0.00701968i \(-0.00223445\pi\)
\(150\) 84.7616 + 63.7611i 0.565077 + 0.425074i
\(151\) 295.609 1.95767 0.978837 0.204640i \(-0.0656023\pi\)
0.978837 + 0.204640i \(0.0656023\pi\)
\(152\) 70.2961 0.462474
\(153\) −117.890 65.0846i −0.770525 0.425390i
\(154\) 48.1277 0.312517
\(155\) 152.813 + 30.3976i 0.985889 + 0.196114i
\(156\) 35.3258 137.077i 0.226447 0.878702i
\(157\) 93.0158i 0.592457i 0.955117 + 0.296229i \(0.0957290\pi\)
−0.955117 + 0.296229i \(0.904271\pi\)
\(158\) −43.5119 −0.275392
\(159\) −107.561 27.7193i −0.676487 0.174335i
\(160\) 27.7408 + 5.51821i 0.173380 + 0.0344888i
\(161\) 14.8423i 0.0921884i
\(162\) −61.0345 96.9370i −0.376756 0.598377i
\(163\) 15.1239i 0.0927848i 0.998923 + 0.0463924i \(0.0147725\pi\)
−0.998923 + 0.0463924i \(0.985228\pi\)
\(164\) 62.8792i 0.383410i
\(165\) 71.5328 148.624i 0.433532 0.900752i
\(166\) −155.900 −0.939159
\(167\) 51.7925 0.310135 0.155067 0.987904i \(-0.450441\pi\)
0.155067 + 0.987904i \(0.450441\pi\)
\(168\) 6.55341 25.4297i 0.0390084 0.151367i
\(169\) −387.615 −2.29358
\(170\) −103.768 20.6416i −0.610401 0.121421i
\(171\) −195.821 108.108i −1.14515 0.632212i
\(172\) 74.9969i 0.436029i
\(173\) −21.8513 −0.126308 −0.0631540 0.998004i \(-0.520116\pi\)
−0.0631540 + 0.998004i \(0.520116\pi\)
\(174\) −45.5128 + 176.607i −0.261568 + 1.01498i
\(175\) 29.6097 71.4810i 0.169199 0.408463i
\(176\) 43.9847i 0.249913i
\(177\) 26.5088 102.864i 0.149767 0.581155i
\(178\) 206.527i 1.16026i
\(179\) 131.395i 0.734050i −0.930211 0.367025i \(-0.880376\pi\)
0.930211 0.367025i \(-0.119624\pi\)
\(180\) −68.7897 58.0343i −0.382165 0.322413i
\(181\) −294.584 −1.62753 −0.813767 0.581191i \(-0.802587\pi\)
−0.813767 + 0.581191i \(0.802587\pi\)
\(182\) −103.260 −0.567361
\(183\) 52.2304 + 13.4601i 0.285412 + 0.0735526i
\(184\) −13.5647 −0.0737210
\(185\) −47.3604 + 238.087i −0.256002 + 1.28696i
\(186\) −128.024 32.9925i −0.688299 0.177379i
\(187\) 164.531i 0.879844i
\(188\) 100.961 0.537027
\(189\) −57.3639 + 60.7600i −0.303513 + 0.321481i
\(190\) −172.363 34.2866i −0.907174 0.180456i
\(191\) 181.966i 0.952700i 0.879256 + 0.476350i \(0.158040\pi\)
−0.879256 + 0.476350i \(0.841960\pi\)
\(192\) −23.2407 5.98927i −0.121045 0.0311941i
\(193\) 8.26140i 0.0428052i −0.999771 0.0214026i \(-0.993187\pi\)
0.999771 0.0214026i \(-0.00681318\pi\)
\(194\) 167.951i 0.865729i
\(195\) −153.476 + 318.878i −0.787058 + 1.63527i
\(196\) 78.8439 0.402265
\(197\) −61.8888 −0.314156 −0.157078 0.987586i \(-0.550207\pi\)
−0.157078 + 0.987586i \(0.550207\pi\)
\(198\) −67.6440 + 122.526i −0.341636 + 0.618819i
\(199\) −314.790 −1.58186 −0.790930 0.611906i \(-0.790403\pi\)
−0.790930 + 0.611906i \(0.790403\pi\)
\(200\) −65.3277 27.0609i −0.326639 0.135304i
\(201\) 51.0559 198.117i 0.254010 0.985655i
\(202\) 216.101i 1.06981i
\(203\) 133.037 0.655356
\(204\) 86.9350 + 22.4037i 0.426152 + 0.109822i
\(205\) 30.6690 154.177i 0.149605 0.752084i
\(206\) 217.676i 1.05668i
\(207\) 37.7865 + 20.8611i 0.182543 + 0.100778i
\(208\) 94.3708i 0.453706i
\(209\) 273.293i 1.30762i
\(210\) −28.4719 + 59.1563i −0.135581 + 0.281697i
\(211\) 97.7183 0.463120 0.231560 0.972821i \(-0.425617\pi\)
0.231560 + 0.972821i \(0.425617\pi\)
\(212\) 74.0505 0.349295
\(213\) −74.7213 + 289.947i −0.350804 + 1.36126i
\(214\) 8.33150 0.0389322
\(215\) −36.5794 + 183.889i −0.170137 + 0.855300i
\(216\) 55.5296 + 52.4258i 0.257081 + 0.242712i
\(217\) 96.4395i 0.444422i
\(218\) −132.122 −0.606066
\(219\) −29.4880 + 114.425i −0.134648 + 0.522487i
\(220\) −21.4533 + 107.849i −0.0975152 + 0.490221i
\(221\) 353.007i 1.59732i
\(222\) 51.4033 199.465i 0.231546 0.898489i
\(223\) 289.459i 1.29802i 0.760779 + 0.649011i \(0.224817\pi\)
−0.760779 + 0.649011i \(0.775183\pi\)
\(224\) 17.5071i 0.0781565i
\(225\) 140.364 + 175.850i 0.623838 + 0.781554i
\(226\) −223.481 −0.988854
\(227\) −272.278 −1.19946 −0.599731 0.800201i \(-0.704726\pi\)
−0.599731 + 0.800201i \(0.704726\pi\)
\(228\) 144.403 + 37.2135i 0.633344 + 0.163217i
\(229\) 97.0820 0.423939 0.211970 0.977276i \(-0.432012\pi\)
0.211970 + 0.977276i \(0.432012\pi\)
\(230\) 33.2600 + 6.61610i 0.144609 + 0.0287657i
\(231\) 98.8641 + 25.4779i 0.427983 + 0.110294i
\(232\) 121.585i 0.524073i
\(233\) 160.963 0.690828 0.345414 0.938450i \(-0.387739\pi\)
0.345414 + 0.938450i \(0.387739\pi\)
\(234\) 145.133 262.884i 0.620225 1.12344i
\(235\) −247.552 49.2433i −1.05341 0.209546i
\(236\) 70.8169i 0.300071i
\(237\) −89.3824 23.0344i −0.377141 0.0971917i
\(238\) 65.4876i 0.275158i
\(239\) 47.0387i 0.196815i 0.995146 + 0.0984073i \(0.0313748\pi\)
−0.995146 + 0.0984073i \(0.968625\pi\)
\(240\) 54.0639 + 26.0210i 0.225266 + 0.108421i
\(241\) 193.872 0.804450 0.402225 0.915541i \(-0.368237\pi\)
0.402225 + 0.915541i \(0.368237\pi\)
\(242\) −0.118992 −0.000491702
\(243\) −74.0606 231.439i −0.304776 0.952424i
\(244\) −35.9580 −0.147369
\(245\) −193.322 38.4558i −0.789070 0.156962i
\(246\) −33.2871 + 129.167i −0.135313 + 0.525068i
\(247\) 586.359i 2.37392i
\(248\) 88.1377 0.355394
\(249\) −320.251 82.5308i −1.28615 0.331449i
\(250\) 146.982 + 98.2154i 0.587928 + 0.392862i
\(251\) 141.050i 0.561953i −0.959715 0.280977i \(-0.909342\pi\)
0.959715 0.280977i \(-0.0906583\pi\)
\(252\) 26.9241 48.7686i 0.106842 0.193526i
\(253\) 52.7358i 0.208442i
\(254\) 286.900i 1.12953i
\(255\) −202.234 97.3351i −0.793073 0.381706i
\(256\) 16.0000 0.0625000
\(257\) 135.744 0.528186 0.264093 0.964497i \(-0.414927\pi\)
0.264093 + 0.964497i \(0.414927\pi\)
\(258\) 39.7020 154.059i 0.153884 0.597128i
\(259\) −150.255 −0.580137
\(260\) 46.0289 231.393i 0.177034 0.889974i
\(261\) −186.985 + 338.694i −0.716419 + 1.29768i
\(262\) 329.089i 1.25607i
\(263\) 305.350 1.16103 0.580513 0.814251i \(-0.302852\pi\)
0.580513 + 0.814251i \(0.302852\pi\)
\(264\) 23.2847 90.3536i 0.0881996 0.342248i
\(265\) −181.569 36.1178i −0.685165 0.136294i
\(266\) 108.778i 0.408938i
\(267\) −109.331 + 424.248i −0.409481 + 1.58894i
\(268\) 136.393i 0.508929i
\(269\) 305.759i 1.13665i 0.822804 + 0.568325i \(0.192408\pi\)
−0.822804 + 0.568325i \(0.807592\pi\)
\(270\) −110.586 155.630i −0.409577 0.576408i
\(271\) 353.781 1.30547 0.652733 0.757588i \(-0.273622\pi\)
0.652733 + 0.757588i \(0.273622\pi\)
\(272\) −59.8502 −0.220038
\(273\) −212.116 54.6638i −0.776983 0.200234i
\(274\) 40.8845 0.149213
\(275\) 105.205 253.977i 0.382565 0.923552i
\(276\) −27.8646 7.18088i −0.100959 0.0260177i
\(277\) 24.6890i 0.0891299i 0.999006 + 0.0445650i \(0.0141902\pi\)
−0.999006 + 0.0445650i \(0.985810\pi\)
\(278\) −27.0031 −0.0971334
\(279\) −245.521 135.547i −0.880004 0.485831i
\(280\) 8.53899 42.9266i 0.0304964 0.153309i
\(281\) 135.704i 0.482931i −0.970409 0.241466i \(-0.922372\pi\)
0.970409 0.241466i \(-0.0776281\pi\)
\(282\) 207.395 + 53.4469i 0.735442 + 0.189528i
\(283\) 34.6037i 0.122275i 0.998129 + 0.0611373i \(0.0194728\pi\)
−0.998129 + 0.0611373i \(0.980527\pi\)
\(284\) 199.614i 0.702866i
\(285\) −335.918 161.678i −1.17866 0.567290i
\(286\) −366.889 −1.28283
\(287\) 97.3005 0.339026
\(288\) −44.5705 24.6064i −0.154759 0.0854388i
\(289\) −65.1219 −0.225335
\(290\) −59.3025 + 298.121i −0.204491 + 1.02801i
\(291\) −88.9104 + 345.006i −0.305534 + 1.18559i
\(292\) 78.7755i 0.269779i
\(293\) 472.467 1.61252 0.806258 0.591563i \(-0.201489\pi\)
0.806258 + 0.591563i \(0.201489\pi\)
\(294\) 161.962 + 41.7385i 0.550890 + 0.141968i
\(295\) 34.5406 173.640i 0.117087 0.588610i
\(296\) 137.321i 0.463922i
\(297\) −203.818 + 215.884i −0.686255 + 0.726883i
\(298\) 2.95834i 0.00992732i
\(299\) 113.147i 0.378417i
\(300\) −119.871 90.1718i −0.399570 0.300573i
\(301\) −116.052 −0.385554
\(302\) −418.054 −1.38429
\(303\) 114.400 443.916i 0.377558 1.46507i
\(304\) −99.4137 −0.327019
\(305\) 88.1675 + 17.5383i 0.289074 + 0.0575027i
\(306\) 166.722 + 92.0436i 0.544843 + 0.300796i
\(307\) 170.489i 0.555340i 0.960676 + 0.277670i \(0.0895622\pi\)
−0.960676 + 0.277670i \(0.910438\pi\)
\(308\) −68.0628 −0.220983
\(309\) −115.234 + 447.151i −0.372924 + 1.44709i
\(310\) −216.110 42.9887i −0.697129 0.138673i
\(311\) 18.3636i 0.0590468i 0.999564 + 0.0295234i \(0.00939896\pi\)
−0.999564 + 0.0295234i \(0.990601\pi\)
\(312\) −49.9582 + 193.857i −0.160122 + 0.621336i
\(313\) 301.845i 0.964361i −0.876072 0.482181i \(-0.839845\pi\)
0.876072 0.482181i \(-0.160155\pi\)
\(314\) 131.544i 0.418930i
\(315\) −89.8034 + 106.447i −0.285090 + 0.337926i
\(316\) 61.5352 0.194732
\(317\) −178.155 −0.562003 −0.281002 0.959707i \(-0.590667\pi\)
−0.281002 + 0.959707i \(0.590667\pi\)
\(318\) 152.115 + 39.2010i 0.478349 + 0.123274i
\(319\) 472.690 1.48179
\(320\) −39.2313 7.80393i −0.122598 0.0243873i
\(321\) 17.1146 + 4.41054i 0.0533165 + 0.0137400i
\(322\) 20.9902i 0.0651870i
\(323\) 371.871 1.15130
\(324\) 86.3158 + 137.090i 0.266407 + 0.423116i
\(325\) −225.722 + 544.916i −0.694529 + 1.67667i
\(326\) 21.3885i 0.0656088i
\(327\) −271.407 69.9432i −0.829989 0.213894i
\(328\) 88.9246i 0.271112i
\(329\) 156.229i 0.474861i
\(330\) −101.163 + 210.186i −0.306554 + 0.636928i
\(331\) 276.457 0.835219 0.417609 0.908627i \(-0.362868\pi\)
0.417609 + 0.908627i \(0.362868\pi\)
\(332\) 220.476 0.664086
\(333\) 211.186 382.529i 0.634192 1.14874i
\(334\) −73.2456 −0.219298
\(335\) 66.5251 334.430i 0.198582 0.998299i
\(336\) −9.26792 + 35.9631i −0.0275831 + 0.107033i
\(337\) 317.196i 0.941236i 0.882337 + 0.470618i \(0.155969\pi\)
−0.882337 + 0.470618i \(0.844031\pi\)
\(338\) 548.170 1.62181
\(339\) −459.076 118.307i −1.35421 0.348988i
\(340\) 146.750 + 29.1917i 0.431619 + 0.0858579i
\(341\) 342.656i 1.00486i
\(342\) 276.932 + 152.888i 0.809743 + 0.447041i
\(343\) 273.652i 0.797819i
\(344\) 106.062i 0.308319i
\(345\) 64.8204 + 31.1981i 0.187885 + 0.0904291i
\(346\) 30.9024 0.0893132
\(347\) 143.949 0.414839 0.207419 0.978252i \(-0.433494\pi\)
0.207419 + 0.978252i \(0.433494\pi\)
\(348\) 64.3649 249.760i 0.184957 0.717702i
\(349\) 392.805 1.12552 0.562758 0.826622i \(-0.309740\pi\)
0.562758 + 0.826622i \(0.309740\pi\)
\(350\) −41.8745 + 101.089i −0.119641 + 0.288827i
\(351\) 437.298 463.188i 1.24586 1.31962i
\(352\) 62.2038i 0.176715i
\(353\) −409.836 −1.16101 −0.580505 0.814257i \(-0.697145\pi\)
−0.580505 + 0.814257i \(0.697145\pi\)
\(354\) −37.4891 + 145.472i −0.105902 + 0.410939i
\(355\) −97.3607 + 489.445i −0.274256 + 1.37872i
\(356\) 292.073i 0.820429i
\(357\) 34.6679 134.525i 0.0971091 0.376820i
\(358\) 185.820i 0.519052i
\(359\) 333.035i 0.927674i −0.885921 0.463837i \(-0.846472\pi\)
0.885921 0.463837i \(-0.153528\pi\)
\(360\) 97.2833 + 82.0729i 0.270231 + 0.227980i
\(361\) 256.692 0.711059
\(362\) 416.604 1.15084
\(363\) −0.244434 0.0629922i −0.000673371 0.000173532i
\(364\) 146.031 0.401185
\(365\) −38.4224 + 193.154i −0.105267 + 0.529190i
\(366\) −73.8650 19.0355i −0.201817 0.0520095i
\(367\) 345.521i 0.941473i −0.882274 0.470737i \(-0.843988\pi\)
0.882274 0.470737i \(-0.156012\pi\)
\(368\) 19.1833 0.0521286
\(369\) −136.757 + 247.713i −0.370615 + 0.671309i
\(370\) 66.9777 336.706i 0.181021 0.910015i
\(371\) 114.587i 0.308860i
\(372\) 181.053 + 46.6585i 0.486701 + 0.125426i
\(373\) 601.127i 1.61160i 0.592188 + 0.805800i \(0.298264\pi\)
−0.592188 + 0.805800i \(0.701736\pi\)
\(374\) 232.682i 0.622144i
\(375\) 249.938 + 279.564i 0.666501 + 0.745504i
\(376\) −142.781 −0.379735
\(377\) −1014.17 −2.69012
\(378\) 81.1248 85.9276i 0.214616 0.227322i
\(379\) 366.586 0.967246 0.483623 0.875277i \(-0.339321\pi\)
0.483623 + 0.875277i \(0.339321\pi\)
\(380\) 243.758 + 48.4886i 0.641469 + 0.127601i
\(381\) 151.880 589.351i 0.398634 1.54685i
\(382\) 257.338i 0.673661i
\(383\) 699.790 1.82713 0.913563 0.406696i \(-0.133319\pi\)
0.913563 + 0.406696i \(0.133319\pi\)
\(384\) 32.8673 + 8.47011i 0.0855918 + 0.0220576i
\(385\) 166.887 + 33.1973i 0.433473 + 0.0862268i
\(386\) 11.6834i 0.0302678i
\(387\) 163.112 295.451i 0.421478 0.763440i
\(388\) 237.519i 0.612163i
\(389\) 192.793i 0.495613i −0.968810 0.247807i \(-0.920290\pi\)
0.968810 0.247807i \(-0.0797097\pi\)
\(390\) 217.048 450.962i 0.556534 1.15631i
\(391\) −71.7579 −0.183524
\(392\) −111.502 −0.284444
\(393\) −174.214 + 676.016i −0.443292 + 1.72014i
\(394\) 87.5240 0.222142
\(395\) −150.882 30.0135i −0.381979 0.0759835i
\(396\) 95.6630 173.278i 0.241573 0.437571i
\(397\) 160.829i 0.405111i −0.979271 0.202555i \(-0.935075\pi\)
0.979271 0.202555i \(-0.0649246\pi\)
\(398\) 445.181 1.11854
\(399\) 57.5849 223.451i 0.144323 0.560028i
\(400\) 92.3873 + 38.2698i 0.230968 + 0.0956746i
\(401\) 771.410i 1.92371i 0.273551 + 0.961857i \(0.411802\pi\)
−0.273551 + 0.961857i \(0.588198\pi\)
\(402\) −72.2040 + 280.179i −0.179612 + 0.696963i
\(403\) 735.181i 1.82427i
\(404\) 305.613i 0.756469i
\(405\) −144.778 378.238i −0.357477 0.933922i
\(406\) −188.143 −0.463407
\(407\) −533.868 −1.31171
\(408\) −122.945 31.6836i −0.301335 0.0776559i
\(409\) 740.399 1.81027 0.905134 0.425127i \(-0.139771\pi\)
0.905134 + 0.425127i \(0.139771\pi\)
\(410\) −43.3726 + 218.039i −0.105787 + 0.531804i
\(411\) 83.9850 + 21.6435i 0.204343 + 0.0526606i
\(412\) 307.840i 0.747185i
\(413\) 109.583 0.265335
\(414\) −53.4381 29.5020i −0.129078 0.0712609i
\(415\) −540.599 107.536i −1.30265 0.259124i
\(416\) 133.460i 0.320818i
\(417\) −55.4698 14.2949i −0.133021 0.0342804i
\(418\) 386.494i 0.924627i
\(419\) 374.440i 0.893652i 0.894621 + 0.446826i \(0.147446\pi\)
−0.894621 + 0.446826i \(0.852554\pi\)
\(420\) 40.2654 83.6596i 0.0958700 0.199190i
\(421\) 112.190 0.266484 0.133242 0.991084i \(-0.457461\pi\)
0.133242 + 0.991084i \(0.457461\pi\)
\(422\) −138.194 −0.327475
\(423\) 397.737 + 219.582i 0.940277 + 0.519106i
\(424\) −104.723 −0.246989
\(425\) −345.588 143.154i −0.813148 0.336832i
\(426\) 105.672 410.048i 0.248056 0.962553i
\(427\) 55.6421i 0.130309i
\(428\) −11.7825 −0.0275292
\(429\) −753.664 194.224i −1.75679 0.452737i
\(430\) 51.7311 260.059i 0.120305 0.604788i
\(431\) 110.755i 0.256973i −0.991711 0.128486i \(-0.958988\pi\)
0.991711 0.128486i \(-0.0410119\pi\)
\(432\) −78.5307 74.1413i −0.181784 0.171623i
\(433\) 505.829i 1.16820i 0.811683 + 0.584099i \(0.198552\pi\)
−0.811683 + 0.584099i \(0.801448\pi\)
\(434\) 136.386i 0.314253i
\(435\) −279.640 + 581.009i −0.642850 + 1.33565i
\(436\) 186.849 0.428554
\(437\) −119.193 −0.272752
\(438\) 41.7023 161.821i 0.0952108 0.369454i
\(439\) 98.1758 0.223635 0.111818 0.993729i \(-0.464333\pi\)
0.111818 + 0.993729i \(0.464333\pi\)
\(440\) 30.3396 152.521i 0.0689536 0.346639i
\(441\) 310.606 + 171.479i 0.704323 + 0.388841i
\(442\) 499.227i 1.12947i
\(443\) 385.457 0.870107 0.435053 0.900405i \(-0.356729\pi\)
0.435053 + 0.900405i \(0.356729\pi\)
\(444\) −72.6953 + 282.085i −0.163728 + 0.635328i
\(445\) −142.457 + 716.151i −0.320129 + 1.60933i
\(446\) 409.356i 0.917839i
\(447\) −1.56609 + 6.07704i −0.00350356 + 0.0135952i
\(448\) 24.7587i 0.0552650i
\(449\) 636.951i 1.41860i −0.704907 0.709300i \(-0.749011\pi\)
0.704907 0.709300i \(-0.250989\pi\)
\(450\) −198.504 248.689i −0.441120 0.552642i
\(451\) 345.715 0.766552
\(452\) 316.050 0.699226
\(453\) −858.768 221.310i −1.89574 0.488543i
\(454\) 385.059 0.848148
\(455\) −358.063 71.2261i −0.786951 0.156541i
\(456\) −204.216 52.6278i −0.447842 0.115412i
\(457\) 335.828i 0.734853i 0.930053 + 0.367427i \(0.119761\pi\)
−0.930053 + 0.367427i \(0.880239\pi\)
\(458\) −137.295 −0.299770
\(459\) 293.755 + 277.336i 0.639989 + 0.604218i
\(460\) −47.0367 9.35658i −0.102254 0.0203404i
\(461\) 480.066i 1.04136i −0.853752 0.520679i \(-0.825679\pi\)
0.853752 0.520679i \(-0.174321\pi\)
\(462\) −139.815 36.0312i −0.302630 0.0779896i
\(463\) 397.487i 0.858504i −0.903185 0.429252i \(-0.858777\pi\)
0.903185 0.429252i \(-0.141223\pi\)
\(464\) 171.947i 0.370576i
\(465\) −421.177 202.712i −0.905756 0.435941i
\(466\) −227.636 −0.488489
\(467\) −360.185 −0.771274 −0.385637 0.922651i \(-0.626018\pi\)
−0.385637 + 0.922651i \(0.626018\pi\)
\(468\) −205.249 + 371.775i −0.438565 + 0.794390i
\(469\) 211.057 0.450016
\(470\) 350.092 + 69.6405i 0.744877 + 0.148171i
\(471\) 69.6371 270.219i 0.147849 0.573712i
\(472\) 100.150i 0.212183i
\(473\) −412.340 −0.871754
\(474\) 126.406 + 32.5756i 0.266679 + 0.0687249i
\(475\) −574.035 237.784i −1.20850 0.500598i
\(476\) 92.6135i 0.194566i
\(477\) 291.723 + 161.054i 0.611578 + 0.337639i
\(478\) 66.5227i 0.139169i
\(479\) 462.822i 0.966226i 0.875558 + 0.483113i \(0.160494\pi\)
−0.875558 + 0.483113i \(0.839506\pi\)
\(480\) −76.4579 36.7992i −0.159287 0.0766650i
\(481\) 1145.43 2.38136
\(482\) −274.177 −0.568832
\(483\) −11.1118 + 43.1182i −0.0230059 + 0.0892717i
\(484\) 0.168280 0.000347686
\(485\) −115.849 + 582.387i −0.238864 + 1.20080i
\(486\) 104.738 + 327.304i 0.215509 + 0.673465i
\(487\) 327.948i 0.673404i 0.941611 + 0.336702i \(0.109311\pi\)
−0.941611 + 0.336702i \(0.890689\pi\)
\(488\) 50.8522 0.104205
\(489\) 11.3227 43.9363i 0.0231547 0.0898492i
\(490\) 273.399 + 54.3847i 0.557957 + 0.110989i
\(491\) 33.6438i 0.0685209i −0.999413 0.0342604i \(-0.989092\pi\)
0.999413 0.0342604i \(-0.0109076\pi\)
\(492\) 47.0750 182.669i 0.0956810 0.371279i
\(493\) 643.192i 1.30465i
\(494\) 829.237i 1.67862i
\(495\) −319.078 + 378.212i −0.644601 + 0.764064i
\(496\) −124.645 −0.251301
\(497\) −308.886 −0.621502
\(498\) 452.904 + 116.716i 0.909445 + 0.234370i
\(499\) 494.945 0.991875 0.495937 0.868358i \(-0.334825\pi\)
0.495937 + 0.868358i \(0.334825\pi\)
\(500\) −207.864 138.898i −0.415728 0.277795i
\(501\) −150.461 38.7749i −0.300322 0.0773950i
\(502\) 199.475i 0.397361i
\(503\) 510.268 1.01445 0.507224 0.861814i \(-0.330672\pi\)
0.507224 + 0.861814i \(0.330672\pi\)
\(504\) −38.0764 + 68.9692i −0.0755484 + 0.136844i
\(505\) 149.062 749.352i 0.295171 1.48387i
\(506\) 74.5797i 0.147391i
\(507\) 1126.05 + 290.191i 2.22101 + 0.572370i
\(508\) 405.738i 0.798696i
\(509\) 5.91018i 0.0116114i 0.999983 + 0.00580568i \(0.00184801\pi\)
−0.999983 + 0.00580568i \(0.998152\pi\)
\(510\) 286.002 + 137.653i 0.560787 + 0.269907i
\(511\) −121.899 −0.238550
\(512\) −22.6274 −0.0441942
\(513\) 487.939 + 460.666i 0.951148 + 0.897985i
\(514\) −191.971 −0.373484
\(515\) −150.148 + 754.811i −0.291549 + 1.46565i
\(516\) −56.1471 + 217.872i −0.108812 + 0.422233i
\(517\) 555.093i 1.07368i
\(518\) 212.493 0.410219
\(519\) 63.4798 + 16.3592i 0.122312 + 0.0315205i
\(520\) −65.0947 + 327.239i −0.125182 + 0.629307i
\(521\) 112.546i 0.216019i 0.994150 + 0.108010i \(0.0344477\pi\)
−0.994150 + 0.108010i \(0.965552\pi\)
\(522\) 264.437 478.985i 0.506585 0.917596i
\(523\) 65.5530i 0.125340i 0.998034 + 0.0626702i \(0.0199616\pi\)
−0.998034 + 0.0626702i \(0.980038\pi\)
\(524\) 465.402i 0.888173i
\(525\) −139.534 + 185.491i −0.265778 + 0.353316i
\(526\) −431.830 −0.820969
\(527\) 466.254 0.884732
\(528\) −32.9295 + 127.779i −0.0623665 + 0.242006i
\(529\) 23.0000 0.0434783
\(530\) 256.777 + 51.0783i 0.484485 + 0.0963741i
\(531\) −154.021 + 278.984i −0.290058 + 0.525393i
\(532\) 153.835i 0.289163i
\(533\) −741.744 −1.39164
\(534\) 154.618 599.977i 0.289547 1.12355i
\(535\) 28.8903 + 5.74687i 0.0540005 + 0.0107418i
\(536\) 192.889i 0.359867i
\(537\) −98.3700 + 381.713i −0.183184 + 0.710825i
\(538\) 432.408i 0.803732i
\(539\) 433.491i 0.804250i
\(540\) 156.392 + 220.094i 0.289615 + 0.407582i
\(541\) 848.977 1.56927 0.784637 0.619955i \(-0.212849\pi\)
0.784637 + 0.619955i \(0.212849\pi\)
\(542\) −500.322 −0.923104
\(543\) 855.791 + 220.543i 1.57604 + 0.406156i
\(544\) 84.6410 0.155590
\(545\) −458.147 91.1349i −0.840637 0.167220i
\(546\) 299.978 + 77.3063i 0.549410 + 0.141587i
\(547\) 341.832i 0.624921i 0.949931 + 0.312461i \(0.101153\pi\)
−0.949931 + 0.312461i \(0.898847\pi\)
\(548\) −57.8194 −0.105510
\(549\) −141.657 78.2056i −0.258027 0.142451i
\(550\) −148.783 + 359.177i −0.270514 + 0.653050i
\(551\) 1068.37i 1.93896i
\(552\) 39.4065 + 10.1553i 0.0713885 + 0.0183973i
\(553\) 95.2208i 0.172189i
\(554\) 34.9155i 0.0630244i
\(555\) 315.832 656.205i 0.569066 1.18235i
\(556\) 38.1881 0.0686837
\(557\) −361.120 −0.648331 −0.324165 0.946000i \(-0.605083\pi\)
−0.324165 + 0.946000i \(0.605083\pi\)
\(558\) 347.219 + 191.692i 0.622257 + 0.343534i
\(559\) 884.690 1.58263
\(560\) −12.0760 + 60.7074i −0.0215642 + 0.108406i
\(561\) 123.178 477.976i 0.219568 0.852007i
\(562\) 191.914i 0.341484i
\(563\) −607.902 −1.07976 −0.539878 0.841744i \(-0.681529\pi\)
−0.539878 + 0.841744i \(0.681529\pi\)
\(564\) −293.300 75.5854i −0.520036 0.134017i
\(565\) −774.942 154.152i −1.37158 0.272835i
\(566\) 48.9370i 0.0864612i
\(567\) 212.135 133.567i 0.374136 0.235568i
\(568\) 282.297i 0.497001i
\(569\) 427.157i 0.750714i −0.926880 0.375357i \(-0.877520\pi\)
0.926880 0.375357i \(-0.122480\pi\)
\(570\) 475.060 + 228.647i 0.833439 + 0.401134i
\(571\) −812.243 −1.42249 −0.711246 0.702944i \(-0.751869\pi\)
−0.711246 + 0.702944i \(0.751869\pi\)
\(572\) 518.859 0.907096
\(573\) 136.230 528.626i 0.237749 0.922558i
\(574\) −137.604 −0.239728
\(575\) 110.769 + 45.8839i 0.192641 + 0.0797981i
\(576\) 63.0322 + 34.7987i 0.109431 + 0.0604143i
\(577\) 780.939i 1.35345i −0.736237 0.676724i \(-0.763399\pi\)
0.736237 0.676724i \(-0.236601\pi\)
\(578\) 92.0962 0.159336
\(579\) −6.18497 + 24.0001i −0.0106822 + 0.0414509i
\(580\) 83.8664 421.607i 0.144597 0.726909i
\(581\) 341.170i 0.587211i
\(582\) 125.738 487.913i 0.216045 0.838338i
\(583\) 407.136i 0.698347i
\(584\) 111.405i 0.190763i
\(585\) 684.592 811.467i 1.17024 1.38712i
\(586\) −668.170 −1.14022
\(587\) −562.376 −0.958051 −0.479026 0.877801i \(-0.659010\pi\)
−0.479026 + 0.877801i \(0.659010\pi\)
\(588\) −229.048 59.0272i −0.389538 0.100386i
\(589\) 774.467 1.31488
\(590\) −48.8478 + 245.564i −0.0827928 + 0.416210i
\(591\) 179.792 + 46.3336i 0.304217 + 0.0783986i
\(592\) 194.201i 0.328043i
\(593\) −305.095 −0.514495 −0.257247 0.966346i \(-0.582816\pi\)
−0.257247 + 0.966346i \(0.582816\pi\)
\(594\) 288.242 305.306i 0.485255 0.513984i
\(595\) 45.1718 227.084i 0.0759190 0.381654i
\(596\) 4.18373i 0.00701968i
\(597\) 914.492 + 235.671i 1.53181 + 0.394758i
\(598\) 160.013i 0.267581i
\(599\) 615.611i 1.02773i −0.857871 0.513866i \(-0.828213\pi\)
0.857871 0.513866i \(-0.171787\pi\)
\(600\) 169.523 + 127.522i 0.282539 + 0.212537i
\(601\) 678.158 1.12838 0.564192 0.825644i \(-0.309188\pi\)
0.564192 + 0.825644i \(0.309188\pi\)
\(602\) 164.122 0.272628
\(603\) −296.643 + 537.322i −0.491946 + 0.891081i
\(604\) 591.218 0.978837
\(605\) −0.412616 0.0820778i −0.000682010 0.000135666i
\(606\) −161.786 + 627.793i −0.266974 + 1.03596i
\(607\) 537.292i 0.885161i −0.896729 0.442580i \(-0.854063\pi\)
0.896729 0.442580i \(-0.145937\pi\)
\(608\) 140.592 0.231237
\(609\) −386.484 99.5995i −0.634621 0.163546i
\(610\) −124.688 24.8029i −0.204406 0.0406606i
\(611\) 1190.97i 1.94922i
\(612\) −235.781 130.169i −0.385262 0.212695i
\(613\) 109.949i 0.179362i −0.995971 0.0896810i \(-0.971415\pi\)
0.995971 0.0896810i \(-0.0285848\pi\)
\(614\) 241.109i 0.392685i
\(615\) −204.522 + 424.937i −0.332556 + 0.690954i
\(616\) 96.2553 0.156259
\(617\) −789.606 −1.27975 −0.639875 0.768479i \(-0.721014\pi\)
−0.639875 + 0.768479i \(0.721014\pi\)
\(618\) 162.965 632.366i 0.263697 1.02325i
\(619\) −387.141 −0.625429 −0.312714 0.949847i \(-0.601238\pi\)
−0.312714 + 0.949847i \(0.601238\pi\)
\(620\) 305.626 + 60.7953i 0.492945 + 0.0980569i
\(621\) −94.1550 88.8923i −0.151618 0.143144i
\(622\) 25.9700i 0.0417524i
\(623\) −451.959 −0.725457
\(624\) 70.6515 274.155i 0.113224 0.439351i
\(625\) 441.928 + 441.956i 0.707084 + 0.707129i
\(626\) 426.873i 0.681906i
\(627\) 204.603 793.938i 0.326320 1.26625i
\(628\) 186.032i 0.296229i
\(629\) 726.437i 1.15491i
\(630\) 127.001 150.538i 0.201589 0.238949i
\(631\) −707.223 −1.12080 −0.560399 0.828223i \(-0.689352\pi\)
−0.560399 + 0.828223i \(0.689352\pi\)
\(632\) −87.0239 −0.137696
\(633\) −283.880 73.1576i −0.448467 0.115573i
\(634\) 251.949 0.397396
\(635\) 197.897 994.852i 0.311648 1.56670i
\(636\) −215.123 55.4386i −0.338244 0.0871676i
\(637\) 930.070i 1.46008i
\(638\) −668.485 −1.04778
\(639\) 434.143 786.381i 0.679411 1.23064i
\(640\) 55.4815 + 11.0364i 0.0866899 + 0.0172444i
\(641\) 628.409i 0.980357i 0.871622 + 0.490179i \(0.163068\pi\)
−0.871622 + 0.490179i \(0.836932\pi\)
\(642\) −24.2037 6.23745i −0.0377005 0.00971565i
\(643\) 949.121i 1.47608i 0.674755 + 0.738042i \(0.264249\pi\)
−0.674755 + 0.738042i \(0.735751\pi\)
\(644\) 29.6847i 0.0460942i
\(645\) 243.937 506.829i 0.378196 0.785781i
\(646\) −525.905 −0.814094
\(647\) 1047.41 1.61887 0.809433 0.587212i \(-0.199774\pi\)
0.809433 + 0.587212i \(0.199774\pi\)
\(648\) −122.069 193.874i −0.188378 0.299188i
\(649\) 389.357 0.599934
\(650\) 319.219 770.628i 0.491106 1.18558i
\(651\) 72.2003 280.165i 0.110907 0.430361i
\(652\) 30.2478i 0.0463924i
\(653\) −115.915 −0.177512 −0.0887558 0.996053i \(-0.528289\pi\)
−0.0887558 + 0.996053i \(0.528289\pi\)
\(654\) 383.827 + 98.9147i 0.586891 + 0.151246i
\(655\) −226.998 + 1141.15i −0.346562 + 1.74221i
\(656\) 125.758i 0.191705i
\(657\) 171.330 310.337i 0.260776 0.472355i
\(658\) 220.941i 0.335777i
\(659\) 735.582i 1.11621i 0.829771 + 0.558104i \(0.188471\pi\)
−0.829771 + 0.558104i \(0.811529\pi\)
\(660\) 143.066 297.248i 0.216766 0.450376i
\(661\) 366.829 0.554960 0.277480 0.960731i \(-0.410501\pi\)
0.277480 + 0.960731i \(0.410501\pi\)
\(662\) −390.970 −0.590589
\(663\) −264.282 + 1025.51i −0.398615 + 1.54678i
\(664\) −311.801 −0.469579
\(665\) 75.0322 377.196i 0.112830 0.567213i
\(666\) −298.662 + 540.978i −0.448441 + 0.812279i
\(667\) 206.157i 0.309082i
\(668\) 103.585 0.155067
\(669\) 216.706 840.902i 0.323925 1.25695i
\(670\) −94.0807 + 472.956i −0.140419 + 0.705904i
\(671\) 197.700i 0.294635i
\(672\) 13.1068 50.8595i 0.0195042 0.0756837i
\(673\) 888.959i 1.32089i −0.750874 0.660445i \(-0.770368\pi\)
0.750874 0.660445i \(-0.229632\pi\)
\(674\) 448.583i 0.665554i
\(675\) −276.117 615.942i −0.409062 0.912507i
\(676\) −775.230 −1.14679
\(677\) −185.045 −0.273331 −0.136666 0.990617i \(-0.543639\pi\)
−0.136666 + 0.990617i \(0.543639\pi\)
\(678\) 649.231 + 167.311i 0.957568 + 0.246772i
\(679\) −367.542 −0.541299
\(680\) −207.536 41.2833i −0.305200 0.0607107i
\(681\) 790.990 + 203.843i 1.16151 + 0.299329i
\(682\) 484.589i 0.710541i
\(683\) −107.048 −0.156733 −0.0783663 0.996925i \(-0.524970\pi\)
−0.0783663 + 0.996925i \(0.524970\pi\)
\(684\) −391.641 216.216i −0.572575 0.316106i
\(685\) 141.771 + 28.2011i 0.206965 + 0.0411695i
\(686\) 387.002i 0.564143i
\(687\) −282.031 72.6813i −0.410526 0.105795i
\(688\) 149.994i 0.218014i
\(689\) 873.525i 1.26782i
\(690\) −91.6699 44.1207i −0.132855 0.0639431i
\(691\) −781.127 −1.13043 −0.565215 0.824944i \(-0.691207\pi\)
−0.565215 + 0.824944i \(0.691207\pi\)
\(692\) −43.7026 −0.0631540
\(693\) −268.134 148.031i −0.386918 0.213609i
\(694\) −203.575 −0.293335
\(695\) −93.6357 18.6261i −0.134728 0.0268001i
\(696\) −91.0257 + 353.215i −0.130784 + 0.507492i
\(697\) 470.417i 0.674916i
\(698\) −555.510 −0.795860
\(699\) −467.611 120.506i −0.668971 0.172398i
\(700\) 59.2195 142.962i 0.0845993 0.204231i
\(701\) 72.2854i 0.103117i 0.998670 + 0.0515587i \(0.0164189\pi\)
−0.998670 + 0.0515587i \(0.983581\pi\)
\(702\) −618.433 + 655.046i −0.880959 + 0.933114i
\(703\) 1206.64i 1.71642i
\(704\) 87.9694i 0.124957i
\(705\) 682.294 + 328.388i 0.967793 + 0.465799i
\(706\) 579.596 0.820958
\(707\) 472.912 0.668900
\(708\) 53.0177 205.729i 0.0748837 0.290578i
\(709\) −1081.84 −1.52587 −0.762934 0.646476i \(-0.776242\pi\)
−0.762934 + 0.646476i \(0.776242\pi\)
\(710\) 137.689 692.180i 0.193928 0.974901i
\(711\) 242.418 + 133.834i 0.340954 + 0.188233i
\(712\) 413.053i 0.580131i
\(713\) −149.445 −0.209600
\(714\) −49.0279 + 190.247i −0.0686665 + 0.266452i
\(715\) −1272.22 253.071i −1.77933 0.353945i
\(716\) 262.790i 0.367025i
\(717\) 35.2159 136.651i 0.0491156 0.190588i
\(718\) 470.983i 0.655964i
\(719\) 905.857i 1.25988i 0.776642 + 0.629942i \(0.216921\pi\)
−0.776642 + 0.629942i \(0.783079\pi\)
\(720\) −137.579 116.069i −0.191083 0.161206i
\(721\) −476.358 −0.660691
\(722\) −363.018 −0.502795
\(723\) −563.216 145.144i −0.778998 0.200753i
\(724\) −589.168 −0.813767
\(725\) −411.274 + 992.859i −0.567275 + 1.36946i
\(726\) 0.345682 + 0.0890844i 0.000476145 + 0.000122706i
\(727\) 385.245i 0.529910i 0.964261 + 0.264955i \(0.0853571\pi\)
−0.964261 + 0.264955i \(0.914643\pi\)
\(728\) −206.519 −0.283680
\(729\) 41.8835 + 727.796i 0.0574533 + 0.998348i
\(730\) 54.3375 273.162i 0.0744349 0.374194i
\(731\) 561.073i 0.767542i
\(732\) 104.461 + 26.9202i 0.142706 + 0.0367763i
\(733\) 873.178i 1.19124i 0.803267 + 0.595619i \(0.203093\pi\)
−0.803267 + 0.595619i \(0.796907\pi\)
\(734\) 488.640i 0.665722i
\(735\) 532.827 + 256.450i 0.724934 + 0.348911i
\(736\) −27.1293 −0.0368605
\(737\) 749.901 1.01750
\(738\) 193.404 350.319i 0.262064 0.474687i
\(739\) 302.677 0.409576 0.204788 0.978806i \(-0.434349\pi\)
0.204788 + 0.978806i \(0.434349\pi\)
\(740\) −94.7208 + 476.174i −0.128001 + 0.643478i
\(741\) −438.983 + 1703.42i −0.592419 + 2.29881i
\(742\) 162.051i 0.218397i
\(743\) 154.859 0.208424 0.104212 0.994555i \(-0.466768\pi\)
0.104212 + 0.994555i \(0.466768\pi\)
\(744\) −256.047 65.9850i −0.344150 0.0886896i
\(745\) −2.04059 + 10.2583i −0.00273905 + 0.0137696i
\(746\) 850.122i 1.13957i
\(747\) 868.569 + 479.518i 1.16274 + 0.641925i
\(748\) 329.062i 0.439922i
\(749\) 18.2325i 0.0243425i
\(750\) −353.465 395.363i −0.471287 0.527151i
\(751\) −1121.82 −1.49377 −0.746885 0.664954i \(-0.768451\pi\)
−0.746885 + 0.664954i \(0.768451\pi\)
\(752\) 201.922 0.268513
\(753\) −105.599 + 409.763i −0.140237 + 0.544174i
\(754\) 1434.26 1.90220
\(755\) −1449.64 288.364i −1.92006 0.381939i
\(756\) −114.728 + 121.520i −0.151756 + 0.160741i
\(757\) 512.648i 0.677210i −0.940929 0.338605i \(-0.890045\pi\)
0.940929 0.338605i \(-0.109955\pi\)
\(758\) −518.431 −0.683946
\(759\) −39.4811 + 153.202i −0.0520173 + 0.201847i
\(760\) −344.726 68.5732i −0.453587 0.0902279i
\(761\) 412.254i 0.541727i 0.962618 + 0.270863i \(0.0873092\pi\)
−0.962618 + 0.270863i \(0.912691\pi\)
\(762\) −214.790 + 833.468i −0.281877 + 1.09379i
\(763\) 289.135i 0.378944i
\(764\) 363.931i 0.476350i
\(765\) 514.635 + 434.171i 0.672725 + 0.567543i
\(766\) −989.652 −1.29197
\(767\) −835.380 −1.08915
\(768\) −46.4813 11.9785i −0.0605226 0.0155971i
\(769\) −550.481 −0.715840 −0.357920 0.933752i \(-0.616514\pi\)
−0.357920 + 0.933752i \(0.616514\pi\)
\(770\) −236.014 46.9481i −0.306512 0.0609716i
\(771\) −394.347 101.626i −0.511475 0.131810i
\(772\) 16.5228i 0.0214026i
\(773\) −299.447 −0.387383 −0.193692 0.981062i \(-0.562046\pi\)
−0.193692 + 0.981062i \(0.562046\pi\)
\(774\) −230.675 + 417.831i −0.298030 + 0.539833i
\(775\) −719.729 298.135i −0.928683 0.384690i
\(776\) 335.903i 0.432864i
\(777\) 436.505 + 112.490i 0.561782 + 0.144775i
\(778\) 272.651i 0.350451i
\(779\) 781.381i 1.00306i
\(780\) −306.952 + 637.757i −0.393529 + 0.817637i
\(781\) −1097.49 −1.40524
\(782\) 101.481 0.129771
\(783\) 796.774 843