Properties

Label 690.3.g.a.461.6
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.6
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(-2.73248 + 1.23837i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-1.75132 - 3.86431i) q^{6} +4.14117 q^{7} -2.82843i q^{8} +(5.93289 - 6.76763i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(-2.73248 + 1.23837i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-1.75132 - 3.86431i) q^{6} +4.14117 q^{7} -2.82843i q^{8} +(5.93289 - 6.76763i) q^{9} +3.16228 q^{10} +18.2040i q^{11} +(5.46496 - 2.47674i) q^{12} -8.45273 q^{13} +5.85650i q^{14} +(2.76908 + 6.11001i) q^{15} +4.00000 q^{16} -14.2788i q^{17} +(9.57088 + 8.39037i) q^{18} -25.5703 q^{19} +4.47214i q^{20} +(-11.3157 + 5.12830i) q^{21} -25.7443 q^{22} +4.79583i q^{23} +(3.50263 + 7.72862i) q^{24} -5.00000 q^{25} -11.9540i q^{26} +(-7.83068 + 25.8395i) q^{27} -8.28235 q^{28} -30.0240i q^{29} +(-8.64086 + 3.91606i) q^{30} -20.5971 q^{31} +5.65685i q^{32} +(-22.5432 - 49.7420i) q^{33} +20.1932 q^{34} -9.25994i q^{35} +(-11.8658 + 13.5353i) q^{36} +58.2578 q^{37} -36.1618i q^{38} +(23.0969 - 10.4676i) q^{39} -6.32456 q^{40} -55.4616i q^{41} +(-7.25251 - 16.0028i) q^{42} -61.0293 q^{43} -36.4080i q^{44} +(-15.1329 - 13.2663i) q^{45} -6.78233 q^{46} -13.9735i q^{47} +(-10.9299 + 4.95347i) q^{48} -31.8507 q^{49} -7.07107i q^{50} +(17.6824 + 39.0165i) q^{51} +16.9055 q^{52} +25.4683i q^{53} +(-36.5426 - 11.0743i) q^{54} +40.7054 q^{55} -11.7130i q^{56} +(69.8702 - 31.6654i) q^{57} +42.4604 q^{58} -79.7148i q^{59} +(-5.53815 - 12.2200i) q^{60} +95.2262 q^{61} -29.1286i q^{62} +(24.5691 - 28.0259i) q^{63} -8.00000 q^{64} +18.9009i q^{65} +(70.3459 - 31.8810i) q^{66} +75.8720 q^{67} +28.5576i q^{68} +(-5.93901 - 13.1045i) q^{69} +13.0955 q^{70} -132.680i q^{71} +(-19.1418 - 16.7807i) q^{72} -73.4381 q^{73} +82.3890i q^{74} +(13.6624 - 6.19184i) q^{75} +51.1405 q^{76} +75.3859i q^{77} +(14.8034 + 32.6640i) q^{78} +23.5709 q^{79} -8.94427i q^{80} +(-10.6017 - 80.3032i) q^{81} +78.4345 q^{82} +134.121i q^{83} +(22.6313 - 10.2566i) q^{84} -31.9283 q^{85} -86.3084i q^{86} +(37.1808 + 82.0401i) q^{87} +51.4887 q^{88} -116.975i q^{89} +(18.7614 - 21.4011i) q^{90} -35.0042 q^{91} -9.59166i q^{92} +(56.2810 - 25.5067i) q^{93} +19.7615 q^{94} +57.1768i q^{95} +(-7.00527 - 15.4572i) q^{96} -82.3630 q^{97} -45.0437i q^{98} +(123.198 + 108.002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + O(q^{10}) \) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + 16q^{12} + 80q^{13} - 40q^{15} + 224q^{16} - 32q^{18} - 64q^{19} + 56q^{21} - 96q^{22} - 32q^{24} - 280q^{25} + 40q^{27} + 32q^{28} - 80q^{31} + 32q^{33} + 192q^{34} + 240q^{37} - 56q^{39} - 144q^{43} - 32q^{48} + 72q^{49} - 24q^{51} - 160q^{52} + 16q^{54} - 16q^{57} + 80q^{60} + 112q^{61} - 64q^{63} - 448q^{64} + 160q^{66} + 832q^{67} + 64q^{72} - 608q^{73} + 40q^{75} + 128q^{76} - 320q^{78} + 48q^{79} - 32q^{81} - 448q^{82} - 112q^{84} + 240q^{85} + 200q^{87} + 192q^{88} + 80q^{91} - 232q^{93} + 160q^{94} + 64q^{96} - 448q^{97} + 464q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −2.73248 + 1.23837i −0.910827 + 0.412789i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) −1.75132 3.86431i −0.291886 0.644052i
\(7\) 4.14117 0.591596 0.295798 0.955250i \(-0.404414\pi\)
0.295798 + 0.955250i \(0.404414\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 5.93289 6.76763i 0.659210 0.751959i
\(10\) 3.16228 0.316228
\(11\) 18.2040i 1.65491i 0.561533 + 0.827454i \(0.310212\pi\)
−0.561533 + 0.827454i \(0.689788\pi\)
\(12\) 5.46496 2.47674i 0.455413 0.206395i
\(13\) −8.45273 −0.650210 −0.325105 0.945678i \(-0.605400\pi\)
−0.325105 + 0.945678i \(0.605400\pi\)
\(14\) 5.85650i 0.418322i
\(15\) 2.76908 + 6.11001i 0.184605 + 0.407334i
\(16\) 4.00000 0.250000
\(17\) 14.2788i 0.839928i −0.907541 0.419964i \(-0.862043\pi\)
0.907541 0.419964i \(-0.137957\pi\)
\(18\) 9.57088 + 8.39037i 0.531715 + 0.466132i
\(19\) −25.5703 −1.34580 −0.672901 0.739732i \(-0.734952\pi\)
−0.672901 + 0.739732i \(0.734952\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −11.3157 + 5.12830i −0.538841 + 0.244205i
\(22\) −25.7443 −1.17020
\(23\) 4.79583i 0.208514i
\(24\) 3.50263 + 7.72862i 0.145943 + 0.322026i
\(25\) −5.00000 −0.200000
\(26\) 11.9540i 0.459768i
\(27\) −7.83068 + 25.8395i −0.290025 + 0.957019i
\(28\) −8.28235 −0.295798
\(29\) 30.0240i 1.03531i −0.855589 0.517656i \(-0.826805\pi\)
0.855589 0.517656i \(-0.173195\pi\)
\(30\) −8.64086 + 3.91606i −0.288029 + 0.130535i
\(31\) −20.5971 −0.664421 −0.332211 0.943205i \(-0.607794\pi\)
−0.332211 + 0.943205i \(0.607794\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −22.5432 49.7420i −0.683129 1.50733i
\(34\) 20.1932 0.593919
\(35\) 9.25994i 0.264570i
\(36\) −11.8658 + 13.5353i −0.329605 + 0.375980i
\(37\) 58.2578 1.57453 0.787267 0.616612i \(-0.211495\pi\)
0.787267 + 0.616612i \(0.211495\pi\)
\(38\) 36.1618i 0.951626i
\(39\) 23.0969 10.4676i 0.592229 0.268400i
\(40\) −6.32456 −0.158114
\(41\) 55.4616i 1.35272i −0.736571 0.676361i \(-0.763556\pi\)
0.736571 0.676361i \(-0.236444\pi\)
\(42\) −7.25251 16.0028i −0.172679 0.381018i
\(43\) −61.0293 −1.41929 −0.709643 0.704562i \(-0.751144\pi\)
−0.709643 + 0.704562i \(0.751144\pi\)
\(44\) 36.4080i 0.827454i
\(45\) −15.1329 13.2663i −0.336286 0.294808i
\(46\) −6.78233 −0.147442
\(47\) 13.9735i 0.297308i −0.988889 0.148654i \(-0.952506\pi\)
0.988889 0.148654i \(-0.0474941\pi\)
\(48\) −10.9299 + 4.95347i −0.227707 + 0.103197i
\(49\) −31.8507 −0.650014
\(50\) 7.07107i 0.141421i
\(51\) 17.6824 + 39.0165i 0.346714 + 0.765029i
\(52\) 16.9055 0.325105
\(53\) 25.4683i 0.480533i 0.970707 + 0.240267i \(0.0772348\pi\)
−0.970707 + 0.240267i \(0.922765\pi\)
\(54\) −36.5426 11.0743i −0.676715 0.205079i
\(55\) 40.7054 0.740098
\(56\) 11.7130i 0.209161i
\(57\) 69.8702 31.6654i 1.22579 0.555533i
\(58\) 42.4604 0.732076
\(59\) 79.7148i 1.35110i −0.737315 0.675549i \(-0.763907\pi\)
0.737315 0.675549i \(-0.236093\pi\)
\(60\) −5.53815 12.2200i −0.0923025 0.203667i
\(61\) 95.2262 1.56109 0.780543 0.625102i \(-0.214943\pi\)
0.780543 + 0.625102i \(0.214943\pi\)
\(62\) 29.1286i 0.469817i
\(63\) 24.5691 28.0259i 0.389986 0.444856i
\(64\) −8.00000 −0.125000
\(65\) 18.9009i 0.290783i
\(66\) 70.3459 31.8810i 1.06585 0.483045i
\(67\) 75.8720 1.13242 0.566209 0.824262i \(-0.308410\pi\)
0.566209 + 0.824262i \(0.308410\pi\)
\(68\) 28.5576i 0.419964i
\(69\) −5.93901 13.1045i −0.0860725 0.189920i
\(70\) 13.0955 0.187079
\(71\) 132.680i 1.86873i −0.356317 0.934365i \(-0.615968\pi\)
0.356317 0.934365i \(-0.384032\pi\)
\(72\) −19.1418 16.7807i −0.265858 0.233066i
\(73\) −73.4381 −1.00600 −0.503000 0.864286i \(-0.667771\pi\)
−0.503000 + 0.864286i \(0.667771\pi\)
\(74\) 82.3890i 1.11336i
\(75\) 13.6624 6.19184i 0.182165 0.0825579i
\(76\) 51.1405 0.672901
\(77\) 75.3859i 0.979038i
\(78\) 14.8034 + 32.6640i 0.189787 + 0.418769i
\(79\) 23.5709 0.298366 0.149183 0.988810i \(-0.452336\pi\)
0.149183 + 0.988810i \(0.452336\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −10.6017 80.3032i −0.130885 0.991398i
\(82\) 78.4345 0.956518
\(83\) 134.121i 1.61591i 0.589243 + 0.807956i \(0.299426\pi\)
−0.589243 + 0.807956i \(0.700574\pi\)
\(84\) 22.6313 10.2566i 0.269421 0.122102i
\(85\) −31.9283 −0.375627
\(86\) 86.3084i 1.00359i
\(87\) 37.1808 + 82.0401i 0.427366 + 0.942989i
\(88\) 51.4887 0.585099
\(89\) 116.975i 1.31432i −0.753751 0.657161i \(-0.771757\pi\)
0.753751 0.657161i \(-0.228243\pi\)
\(90\) 18.7614 21.4011i 0.208460 0.237790i
\(91\) −35.0042 −0.384662
\(92\) 9.59166i 0.104257i
\(93\) 56.2810 25.5067i 0.605172 0.274266i
\(94\) 19.7615 0.210229
\(95\) 57.1768i 0.601861i
\(96\) −7.00527 15.4572i −0.0729715 0.161013i
\(97\) −82.3630 −0.849104 −0.424552 0.905404i \(-0.639568\pi\)
−0.424552 + 0.905404i \(0.639568\pi\)
\(98\) 45.0437i 0.459629i
\(99\) 123.198 + 108.002i 1.24442 + 1.09093i
\(100\) 10.0000 0.100000
\(101\) 133.725i 1.32401i −0.749501 0.662003i \(-0.769706\pi\)
0.749501 0.662003i \(-0.230294\pi\)
\(102\) −55.1776 + 25.0067i −0.540957 + 0.245163i
\(103\) −157.226 −1.52647 −0.763233 0.646124i \(-0.776389\pi\)
−0.763233 + 0.646124i \(0.776389\pi\)
\(104\) 23.9079i 0.229884i
\(105\) 11.4672 + 25.3026i 0.109212 + 0.240977i
\(106\) −36.0175 −0.339788
\(107\) 68.1719i 0.637120i −0.947903 0.318560i \(-0.896801\pi\)
0.947903 0.318560i \(-0.103199\pi\)
\(108\) 15.6614 51.6790i 0.145013 0.478510i
\(109\) −3.60776 −0.0330987 −0.0165494 0.999863i \(-0.505268\pi\)
−0.0165494 + 0.999863i \(0.505268\pi\)
\(110\) 57.5661i 0.523328i
\(111\) −159.188 + 72.1446i −1.43413 + 0.649951i
\(112\) 16.5647 0.147899
\(113\) 82.8721i 0.733382i −0.930343 0.366691i \(-0.880491\pi\)
0.930343 0.366691i \(-0.119509\pi\)
\(114\) 44.7816 + 98.8114i 0.392821 + 0.866767i
\(115\) 10.7238 0.0932505
\(116\) 60.0481i 0.517656i
\(117\) −50.1491 + 57.2050i −0.428625 + 0.488932i
\(118\) 112.734 0.955371
\(119\) 59.1309i 0.496898i
\(120\) 17.2817 7.83213i 0.144014 0.0652677i
\(121\) −210.385 −1.73872
\(122\) 134.670i 1.10385i
\(123\) 68.6818 + 151.548i 0.558389 + 1.23209i
\(124\) 41.1941 0.332211
\(125\) 11.1803i 0.0894427i
\(126\) 39.6347 + 34.7460i 0.314561 + 0.275762i
\(127\) −12.8307 −0.101029 −0.0505145 0.998723i \(-0.516086\pi\)
−0.0505145 + 0.998723i \(0.516086\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 166.761 75.5767i 1.29272 0.585866i
\(130\) −26.7299 −0.205615
\(131\) 260.678i 1.98991i −0.100330 0.994954i \(-0.531990\pi\)
0.100330 0.994954i \(-0.468010\pi\)
\(132\) 45.0865 + 99.4841i 0.341564 + 0.753667i
\(133\) −105.891 −0.796172
\(134\) 107.299i 0.800740i
\(135\) 57.7789 + 17.5099i 0.427992 + 0.129703i
\(136\) −40.3865 −0.296960
\(137\) 122.563i 0.894619i 0.894379 + 0.447309i \(0.147618\pi\)
−0.894379 + 0.447309i \(0.852382\pi\)
\(138\) 18.5326 8.39902i 0.134294 0.0608625i
\(139\) −79.5231 −0.572109 −0.286054 0.958213i \(-0.592344\pi\)
−0.286054 + 0.958213i \(0.592344\pi\)
\(140\) 18.5199i 0.132285i
\(141\) 17.3043 + 38.1822i 0.122726 + 0.270796i
\(142\) 187.638 1.32139
\(143\) 153.874i 1.07604i
\(144\) 23.7316 27.0705i 0.164802 0.187990i
\(145\) −67.1358 −0.463006
\(146\) 103.857i 0.711350i
\(147\) 87.0314 39.4429i 0.592050 0.268319i
\(148\) −116.516 −0.787267
\(149\) 14.2215i 0.0954460i −0.998861 0.0477230i \(-0.984804\pi\)
0.998861 0.0477230i \(-0.0151965\pi\)
\(150\) 8.75659 + 19.3215i 0.0583772 + 0.128810i
\(151\) 199.067 1.31832 0.659161 0.752002i \(-0.270912\pi\)
0.659161 + 0.752002i \(0.270912\pi\)
\(152\) 72.3236i 0.475813i
\(153\) −96.6335 84.7144i −0.631592 0.553689i
\(154\) −106.612 −0.692284
\(155\) 46.0564i 0.297138i
\(156\) −46.1938 + 20.9352i −0.296114 + 0.134200i
\(157\) −150.983 −0.961676 −0.480838 0.876809i \(-0.659668\pi\)
−0.480838 + 0.876809i \(0.659668\pi\)
\(158\) 33.3343i 0.210977i
\(159\) −31.5391 69.5915i −0.198359 0.437682i
\(160\) 12.6491 0.0790569
\(161\) 19.8604i 0.123356i
\(162\) 113.566 14.9930i 0.701024 0.0925495i
\(163\) 157.063 0.963577 0.481789 0.876287i \(-0.339987\pi\)
0.481789 + 0.876287i \(0.339987\pi\)
\(164\) 110.923i 0.676361i
\(165\) −111.227 + 50.4082i −0.674101 + 0.305504i
\(166\) −189.675 −1.14262
\(167\) 140.625i 0.842065i −0.907046 0.421032i \(-0.861668\pi\)
0.907046 0.421032i \(-0.138332\pi\)
\(168\) 14.5050 + 32.0055i 0.0863394 + 0.190509i
\(169\) −97.5513 −0.577226
\(170\) 45.1535i 0.265609i
\(171\) −151.705 + 173.050i −0.887167 + 1.01199i
\(172\) 122.059 0.709643
\(173\) 129.805i 0.750317i 0.926961 + 0.375158i \(0.122412\pi\)
−0.926961 + 0.375158i \(0.877588\pi\)
\(174\) −116.022 + 52.5816i −0.666794 + 0.302193i
\(175\) −20.7059 −0.118319
\(176\) 72.8160i 0.413727i
\(177\) 98.7163 + 217.819i 0.557719 + 1.23062i
\(178\) 165.427 0.929365
\(179\) 277.661i 1.55118i 0.631239 + 0.775588i \(0.282547\pi\)
−0.631239 + 0.775588i \(0.717453\pi\)
\(180\) 30.2658 + 26.5327i 0.168143 + 0.147404i
\(181\) −248.306 −1.37185 −0.685927 0.727670i \(-0.740603\pi\)
−0.685927 + 0.727670i \(0.740603\pi\)
\(182\) 49.5035i 0.271997i
\(183\) −260.204 + 117.925i −1.42188 + 0.644400i
\(184\) 13.5647 0.0737210
\(185\) 130.268i 0.704153i
\(186\) 36.0720 + 79.5934i 0.193935 + 0.427922i
\(187\) 259.931 1.39000
\(188\) 27.9470i 0.148654i
\(189\) −32.4282 + 107.006i −0.171578 + 0.566169i
\(190\) −80.8602 −0.425580
\(191\) 114.375i 0.598820i 0.954125 + 0.299410i \(0.0967898\pi\)
−0.954125 + 0.299410i \(0.903210\pi\)
\(192\) 21.8598 9.90695i 0.113853 0.0515987i
\(193\) −224.783 −1.16468 −0.582341 0.812945i \(-0.697863\pi\)
−0.582341 + 0.812945i \(0.697863\pi\)
\(194\) 116.479i 0.600407i
\(195\) −23.4063 51.6463i −0.120032 0.264853i
\(196\) 63.7014 0.325007
\(197\) 237.189i 1.20401i −0.798493 0.602004i \(-0.794369\pi\)
0.798493 0.602004i \(-0.205631\pi\)
\(198\) −152.738 + 174.228i −0.771406 + 0.879940i
\(199\) −200.271 −1.00639 −0.503194 0.864174i \(-0.667842\pi\)
−0.503194 + 0.864174i \(0.667842\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) −207.319 + 93.9574i −1.03144 + 0.467450i
\(202\) 189.115 0.936214
\(203\) 124.335i 0.612486i
\(204\) −35.3648 78.0330i −0.173357 0.382515i
\(205\) −124.016 −0.604955
\(206\) 222.351i 1.07937i
\(207\) 32.4564 + 28.4531i 0.156794 + 0.137455i
\(208\) −33.8109 −0.162553
\(209\) 465.481i 2.22718i
\(210\) −35.7833 + 16.2171i −0.170397 + 0.0772243i
\(211\) −199.810 −0.946967 −0.473483 0.880803i \(-0.657004\pi\)
−0.473483 + 0.880803i \(0.657004\pi\)
\(212\) 50.9365i 0.240267i
\(213\) 164.307 + 362.545i 0.771392 + 1.70209i
\(214\) 96.4096 0.450512
\(215\) 136.466i 0.634724i
\(216\) 73.0852 + 22.1485i 0.338357 + 0.102539i
\(217\) −85.2960 −0.393069
\(218\) 5.10215i 0.0234043i
\(219\) 200.668 90.9434i 0.916292 0.415266i
\(220\) −81.4107 −0.370049
\(221\) 120.695i 0.546130i
\(222\) −102.028 225.126i −0.459585 1.01408i
\(223\) 251.698 1.12869 0.564345 0.825539i \(-0.309129\pi\)
0.564345 + 0.825539i \(0.309129\pi\)
\(224\) 23.4260i 0.104580i
\(225\) −29.6644 + 33.8382i −0.131842 + 0.150392i
\(226\) 117.199 0.518579
\(227\) 209.743i 0.923977i 0.886886 + 0.461988i \(0.152864\pi\)
−0.886886 + 0.461988i \(0.847136\pi\)
\(228\) −139.740 + 63.3308i −0.612896 + 0.277767i
\(229\) 310.423 1.35556 0.677781 0.735264i \(-0.262942\pi\)
0.677781 + 0.735264i \(0.262942\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) −93.3555 205.990i −0.404136 0.891733i
\(232\) −84.9208 −0.366038
\(233\) 13.5244i 0.0580446i 0.999579 + 0.0290223i \(0.00923938\pi\)
−0.999579 + 0.0290223i \(0.990761\pi\)
\(234\) −80.9001 70.9216i −0.345727 0.303084i
\(235\) −31.2457 −0.132960
\(236\) 159.430i 0.675549i
\(237\) −64.4070 + 29.1895i −0.271760 + 0.123162i
\(238\) 83.6237 0.351360
\(239\) 162.359i 0.679328i 0.940547 + 0.339664i \(0.110313\pi\)
−0.940547 + 0.339664i \(0.889687\pi\)
\(240\) 11.0763 + 24.4400i 0.0461513 + 0.101833i
\(241\) 114.412 0.474740 0.237370 0.971419i \(-0.423715\pi\)
0.237370 + 0.971419i \(0.423715\pi\)
\(242\) 297.530i 1.22946i
\(243\) 128.414 + 206.298i 0.528452 + 0.848963i
\(244\) −190.452 −0.780543
\(245\) 71.2203i 0.290695i
\(246\) −214.321 + 97.1308i −0.871222 + 0.394841i
\(247\) 216.139 0.875055
\(248\) 58.2573i 0.234908i
\(249\) −166.091 366.482i −0.667031 1.47181i
\(250\) −15.8114 −0.0632456
\(251\) 77.7456i 0.309743i −0.987935 0.154872i \(-0.950504\pi\)
0.987935 0.154872i \(-0.0494964\pi\)
\(252\) −49.1382 + 56.0519i −0.194993 + 0.222428i
\(253\) −87.3033 −0.345072
\(254\) 18.1453i 0.0714383i
\(255\) 87.2435 39.5390i 0.342131 0.155055i
\(256\) 16.0000 0.0625000
\(257\) 252.344i 0.981883i 0.871193 + 0.490941i \(0.163347\pi\)
−0.871193 + 0.490941i \(0.836653\pi\)
\(258\) 106.882 + 235.836i 0.414270 + 0.914093i
\(259\) 241.256 0.931489
\(260\) 37.8018i 0.145391i
\(261\) −203.192 178.129i −0.778512 0.682488i
\(262\) 368.654 1.40708
\(263\) 192.257i 0.731016i −0.930808 0.365508i \(-0.880895\pi\)
0.930808 0.365508i \(-0.119105\pi\)
\(264\) −140.692 + 63.7619i −0.532923 + 0.241522i
\(265\) 56.9487 0.214901
\(266\) 149.752i 0.562978i
\(267\) 144.858 + 319.631i 0.542538 + 1.19712i
\(268\) −151.744 −0.566209
\(269\) 334.333i 1.24287i 0.783464 + 0.621437i \(0.213451\pi\)
−0.783464 + 0.621437i \(0.786549\pi\)
\(270\) −24.7628 + 81.7117i −0.0917140 + 0.302636i
\(271\) −415.940 −1.53483 −0.767416 0.641149i \(-0.778458\pi\)
−0.767416 + 0.641149i \(0.778458\pi\)
\(272\) 57.1151i 0.209982i
\(273\) 95.6484 43.3481i 0.350360 0.158784i
\(274\) −173.330 −0.632591
\(275\) 91.0200i 0.330982i
\(276\) 11.8780 + 26.2090i 0.0430363 + 0.0949602i
\(277\) 95.1282 0.343423 0.171712 0.985147i \(-0.445070\pi\)
0.171712 + 0.985147i \(0.445070\pi\)
\(278\) 112.463i 0.404542i
\(279\) −122.200 + 139.393i −0.437993 + 0.499617i
\(280\) −26.1911 −0.0935396
\(281\) 62.8658i 0.223722i −0.993724 0.111861i \(-0.964319\pi\)
0.993724 0.111861i \(-0.0356811\pi\)
\(282\) −53.9979 + 24.4720i −0.191482 + 0.0867801i
\(283\) 469.458 1.65886 0.829431 0.558609i \(-0.188665\pi\)
0.829431 + 0.558609i \(0.188665\pi\)
\(284\) 265.360i 0.934365i
\(285\) −70.8060 156.235i −0.248442 0.548191i
\(286\) 217.610 0.760874
\(287\) 229.676i 0.800265i
\(288\) 38.2835 + 33.5615i 0.132929 + 0.116533i
\(289\) 85.1164 0.294520
\(290\) 94.9444i 0.327394i
\(291\) 225.055 101.996i 0.773386 0.350501i
\(292\) 146.876 0.503000
\(293\) 288.659i 0.985184i 0.870260 + 0.492592i \(0.163951\pi\)
−0.870260 + 0.492592i \(0.836049\pi\)
\(294\) 55.7807 + 123.081i 0.189730 + 0.418643i
\(295\) −178.248 −0.604229
\(296\) 164.778i 0.556682i
\(297\) −470.382 142.550i −1.58378 0.479965i
\(298\) 20.1122 0.0674905
\(299\) 40.5379i 0.135578i
\(300\) −27.3248 + 12.3837i −0.0910827 + 0.0412789i
\(301\) −252.733 −0.839644
\(302\) 281.523i 0.932194i
\(303\) 165.600 + 365.400i 0.546536 + 1.20594i
\(304\) −102.281 −0.336451
\(305\) 212.932i 0.698139i
\(306\) 119.804 136.660i 0.391517 0.446603i
\(307\) −453.095 −1.47588 −0.737940 0.674867i \(-0.764201\pi\)
−0.737940 + 0.674867i \(0.764201\pi\)
\(308\) 150.772i 0.489519i
\(309\) 429.617 194.704i 1.39035 0.630109i
\(310\) −65.1336 −0.210108
\(311\) 445.022i 1.43094i 0.698644 + 0.715470i \(0.253787\pi\)
−0.698644 + 0.715470i \(0.746213\pi\)
\(312\) −29.6068 65.3280i −0.0948937 0.209385i
\(313\) −548.133 −1.75122 −0.875612 0.483016i \(-0.839541\pi\)
−0.875612 + 0.483016i \(0.839541\pi\)
\(314\) 213.522i 0.680008i
\(315\) −62.6679 54.9382i −0.198946 0.174407i
\(316\) −47.1418 −0.149183
\(317\) 1.18880i 0.00375016i 0.999998 + 0.00187508i \(0.000596858\pi\)
−0.999998 + 0.00187508i \(0.999403\pi\)
\(318\) 98.4172 44.6030i 0.309488 0.140261i
\(319\) 546.558 1.71335
\(320\) 17.8885i 0.0559017i
\(321\) 84.4219 + 186.278i 0.262996 + 0.580306i
\(322\) −28.0868 −0.0872261
\(323\) 365.112i 1.13038i
\(324\) 21.2033 + 160.606i 0.0654424 + 0.495699i
\(325\) 42.2637 0.130042
\(326\) 222.121i 0.681352i
\(327\) 9.85814 4.46774i 0.0301472 0.0136628i
\(328\) −156.869 −0.478259
\(329\) 57.8666i 0.175886i
\(330\) −71.2880 157.298i −0.216024 0.476661i
\(331\) −84.6998 −0.255891 −0.127945 0.991781i \(-0.540838\pi\)
−0.127945 + 0.991781i \(0.540838\pi\)
\(332\) 268.241i 0.807956i
\(333\) 345.637 394.267i 1.03795 1.18399i
\(334\) 198.874 0.595430
\(335\) 169.655i 0.506432i
\(336\) −45.2627 + 20.5132i −0.134710 + 0.0610511i
\(337\) 301.194 0.893752 0.446876 0.894596i \(-0.352537\pi\)
0.446876 + 0.894596i \(0.352537\pi\)
\(338\) 137.958i 0.408161i
\(339\) 102.626 + 226.446i 0.302732 + 0.667983i
\(340\) 63.8567 0.187814
\(341\) 374.949i 1.09956i
\(342\) −244.730 214.544i −0.715584 0.627321i
\(343\) −334.817 −0.976142
\(344\) 172.617i 0.501793i
\(345\) −29.3026 + 13.2800i −0.0849350 + 0.0384928i
\(346\) −183.572 −0.530554
\(347\) 74.3987i 0.214405i 0.994237 + 0.107203i \(0.0341894\pi\)
−0.994237 + 0.107203i \(0.965811\pi\)
\(348\) −74.3616 164.080i −0.213683 0.471495i
\(349\) 122.217 0.350193 0.175096 0.984551i \(-0.443976\pi\)
0.175096 + 0.984551i \(0.443976\pi\)
\(350\) 29.2825i 0.0836643i
\(351\) 66.1906 218.415i 0.188577 0.622264i
\(352\) −102.977 −0.292549
\(353\) 257.047i 0.728179i −0.931364 0.364089i \(-0.881380\pi\)
0.931364 0.364089i \(-0.118620\pi\)
\(354\) −308.043 + 139.606i −0.870177 + 0.394367i
\(355\) −296.681 −0.835722
\(356\) 233.949i 0.657161i
\(357\) 73.2258 + 161.574i 0.205114 + 0.452588i
\(358\) −392.671 −1.09685
\(359\) 411.848i 1.14721i 0.819133 + 0.573604i \(0.194455\pi\)
−0.819133 + 0.573604i \(0.805545\pi\)
\(360\) −37.5229 + 42.8023i −0.104230 + 0.118895i
\(361\) 292.838 0.811185
\(362\) 351.157i 0.970047i
\(363\) 574.874 260.535i 1.58368 0.717726i
\(364\) 70.0085 0.192331
\(365\) 164.213i 0.449897i
\(366\) −166.771 367.984i −0.455659 1.00542i
\(367\) 390.609 1.06433 0.532165 0.846640i \(-0.321378\pi\)
0.532165 + 0.846640i \(0.321378\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) −375.343 329.047i −1.01719 0.891727i
\(370\) 184.227 0.497912
\(371\) 105.468i 0.284281i
\(372\) −112.562 + 51.0135i −0.302586 + 0.137133i
\(373\) −358.049 −0.959916 −0.479958 0.877292i \(-0.659348\pi\)
−0.479958 + 0.877292i \(0.659348\pi\)
\(374\) 367.598i 0.982882i
\(375\) −13.8454 30.5500i −0.0369210 0.0814668i
\(376\) −39.5230 −0.105114
\(377\) 253.785i 0.673170i
\(378\) −151.329 45.8604i −0.400342 0.121324i
\(379\) −292.500 −0.771769 −0.385884 0.922547i \(-0.626104\pi\)
−0.385884 + 0.922547i \(0.626104\pi\)
\(380\) 114.354i 0.300931i
\(381\) 35.0596 15.8891i 0.0920199 0.0417037i
\(382\) −161.750 −0.423430
\(383\) 67.9007i 0.177286i 0.996063 + 0.0886432i \(0.0282531\pi\)
−0.996063 + 0.0886432i \(0.971747\pi\)
\(384\) 14.0105 + 30.9145i 0.0364858 + 0.0805064i
\(385\) 168.568 0.437839
\(386\) 317.892i 0.823554i
\(387\) −362.080 + 413.024i −0.935607 + 1.06724i
\(388\) 164.726 0.424552
\(389\) 332.519i 0.854806i 0.904061 + 0.427403i \(0.140571\pi\)
−0.904061 + 0.427403i \(0.859429\pi\)
\(390\) 73.0389 33.1015i 0.187279 0.0848755i
\(391\) 68.4786 0.175137
\(392\) 90.0874i 0.229815i
\(393\) 322.815 + 712.297i 0.821413 + 1.81246i
\(394\) 335.437 0.851362
\(395\) 52.7061i 0.133433i
\(396\) −246.396 216.005i −0.622212 0.545466i
\(397\) 185.010 0.466020 0.233010 0.972474i \(-0.425142\pi\)
0.233010 + 0.972474i \(0.425142\pi\)
\(398\) 283.226i 0.711624i
\(399\) 289.345 131.132i 0.725174 0.328651i
\(400\) −20.0000 −0.0500000
\(401\) 28.7486i 0.0716924i −0.999357 0.0358462i \(-0.988587\pi\)
0.999357 0.0358462i \(-0.0114126\pi\)
\(402\) −132.876 293.193i −0.330537 0.729335i
\(403\) 174.101 0.432014
\(404\) 267.449i 0.662003i
\(405\) −179.563 + 23.7060i −0.443366 + 0.0585334i
\(406\) 175.836 0.433093
\(407\) 1060.52i 2.60571i
\(408\) 110.355 50.0134i 0.270479 0.122582i
\(409\) 307.733 0.752402 0.376201 0.926538i \(-0.377230\pi\)
0.376201 + 0.926538i \(0.377230\pi\)
\(410\) 175.385i 0.427768i
\(411\) −151.778 334.900i −0.369289 0.814842i
\(412\) 314.452 0.763233
\(413\) 330.113i 0.799304i
\(414\) −40.2388 + 45.9003i −0.0971952 + 0.110870i
\(415\) 299.903 0.722657
\(416\) 47.8159i 0.114942i
\(417\) 217.295 98.4789i 0.521092 0.236161i
\(418\) 658.289 1.57485
\(419\) 346.936i 0.828010i −0.910275 0.414005i \(-0.864130\pi\)
0.910275 0.414005i \(-0.135870\pi\)
\(420\) −22.9344 50.6052i −0.0546058 0.120489i
\(421\) 216.953 0.515329 0.257664 0.966234i \(-0.417047\pi\)
0.257664 + 0.966234i \(0.417047\pi\)
\(422\) 282.574i 0.669607i
\(423\) −94.5674 82.9031i −0.223563 0.195988i
\(424\) 72.0351 0.169894
\(425\) 71.3939i 0.167986i
\(426\) −512.716 + 232.364i −1.20356 + 0.545457i
\(427\) 394.348 0.923532
\(428\) 136.344i 0.318560i
\(429\) 190.552 + 420.456i 0.444177 + 0.980085i
\(430\) −192.991 −0.448817
\(431\) 595.252i 1.38109i −0.723287 0.690547i \(-0.757370\pi\)
0.723287 0.690547i \(-0.242630\pi\)
\(432\) −31.3227 + 103.358i −0.0725063 + 0.239255i
\(433\) −162.757 −0.375882 −0.187941 0.982180i \(-0.560181\pi\)
−0.187941 + 0.982180i \(0.560181\pi\)
\(434\) 120.627i 0.277942i
\(435\) 183.447 83.1388i 0.421718 0.191124i
\(436\) 7.21553 0.0165494
\(437\) 122.631i 0.280619i
\(438\) 128.613 + 283.787i 0.293638 + 0.647916i
\(439\) −137.285 −0.312721 −0.156361 0.987700i \(-0.549976\pi\)
−0.156361 + 0.987700i \(0.549976\pi\)
\(440\) 115.132i 0.261664i
\(441\) −188.967 + 215.554i −0.428496 + 0.488784i
\(442\) −170.688 −0.386172
\(443\) 309.185i 0.697935i −0.937135 0.348967i \(-0.886532\pi\)
0.937135 0.348967i \(-0.113468\pi\)
\(444\) 318.376 144.289i 0.717064 0.324976i
\(445\) −261.563 −0.587782
\(446\) 355.954i 0.798104i
\(447\) 17.6114 + 38.8598i 0.0393991 + 0.0869348i
\(448\) −33.1294 −0.0739495
\(449\) 61.1567i 0.136206i 0.997678 + 0.0681032i \(0.0216947\pi\)
−0.997678 + 0.0681032i \(0.978305\pi\)
\(450\) −47.8544 41.9519i −0.106343 0.0932264i
\(451\) 1009.62 2.23863
\(452\) 165.744i 0.366691i
\(453\) −543.945 + 246.518i −1.20076 + 0.544189i
\(454\) −296.621 −0.653350
\(455\) 78.2718i 0.172026i
\(456\) −89.5632 197.623i −0.196411 0.433383i
\(457\) 325.253 0.711714 0.355857 0.934540i \(-0.384189\pi\)
0.355857 + 0.934540i \(0.384189\pi\)
\(458\) 439.005i 0.958526i
\(459\) 368.957 + 111.813i 0.803827 + 0.243600i
\(460\) −21.4476 −0.0466252
\(461\) 178.646i 0.387518i −0.981049 0.193759i \(-0.937932\pi\)
0.981049 0.193759i \(-0.0620679\pi\)
\(462\) 291.314 132.025i 0.630551 0.285768i
\(463\) 753.662 1.62778 0.813890 0.581019i \(-0.197346\pi\)
0.813890 + 0.581019i \(0.197346\pi\)
\(464\) 120.096i 0.258828i
\(465\) −57.0348 125.848i −0.122655 0.270641i
\(466\) −19.1264 −0.0410437
\(467\) 341.612i 0.731504i 0.930712 + 0.365752i \(0.119188\pi\)
−0.930712 + 0.365752i \(0.880812\pi\)
\(468\) 100.298 114.410i 0.214313 0.244466i
\(469\) 314.199 0.669934
\(470\) 44.1880i 0.0940171i
\(471\) 412.558 186.973i 0.875920 0.396970i
\(472\) −225.467 −0.477685
\(473\) 1110.98i 2.34879i
\(474\) −41.2801 91.0853i −0.0870889 0.192163i
\(475\) 127.851 0.269161
\(476\) 118.262i 0.248449i
\(477\) 172.360 + 151.100i 0.361341 + 0.316772i
\(478\) −229.611 −0.480358
\(479\) 129.264i 0.269862i −0.990855 0.134931i \(-0.956919\pi\)
0.990855 0.134931i \(-0.0430813\pi\)
\(480\) −34.5634 + 15.6643i −0.0720072 + 0.0326339i
\(481\) −492.438 −1.02378
\(482\) 161.803i 0.335692i
\(483\) −24.5944 54.2680i −0.0509202 0.112356i
\(484\) 420.771 0.869362
\(485\) 184.169i 0.379731i
\(486\) −291.750 + 181.604i −0.600308 + 0.373672i
\(487\) −356.900 −0.732855 −0.366428 0.930447i \(-0.619419\pi\)
−0.366428 + 0.930447i \(0.619419\pi\)
\(488\) 269.340i 0.551927i
\(489\) −429.172 + 194.502i −0.877652 + 0.397755i
\(490\) −100.721 −0.205552
\(491\) 576.525i 1.17419i −0.809520 0.587093i \(-0.800272\pi\)
0.809520 0.587093i \(-0.199728\pi\)
\(492\) −137.364 303.095i −0.279194 0.616047i
\(493\) −428.707 −0.869588
\(494\) 305.666i 0.618757i
\(495\) 241.500 275.479i 0.487880 0.556523i
\(496\) −82.3882 −0.166105
\(497\) 549.450i 1.10553i
\(498\) 518.284 234.888i 1.04073 0.471662i
\(499\) −622.821 −1.24814 −0.624069 0.781369i \(-0.714522\pi\)
−0.624069 + 0.781369i \(0.714522\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 174.145 + 384.255i 0.347595 + 0.766975i
\(502\) 109.949 0.219022
\(503\) 407.531i 0.810200i −0.914272 0.405100i \(-0.867237\pi\)
0.914272 0.405100i \(-0.132763\pi\)
\(504\) −79.2693 69.4920i −0.157280 0.137881i
\(505\) −299.018 −0.592114
\(506\) 123.466i 0.244003i
\(507\) 266.557 120.804i 0.525753 0.238273i
\(508\) 25.6614 0.0505145
\(509\) 274.372i 0.539041i −0.962995 0.269520i \(-0.913135\pi\)
0.962995 0.269520i \(-0.0868651\pi\)
\(510\) 55.9166 + 123.381i 0.109640 + 0.241923i
\(511\) −304.120 −0.595146
\(512\) 22.6274i 0.0441942i
\(513\) 200.232 660.723i 0.390317 1.28796i
\(514\) −356.868 −0.694296
\(515\) 351.568i 0.682656i
\(516\) −333.522 + 151.153i −0.646361 + 0.292933i
\(517\) 254.373 0.492018
\(518\) 341.187i 0.658662i
\(519\) −160.746 354.689i −0.309723 0.683409i
\(520\) 53.4598 0.102807
\(521\) 227.719i 0.437080i −0.975828 0.218540i \(-0.929871\pi\)
0.975828 0.218540i \(-0.0701295\pi\)
\(522\) 251.913 287.356i 0.482592 0.550491i
\(523\) 178.583 0.341460 0.170730 0.985318i \(-0.445387\pi\)
0.170730 + 0.985318i \(0.445387\pi\)
\(524\) 521.356i 0.994954i
\(525\) 56.5783 25.6415i 0.107768 0.0488409i
\(526\) 271.893 0.516907
\(527\) 294.101i 0.558066i
\(528\) −90.1730 198.968i −0.170782 0.376834i
\(529\) −23.0000 −0.0434783
\(530\) 80.5377i 0.151958i
\(531\) −539.480 472.939i −1.01597 0.890657i
\(532\) 211.782 0.398086
\(533\) 468.802i 0.879553i
\(534\) −452.026 + 204.860i −0.846491 + 0.383632i
\(535\) −152.437 −0.284929
\(536\) 214.598i 0.400370i
\(537\) −343.846 758.702i −0.640309 1.41285i
\(538\) −472.818 −0.878845
\(539\) 579.810i 1.07571i
\(540\) −115.558 35.0199i −0.213996 0.0648516i
\(541\) −406.572 −0.751519 −0.375760 0.926717i \(-0.622618\pi\)
−0.375760 + 0.926717i \(0.622618\pi\)
\(542\) 588.228i 1.08529i
\(543\) 678.490 307.494i 1.24952 0.566287i
\(544\) 80.7730 0.148480
\(545\) 8.06720i 0.0148022i
\(546\) 61.3035 + 135.267i 0.112277 + 0.247742i
\(547\) −762.540 −1.39404 −0.697020 0.717051i \(-0.745491\pi\)
−0.697020 + 0.717051i \(0.745491\pi\)
\(548\) 245.126i 0.447309i
\(549\) 564.967 644.456i 1.02908 1.17387i
\(550\) 128.722 0.234039
\(551\) 767.722i 1.39333i
\(552\) −37.0652 + 16.7980i −0.0671470 + 0.0304312i
\(553\) 97.6112 0.176512
\(554\) 134.532i 0.242837i
\(555\) 161.320 + 355.956i 0.290667 + 0.641362i
\(556\) 159.046 0.286054
\(557\) 868.898i 1.55996i −0.625804 0.779980i \(-0.715229\pi\)
0.625804 0.779980i \(-0.284771\pi\)
\(558\) −197.132 172.817i −0.353283 0.309708i
\(559\) 515.864 0.922834
\(560\) 37.0398i 0.0661425i
\(561\) −710.256 + 321.890i −1.26605 + 0.573779i
\(562\) 88.9056 0.158195
\(563\) 703.584i 1.24971i −0.780743 0.624853i \(-0.785159\pi\)
0.780743 0.624853i \(-0.214841\pi\)
\(564\) −34.6086 76.3645i −0.0613628 0.135398i
\(565\) −185.308 −0.327978
\(566\) 663.914i 1.17299i
\(567\) −43.9033 332.549i −0.0774309 0.586507i
\(568\) −375.275 −0.660696
\(569\) 594.365i 1.04458i 0.852768 + 0.522289i \(0.174922\pi\)
−0.852768 + 0.522289i \(0.825078\pi\)
\(570\) 220.949 100.135i 0.387630 0.175675i
\(571\) 526.041 0.921263 0.460631 0.887592i \(-0.347623\pi\)
0.460631 + 0.887592i \(0.347623\pi\)
\(572\) 307.747i 0.538019i
\(573\) −141.638 312.526i −0.247186 0.545421i
\(574\) 324.811 0.565872
\(575\) 23.9792i 0.0417029i
\(576\) −47.4631 + 54.1410i −0.0824012 + 0.0939949i
\(577\) −146.152 −0.253296 −0.126648 0.991948i \(-0.540422\pi\)
−0.126648 + 0.991948i \(0.540422\pi\)
\(578\) 120.373i 0.208257i
\(579\) 614.216 278.365i 1.06082 0.480768i
\(580\) 134.272 0.231503
\(581\) 555.417i 0.955967i
\(582\) 144.244 + 318.276i 0.247842 + 0.546866i
\(583\) −463.624 −0.795238
\(584\) 207.714i 0.355675i
\(585\) 127.914 + 112.137i 0.218657 + 0.191687i
\(586\) −408.226 −0.696631
\(587\) 478.018i 0.814340i −0.913352 0.407170i \(-0.866516\pi\)
0.913352 0.407170i \(-0.133484\pi\)
\(588\) −174.063 + 78.8858i −0.296025 + 0.134159i
\(589\) 526.672 0.894180
\(590\) 252.080i 0.427255i
\(591\) 293.728 + 648.115i 0.497002 + 1.09664i
\(592\) 233.031 0.393634
\(593\) 793.839i 1.33868i 0.742955 + 0.669341i \(0.233424\pi\)
−0.742955 + 0.669341i \(0.766576\pi\)
\(594\) 201.596 665.221i 0.339387 1.11990i
\(595\) −132.221 −0.222220
\(596\) 28.4429i 0.0477230i
\(597\) 547.237 248.009i 0.916645 0.415426i
\(598\) 57.3292 0.0958683
\(599\) 329.048i 0.549329i 0.961540 + 0.274664i \(0.0885667\pi\)
−0.961540 + 0.274664i \(0.911433\pi\)
\(600\) −17.5132 38.6431i −0.0291886 0.0644052i
\(601\) −98.7656 −0.164335 −0.0821677 0.996619i \(-0.526184\pi\)
−0.0821677 + 0.996619i \(0.526184\pi\)
\(602\) 357.418i 0.593718i
\(603\) 450.140 513.473i 0.746501 0.851531i
\(604\) −398.133 −0.659161
\(605\) 470.436i 0.777581i
\(606\) −516.754 + 234.194i −0.852729 + 0.386459i
\(607\) 131.584 0.216777 0.108389 0.994109i \(-0.465431\pi\)
0.108389 + 0.994109i \(0.465431\pi\)
\(608\) 144.647i 0.237907i
\(609\) 153.972 + 339.742i 0.252828 + 0.557869i
\(610\) 301.132 0.493659
\(611\) 118.114i 0.193313i
\(612\) 193.267 + 169.429i 0.315796 + 0.276845i
\(613\) 537.185 0.876322 0.438161 0.898897i \(-0.355630\pi\)
0.438161 + 0.898897i \(0.355630\pi\)
\(614\) 640.773i 1.04360i
\(615\) 338.871 153.577i 0.551009 0.249719i
\(616\) 213.224 0.346142
\(617\) 997.204i 1.61621i 0.589036 + 0.808107i \(0.299508\pi\)
−0.589036 + 0.808107i \(0.700492\pi\)
\(618\) 275.352 + 607.570i 0.445554 + 0.983123i
\(619\) −146.256 −0.236277 −0.118139 0.992997i \(-0.537693\pi\)
−0.118139 + 0.992997i \(0.537693\pi\)
\(620\) 92.1128i 0.148569i
\(621\) −123.922 37.5546i −0.199552 0.0604744i
\(622\) −629.356 −1.01183
\(623\) 484.412i 0.777547i
\(624\) 92.3877 41.8704i 0.148057 0.0671000i
\(625\) 25.0000 0.0400000
\(626\) 775.177i 1.23830i
\(627\) 576.437 + 1271.92i 0.919357 + 2.02858i
\(628\) 301.966 0.480838
\(629\) 831.850i 1.32250i
\(630\) 77.6944 88.6258i 0.123324 0.140676i
\(631\) −520.059 −0.824182 −0.412091 0.911143i \(-0.635201\pi\)
−0.412091 + 0.911143i \(0.635201\pi\)
\(632\) 66.6686i 0.105488i
\(633\) 545.977 247.438i 0.862522 0.390898i
\(634\) −1.68122 −0.00265177
\(635\) 28.6903i 0.0451815i
\(636\) 63.0781 + 139.183i 0.0991795 + 0.218841i
\(637\) 269.225 0.422646
\(638\) 772.949i 1.21152i
\(639\) −897.928 787.175i −1.40521 1.23189i
\(640\) −25.2982 −0.0395285
\(641\) 343.613i 0.536058i −0.963411 0.268029i \(-0.913628\pi\)
0.963411 0.268029i \(-0.0863723\pi\)
\(642\) −263.437 + 119.391i −0.410338 + 0.185967i
\(643\) −972.075 −1.51178 −0.755890 0.654698i \(-0.772796\pi\)
−0.755890 + 0.654698i \(0.772796\pi\)
\(644\) 39.7207i 0.0616782i
\(645\) −168.995 372.889i −0.262007 0.578123i
\(646\) −516.347 −0.799298
\(647\) 356.832i 0.551518i −0.961227 0.275759i \(-0.911071\pi\)
0.961227 0.275759i \(-0.0889292\pi\)
\(648\) −227.132 + 29.9860i −0.350512 + 0.0462747i
\(649\) 1451.13 2.23594
\(650\) 59.7699i 0.0919536i
\(651\) 233.069 105.628i 0.358018 0.162255i
\(652\) −314.126 −0.481789
\(653\) 374.245i 0.573116i 0.958063 + 0.286558i \(0.0925111\pi\)
−0.958063 + 0.286558i \(0.907489\pi\)
\(654\) 6.31834 + 13.9415i 0.00966107 + 0.0213173i
\(655\) −582.894 −0.889914
\(656\) 221.846i 0.338180i
\(657\) −435.700 + 497.002i −0.663166 + 0.756471i
\(658\) 81.8357 0.124370
\(659\) 30.2813i 0.0459504i −0.999736 0.0229752i \(-0.992686\pi\)
0.999736 0.0229752i \(-0.00731387\pi\)
\(660\) 222.453 100.816i 0.337050 0.152752i
\(661\) −1230.40 −1.86143 −0.930714 0.365749i \(-0.880813\pi\)
−0.930714 + 0.365749i \(0.880813\pi\)
\(662\) 119.784i 0.180942i
\(663\) −149.465 329.796i −0.225437 0.497430i
\(664\) 379.350 0.571311
\(665\) 236.779i 0.356059i
\(666\) 557.578 + 488.805i 0.837204 + 0.733941i
\(667\) 143.990 0.215877
\(668\) 281.250i 0.421032i
\(669\) −687.759 + 311.695i −1.02804 + 0.465911i
\(670\) 239.928 0.358102
\(671\) 1733.50i 2.58345i
\(672\) −29.0100 64.0111i −0.0431697 0.0952546i
\(673\) 746.022 1.10850 0.554251 0.832350i \(-0.313005\pi\)
0.554251 + 0.832350i \(0.313005\pi\)
\(674\) 425.953i 0.631978i
\(675\) 39.1534 129.198i 0.0580050 0.191404i
\(676\) 195.103 0.288613
\(677\) 491.931i 0.726634i 0.931666 + 0.363317i \(0.118356\pi\)
−0.931666 + 0.363317i \(0.881644\pi\)
\(678\) −320.243 + 145.135i −0.472336 + 0.214064i
\(679\) −341.080 −0.502326
\(680\) 90.3070i 0.132804i
\(681\) −259.739 573.118i −0.381408 0.841583i
\(682\) 530.258 0.777504
\(683\) 399.771i 0.585316i −0.956217 0.292658i \(-0.905460\pi\)
0.956217 0.292658i \(-0.0945397\pi\)
\(684\) 303.411 346.100i 0.443583 0.505994i
\(685\) 274.059 0.400086
\(686\) 473.502i 0.690237i
\(687\) −848.226 + 384.419i −1.23468 + 0.559561i
\(688\) −244.117 −0.354821
\(689\) 215.276i 0.312448i
\(690\) −18.7808 41.4401i −0.0272185 0.0600581i
\(691\) 205.782 0.297804 0.148902 0.988852i \(-0.452426\pi\)
0.148902 + 0.988852i \(0.452426\pi\)
\(692\) 259.610i 0.375158i
\(693\) 510.184 + 447.256i 0.736196 + 0.645391i
\(694\) −105.216 −0.151608
\(695\) 177.819i 0.255855i
\(696\) 232.044 105.163i 0.333397 0.151097i
\(697\) −791.924 −1.13619
\(698\) 172.841i 0.247624i
\(699\) −16.7482 36.9551i −0.0239602 0.0528686i
\(700\) 41.4117 0.0591596
\(701\) 95.2339i 0.135854i −0.997690 0.0679272i \(-0.978361\pi\)
0.997690 0.0679272i \(-0.0216385\pi\)
\(702\) 308.885 + 93.6077i 0.440007 + 0.133344i
\(703\) −1489.67 −2.11901
\(704\) 145.632i 0.206864i
\(705\) 85.3781 38.6936i 0.121104 0.0548846i
\(706\) 363.519 0.514900
\(707\) 553.777i 0.783277i
\(708\) −197.433 435.638i −0.278859 0.615308i
\(709\) −1225.99 −1.72918 −0.864589 0.502479i \(-0.832421\pi\)
−0.864589 + 0.502479i \(0.832421\pi\)
\(710\) 419.571i 0.590944i
\(711\) 139.844 159.519i 0.196686 0.224359i
\(712\) −330.854 −0.464683
\(713\) 98.7800i 0.138541i
\(714\) −228.500 + 103.557i −0.320028 + 0.145038i
\(715\) −344.072 −0.481219
\(716\) 555.321i 0.775588i
\(717\) −201.061 443.644i −0.280420 0.618750i
\(718\) −582.441 −0.811199
\(719\) 1015.78i 1.41277i 0.707826 + 0.706387i \(0.249676\pi\)
−0.707826 + 0.706387i \(0.750324\pi\)
\(720\) −60.5315 53.0654i −0.0840716 0.0737019i
\(721\) −651.100 −0.903051
\(722\) 414.135i 0.573595i
\(723\) −312.629 + 141.685i −0.432406 + 0.195968i
\(724\) 496.611 0.685927
\(725\) 150.120i 0.207062i
\(726\) 368.452 + 812.995i 0.507509 + 1.11983i
\(727\) −794.186 −1.09242 −0.546208 0.837650i \(-0.683929\pi\)
−0.546208 + 0.837650i \(0.683929\pi\)
\(728\) 99.0069i 0.135999i
\(729\) −606.361 404.682i −0.831771 0.555119i
\(730\) −232.232 −0.318125
\(731\) 871.424i 1.19210i
\(732\) 520.407 235.850i 0.710939 0.322200i
\(733\) 502.321 0.685295 0.342648 0.939464i \(-0.388676\pi\)
0.342648 + 0.939464i \(0.388676\pi\)
\(734\) 552.405i 0.752595i
\(735\) −88.1970 194.608i −0.119996 0.264773i
\(736\) −27.1293 −0.0368605
\(737\) 1381.17i 1.87405i
\(738\) 465.343 530.816i 0.630546 0.719263i
\(739\) 505.526 0.684067 0.342034 0.939688i \(-0.388884\pi\)
0.342034 + 0.939688i \(0.388884\pi\)
\(740\) 260.537i 0.352077i
\(741\) −590.594 + 267.659i −0.797023 + 0.361213i
\(742\) −149.155 −0.201017
\(743\) 345.072i 0.464430i 0.972664 + 0.232215i \(0.0745973\pi\)
−0.972664 + 0.232215i \(0.925403\pi\)
\(744\) −72.1439 159.187i −0.0969677 0.213961i
\(745\) −31.8001 −0.0426848
\(746\) 506.357i 0.678763i
\(747\) 907.679 + 795.723i 1.21510 + 1.06522i
\(748\) −519.862 −0.695002
\(749\) 282.311i 0.376918i
\(750\) 43.2043 19.5803i 0.0576057 0.0261071i
\(751\) 691.345 0.920566 0.460283 0.887772i \(-0.347748\pi\)
0.460283 + 0.887772i \(0.347748\pi\)
\(752\) 55.8939i 0.0743270i
\(753\) 96.2776 + 212.438i 0.127859 + 0.282122i
\(754\) −358.907 −0.476003
\(755\) 445.126i 0.589571i
\(756\) 64.8564 214.012i 0.0857889 0.283084i
\(757\) −127.590 −0.168546 −0.0842732 0.996443i \(-0.526857\pi\)
−0.0842732 + 0.996443i \(0.526857\pi\)
\(758\) 413.658i 0.545723i
\(759\) 238.554 108.114i 0.314301 0.142442i
\(760\) 161.720 0.212790
\(761\) 183.936i 0.241703i 0.992671 + 0.120852i \(0.0385625\pi\)
−0.992671 + 0.120852i \(0.961438\pi\)
\(762\) 22.4706 + 49.5817i 0.0294890 + 0.0650679i
\(763\) −14.9404 −0.0195811
\(764\) 228.749i 0.299410i
\(765\) −189.427 + 216.079i −0.247617 + 0.282456i
\(766\) −96.0261 −0.125360
\(767\) 673.808i 0.878498i
\(768\) −43.7197 + 19.8139i −0.0569267 + 0.0257993i
\(769\) −1436.65 −1.86821 −0.934104 0.357002i \(-0.883799\pi\)
−0.934104 + 0.357002i \(0.883799\pi\)
\(770\) 238.391i 0.309599i
\(771\) −312.495 689.524i −0.405311 0.894325i
\(772\) 449.567 0.582341
\(773\) 666.904i 0.862748i 0.902173 + 0.431374i \(0.141971\pi\)
−0.902173 + 0.431374i \(0.858029\pi\)
\(774\) −584.103 512.058i −0.754656 0.661574i
\(775\) 102.985 0.132884
\(776\) 232.958i 0.300203i
\(777\) −659.226 + 298.763i −0.848425 + 0.384509i
\(778\) −470.254 −0.604439
\(779\) 1418.17i 1.82050i
\(780\) 46.8125 + 103.293i 0.0600161 + 0.132426i
\(781\) 2415.30 3.09258
\(782\) 96.8434i 0.123841i
\(783\) 775.807 + 235.109i 0.990813 + 0.300266i
\(784\) −127.403 −0.162504
\(785\) 337.609i 0.430075i
\(786\) −1007.34