Properties

Label 336.4.q.j.289.2
Level $336$
Weight $4$
Character 336.289
Analytic conductor $19.825$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
Defining polynomial: \(x^{4} - x^{3} + 337 x^{2} + 336 x + 112896\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.2
Root \(-8.91856 + 15.4474i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.4.q.j.193.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 2.59808i) q^{3} +(7.91856 - 13.7153i) q^{5} +(-18.3371 - 2.59808i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 + 2.59808i) q^{3} +(7.91856 - 13.7153i) q^{5} +(-18.3371 - 2.59808i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(25.9186 + 44.8923i) q^{11} +38.8371 q^{13} +47.5114 q^{15} +(-13.6742 - 23.6845i) q^{17} +(38.2557 - 66.2608i) q^{19} +(-20.7557 - 51.5384i) q^{21} +(73.6742 - 127.608i) q^{23} +(-62.9072 - 108.958i) q^{25} -27.0000 q^{27} +240.208 q^{29} +(-148.337 - 256.927i) q^{31} +(-77.7557 + 134.677i) q^{33} +(-180.837 + 230.927i) q^{35} +(80.7670 - 139.893i) q^{37} +(58.2557 + 100.902i) q^{39} -102.977 q^{41} +328.557 q^{43} +(71.2670 + 123.438i) q^{45} +(33.9773 - 58.8504i) q^{47} +(329.500 + 95.2825i) q^{49} +(41.0227 - 71.0534i) q^{51} +(33.2443 + 57.5808i) q^{53} +820.951 q^{55} +229.534 q^{57} +(-230.964 - 400.041i) q^{59} +(-92.6742 + 160.516i) q^{61} +(102.767 - 131.232i) q^{63} +(307.534 - 532.665i) q^{65} +(272.604 + 472.164i) q^{67} +442.045 q^{69} +130.742 q^{71} +(-90.6496 - 157.010i) q^{73} +(188.722 - 326.875i) q^{75} +(-358.638 - 890.533i) q^{77} +(-204.848 + 354.808i) q^{79} +(-40.5000 - 70.1481i) q^{81} -347.928 q^{83} -433.121 q^{85} +(360.312 + 624.080i) q^{87} +(-578.580 + 1002.13i) q^{89} +(-712.161 - 100.902i) q^{91} +(445.011 - 770.782i) q^{93} +(-605.860 - 1049.38i) q^{95} +1618.30 q^{97} -466.534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{3} - 5q^{5} - 18q^{9} + O(q^{10}) \) \( 4q + 6q^{3} - 5q^{5} - 18q^{9} + 67q^{11} + 82q^{13} - 30q^{15} + 92q^{17} + 43q^{19} + 27q^{21} + 148q^{23} - 435q^{25} - 108q^{27} + 154q^{29} - 520q^{31} - 201q^{33} - 650q^{35} - 7q^{37} + 123q^{39} - 852q^{41} + 214q^{43} - 45q^{45} + 576q^{47} + 1318q^{49} - 276q^{51} + 243q^{53} + 1010q^{55} + 258q^{57} - 7q^{59} - 224q^{61} + 81q^{63} + 570q^{65} + 687q^{67} + 888q^{69} - 944q^{71} + 921q^{73} + 1305q^{75} - 371q^{77} - 526q^{79} - 162q^{81} + 442q^{83} - 5840q^{85} + 231q^{87} - 774q^{89} - 1345q^{91} + 1560q^{93} - 1910q^{95} + 3906q^{97} - 1206q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 7.91856 13.7153i 0.708258 1.22674i −0.257245 0.966346i \(-0.582815\pi\)
0.965503 0.260392i \(-0.0838518\pi\)
\(6\) 0 0
\(7\) −18.3371 2.59808i −0.990111 0.140283i
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 25.9186 + 44.8923i 0.710431 + 1.23050i 0.964696 + 0.263368i \(0.0848333\pi\)
−0.254265 + 0.967135i \(0.581833\pi\)
\(12\) 0 0
\(13\) 38.8371 0.828575 0.414288 0.910146i \(-0.364031\pi\)
0.414288 + 0.910146i \(0.364031\pi\)
\(14\) 0 0
\(15\) 47.5114 0.817825
\(16\) 0 0
\(17\) −13.6742 23.6845i −0.195088 0.337902i 0.751842 0.659344i \(-0.229166\pi\)
−0.946929 + 0.321442i \(0.895832\pi\)
\(18\) 0 0
\(19\) 38.2557 66.2608i 0.461919 0.800067i −0.537138 0.843494i \(-0.680495\pi\)
0.999057 + 0.0434278i \(0.0138279\pi\)
\(20\) 0 0
\(21\) −20.7557 51.5384i −0.215679 0.535552i
\(22\) 0 0
\(23\) 73.6742 127.608i 0.667919 1.15687i −0.310566 0.950552i \(-0.600519\pi\)
0.978485 0.206318i \(-0.0661482\pi\)
\(24\) 0 0
\(25\) −62.9072 108.958i −0.503258 0.871668i
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 240.208 1.53812 0.769061 0.639175i \(-0.220724\pi\)
0.769061 + 0.639175i \(0.220724\pi\)
\(30\) 0 0
\(31\) −148.337 256.927i −0.859424 1.48857i −0.872480 0.488651i \(-0.837489\pi\)
0.0130559 0.999915i \(-0.495844\pi\)
\(32\) 0 0
\(33\) −77.7557 + 134.677i −0.410167 + 0.710431i
\(34\) 0 0
\(35\) −180.837 + 230.927i −0.873344 + 1.11525i
\(36\) 0 0
\(37\) 80.7670 139.893i 0.358865 0.621573i −0.628906 0.777481i \(-0.716497\pi\)
0.987772 + 0.155908i \(0.0498304\pi\)
\(38\) 0 0
\(39\) 58.2557 + 100.902i 0.239189 + 0.414288i
\(40\) 0 0
\(41\) −102.977 −0.392252 −0.196126 0.980579i \(-0.562836\pi\)
−0.196126 + 0.980579i \(0.562836\pi\)
\(42\) 0 0
\(43\) 328.557 1.16522 0.582610 0.812752i \(-0.302032\pi\)
0.582610 + 0.812752i \(0.302032\pi\)
\(44\) 0 0
\(45\) 71.2670 + 123.438i 0.236086 + 0.408913i
\(46\) 0 0
\(47\) 33.9773 58.8504i 0.105449 0.182643i −0.808473 0.588534i \(-0.799705\pi\)
0.913921 + 0.405891i \(0.133039\pi\)
\(48\) 0 0
\(49\) 329.500 + 95.2825i 0.960641 + 0.277791i
\(50\) 0 0
\(51\) 41.0227 71.0534i 0.112634 0.195088i
\(52\) 0 0
\(53\) 33.2443 + 57.5808i 0.0861596 + 0.149233i 0.905885 0.423524i \(-0.139207\pi\)
−0.819725 + 0.572757i \(0.805874\pi\)
\(54\) 0 0
\(55\) 820.951 2.01267
\(56\) 0 0
\(57\) 229.534 0.533378
\(58\) 0 0
\(59\) −230.964 400.041i −0.509643 0.882728i −0.999938 0.0111711i \(-0.996444\pi\)
0.490294 0.871557i \(-0.336889\pi\)
\(60\) 0 0
\(61\) −92.6742 + 160.516i −0.194520 + 0.336919i −0.946743 0.321990i \(-0.895648\pi\)
0.752223 + 0.658909i \(0.228982\pi\)
\(62\) 0 0
\(63\) 102.767 131.232i 0.205515 0.262440i
\(64\) 0 0
\(65\) 307.534 532.665i 0.586845 1.01644i
\(66\) 0 0
\(67\) 272.604 + 472.164i 0.497073 + 0.860956i 0.999994 0.00337637i \(-0.00107474\pi\)
−0.502921 + 0.864332i \(0.667741\pi\)
\(68\) 0 0
\(69\) 442.045 0.771247
\(70\) 0 0
\(71\) 130.742 0.218539 0.109270 0.994012i \(-0.465149\pi\)
0.109270 + 0.994012i \(0.465149\pi\)
\(72\) 0 0
\(73\) −90.6496 157.010i −0.145339 0.251734i 0.784160 0.620558i \(-0.213094\pi\)
−0.929499 + 0.368824i \(0.879761\pi\)
\(74\) 0 0
\(75\) 188.722 326.875i 0.290556 0.503258i
\(76\) 0 0
\(77\) −358.638 890.533i −0.530787 1.31800i
\(78\) 0 0
\(79\) −204.848 + 354.808i −0.291737 + 0.505304i −0.974221 0.225597i \(-0.927567\pi\)
0.682483 + 0.730901i \(0.260900\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −347.928 −0.460121 −0.230061 0.973176i \(-0.573892\pi\)
−0.230061 + 0.973176i \(0.573892\pi\)
\(84\) 0 0
\(85\) −433.121 −0.552689
\(86\) 0 0
\(87\) 360.312 + 624.080i 0.444018 + 0.769061i
\(88\) 0 0
\(89\) −578.580 + 1002.13i −0.689093 + 1.19354i 0.283038 + 0.959109i \(0.408658\pi\)
−0.972132 + 0.234436i \(0.924676\pi\)
\(90\) 0 0
\(91\) −712.161 100.902i −0.820382 0.116235i
\(92\) 0 0
\(93\) 445.011 770.782i 0.496188 0.859424i
\(94\) 0 0
\(95\) −605.860 1049.38i −0.654315 1.13331i
\(96\) 0 0
\(97\) 1618.30 1.69395 0.846976 0.531631i \(-0.178421\pi\)
0.846976 + 0.531631i \(0.178421\pi\)
\(98\) 0 0
\(99\) −466.534 −0.473621
\(100\) 0 0
\(101\) −359.371 622.449i −0.354047 0.613228i 0.632907 0.774228i \(-0.281861\pi\)
−0.986954 + 0.161000i \(0.948528\pi\)
\(102\) 0 0
\(103\) −805.790 + 1395.67i −0.770843 + 1.33514i 0.166259 + 0.986082i \(0.446831\pi\)
−0.937102 + 0.349057i \(0.886502\pi\)
\(104\) 0 0
\(105\) −871.222 123.438i −0.809738 0.114727i
\(106\) 0 0
\(107\) 467.335 809.448i 0.422234 0.731330i −0.573924 0.818909i \(-0.694580\pi\)
0.996158 + 0.0875784i \(0.0279128\pi\)
\(108\) 0 0
\(109\) 598.509 + 1036.65i 0.525934 + 0.910944i 0.999544 + 0.0302095i \(0.00961746\pi\)
−0.473610 + 0.880735i \(0.657049\pi\)
\(110\) 0 0
\(111\) 484.602 0.414382
\(112\) 0 0
\(113\) −2384.64 −1.98521 −0.992604 0.121400i \(-0.961262\pi\)
−0.992604 + 0.121400i \(0.961262\pi\)
\(114\) 0 0
\(115\) −1166.79 2020.94i −0.946118 1.63872i
\(116\) 0 0
\(117\) −174.767 + 302.705i −0.138096 + 0.239189i
\(118\) 0 0
\(119\) 189.212 + 469.832i 0.145757 + 0.361928i
\(120\) 0 0
\(121\) −678.044 + 1174.41i −0.509424 + 0.882349i
\(122\) 0 0
\(123\) −154.466 267.543i −0.113234 0.196126i
\(124\) 0 0
\(125\) −12.8977 −0.00922883
\(126\) 0 0
\(127\) 2673.92 1.86829 0.934143 0.356898i \(-0.116166\pi\)
0.934143 + 0.356898i \(0.116166\pi\)
\(128\) 0 0
\(129\) 492.835 + 853.616i 0.336370 + 0.582610i
\(130\) 0 0
\(131\) −19.4299 + 33.6536i −0.0129588 + 0.0224453i −0.872432 0.488735i \(-0.837458\pi\)
0.859473 + 0.511181i \(0.170792\pi\)
\(132\) 0 0
\(133\) −873.650 + 1115.64i −0.569587 + 0.727356i
\(134\) 0 0
\(135\) −213.801 + 370.314i −0.136304 + 0.236086i
\(136\) 0 0
\(137\) 384.072 + 665.232i 0.239514 + 0.414851i 0.960575 0.278021i \(-0.0896784\pi\)
−0.721061 + 0.692872i \(0.756345\pi\)
\(138\) 0 0
\(139\) −1052.55 −0.642274 −0.321137 0.947033i \(-0.604065\pi\)
−0.321137 + 0.947033i \(0.604065\pi\)
\(140\) 0 0
\(141\) 203.864 0.121762
\(142\) 0 0
\(143\) 1006.60 + 1743.49i 0.588646 + 1.01956i
\(144\) 0 0
\(145\) 1902.10 3294.54i 1.08939 1.88687i
\(146\) 0 0
\(147\) 246.699 + 998.990i 0.138418 + 0.560512i
\(148\) 0 0
\(149\) −180.489 + 312.615i −0.0992363 + 0.171882i −0.911369 0.411591i \(-0.864973\pi\)
0.812132 + 0.583473i \(0.198307\pi\)
\(150\) 0 0
\(151\) 774.195 + 1340.95i 0.417239 + 0.722679i 0.995661 0.0930587i \(-0.0296644\pi\)
−0.578422 + 0.815738i \(0.696331\pi\)
\(152\) 0 0
\(153\) 246.136 0.130058
\(154\) 0 0
\(155\) −4698.47 −2.43477
\(156\) 0 0
\(157\) 483.534 + 837.506i 0.245798 + 0.425734i 0.962356 0.271794i \(-0.0876168\pi\)
−0.716558 + 0.697528i \(0.754283\pi\)
\(158\) 0 0
\(159\) −99.7330 + 172.743i −0.0497443 + 0.0861596i
\(160\) 0 0
\(161\) −1682.51 + 2148.54i −0.823604 + 1.05173i
\(162\) 0 0
\(163\) −663.250 + 1148.78i −0.318710 + 0.552022i −0.980219 0.197915i \(-0.936583\pi\)
0.661509 + 0.749937i \(0.269916\pi\)
\(164\) 0 0
\(165\) 1231.43 + 2132.89i 0.581008 + 1.00634i
\(166\) 0 0
\(167\) −1416.70 −0.656451 −0.328225 0.944599i \(-0.606451\pi\)
−0.328225 + 0.944599i \(0.606451\pi\)
\(168\) 0 0
\(169\) −688.678 −0.313463
\(170\) 0 0
\(171\) 344.301 + 596.347i 0.153973 + 0.266689i
\(172\) 0 0
\(173\) 518.299 897.721i 0.227778 0.394523i −0.729371 0.684118i \(-0.760187\pi\)
0.957149 + 0.289595i \(0.0935207\pi\)
\(174\) 0 0
\(175\) 870.454 + 2161.42i 0.376001 + 0.933647i
\(176\) 0 0
\(177\) 692.892 1200.12i 0.294243 0.509643i
\(178\) 0 0
\(179\) −383.716 664.615i −0.160225 0.277518i 0.774724 0.632299i \(-0.217889\pi\)
−0.934949 + 0.354781i \(0.884555\pi\)
\(180\) 0 0
\(181\) −3957.71 −1.62527 −0.812636 0.582772i \(-0.801968\pi\)
−0.812636 + 0.582772i \(0.801968\pi\)
\(182\) 0 0
\(183\) −556.045 −0.224612
\(184\) 0 0
\(185\) −1279.12 2215.50i −0.508338 0.880468i
\(186\) 0 0
\(187\) 708.833 1227.74i 0.277193 0.480112i
\(188\) 0 0
\(189\) 495.102 + 70.1481i 0.190547 + 0.0269975i
\(190\) 0 0
\(191\) −902.648 + 1563.43i −0.341954 + 0.592282i −0.984796 0.173717i \(-0.944422\pi\)
0.642841 + 0.765999i \(0.277756\pi\)
\(192\) 0 0
\(193\) −1685.42 2919.23i −0.628597 1.08876i −0.987833 0.155515i \(-0.950296\pi\)
0.359237 0.933247i \(-0.383037\pi\)
\(194\) 0 0
\(195\) 1845.20 0.677630
\(196\) 0 0
\(197\) −4612.31 −1.66809 −0.834044 0.551697i \(-0.813980\pi\)
−0.834044 + 0.551697i \(0.813980\pi\)
\(198\) 0 0
\(199\) −1114.93 1931.12i −0.397163 0.687906i 0.596212 0.802827i \(-0.296672\pi\)
−0.993375 + 0.114921i \(0.963339\pi\)
\(200\) 0 0
\(201\) −817.812 + 1416.49i −0.286985 + 0.497073i
\(202\) 0 0
\(203\) −4404.73 624.080i −1.52291 0.215772i
\(204\) 0 0
\(205\) −815.432 + 1412.37i −0.277816 + 0.481191i
\(206\) 0 0
\(207\) 663.068 + 1148.47i 0.222640 + 0.385623i
\(208\) 0 0
\(209\) 3966.13 1.31265
\(210\) 0 0
\(211\) −912.614 −0.297758 −0.148879 0.988855i \(-0.547566\pi\)
−0.148879 + 0.988855i \(0.547566\pi\)
\(212\) 0 0
\(213\) 196.114 + 339.679i 0.0630868 + 0.109270i
\(214\) 0 0
\(215\) 2601.70 4506.27i 0.825276 1.42942i
\(216\) 0 0
\(217\) 2052.56 + 5096.70i 0.642105 + 1.59441i
\(218\) 0 0
\(219\) 271.949 471.029i 0.0839114 0.145339i
\(220\) 0 0
\(221\) −531.068 919.837i −0.161645 0.279977i
\(222\) 0 0
\(223\) 4319.47 1.29710 0.648549 0.761173i \(-0.275376\pi\)
0.648549 + 0.761173i \(0.275376\pi\)
\(224\) 0 0
\(225\) 1132.33 0.335505
\(226\) 0 0
\(227\) 1030.64 + 1785.12i 0.301349 + 0.521951i 0.976442 0.215782i \(-0.0692299\pi\)
−0.675093 + 0.737733i \(0.735897\pi\)
\(228\) 0 0
\(229\) 1737.32 3009.12i 0.501332 0.868333i −0.498667 0.866794i \(-0.666177\pi\)
0.999999 0.00153905i \(-0.000489896\pi\)
\(230\) 0 0
\(231\) 1775.72 2267.57i 0.505773 0.645866i
\(232\) 0 0
\(233\) −388.049 + 672.121i −0.109107 + 0.188979i −0.915409 0.402525i \(-0.868132\pi\)
0.806302 + 0.591505i \(0.201466\pi\)
\(234\) 0 0
\(235\) −538.102 932.020i −0.149370 0.258716i
\(236\) 0 0
\(237\) −1229.09 −0.336869
\(238\) 0 0
\(239\) −2006.80 −0.543133 −0.271567 0.962420i \(-0.587542\pi\)
−0.271567 + 0.962420i \(0.587542\pi\)
\(240\) 0 0
\(241\) −402.824 697.711i −0.107669 0.186488i 0.807157 0.590337i \(-0.201005\pi\)
−0.914825 + 0.403850i \(0.867672\pi\)
\(242\) 0 0
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 3916.00 3764.71i 1.02116 0.981707i
\(246\) 0 0
\(247\) 1485.74 2573.38i 0.382734 0.662915i
\(248\) 0 0
\(249\) −521.892 903.944i −0.132826 0.230061i
\(250\) 0 0
\(251\) −1421.78 −0.357539 −0.178769 0.983891i \(-0.557212\pi\)
−0.178769 + 0.983891i \(0.557212\pi\)
\(252\) 0 0
\(253\) 7638.12 1.89804
\(254\) 0 0
\(255\) −649.682 1125.28i −0.159548 0.276345i
\(256\) 0 0
\(257\) 732.909 1269.44i 0.177890 0.308114i −0.763268 0.646082i \(-0.776406\pi\)
0.941157 + 0.337968i \(0.109740\pi\)
\(258\) 0 0
\(259\) −1844.49 + 2355.39i −0.442513 + 0.565084i
\(260\) 0 0
\(261\) −1080.94 + 1872.24i −0.256354 + 0.444018i
\(262\) 0 0
\(263\) 3495.69 + 6054.72i 0.819596 + 1.41958i 0.905980 + 0.423320i \(0.139135\pi\)
−0.0863847 + 0.996262i \(0.527531\pi\)
\(264\) 0 0
\(265\) 1052.99 0.244093
\(266\) 0 0
\(267\) −3471.48 −0.795696
\(268\) 0 0
\(269\) −404.479 700.578i −0.0916786 0.158792i 0.816539 0.577290i \(-0.195890\pi\)
−0.908218 + 0.418498i \(0.862557\pi\)
\(270\) 0 0
\(271\) 3330.88 5769.26i 0.746630 1.29320i −0.202799 0.979220i \(-0.565004\pi\)
0.949429 0.313981i \(-0.101663\pi\)
\(272\) 0 0
\(273\) −806.091 2001.60i −0.178706 0.443745i
\(274\) 0 0
\(275\) 3260.93 5648.09i 0.715059 1.23852i
\(276\) 0 0
\(277\) 3765.73 + 6522.44i 0.816827 + 1.41479i 0.908009 + 0.418951i \(0.137602\pi\)
−0.0911823 + 0.995834i \(0.529065\pi\)
\(278\) 0 0
\(279\) 2670.07 0.572949
\(280\) 0 0
\(281\) 1690.19 0.358819 0.179410 0.983774i \(-0.442581\pi\)
0.179410 + 0.983774i \(0.442581\pi\)
\(282\) 0 0
\(283\) 1589.12 + 2752.43i 0.333792 + 0.578145i 0.983252 0.182251i \(-0.0583384\pi\)
−0.649460 + 0.760396i \(0.725005\pi\)
\(284\) 0 0
\(285\) 1817.58 3148.14i 0.377769 0.654315i
\(286\) 0 0
\(287\) 1888.31 + 267.543i 0.388374 + 0.0550263i
\(288\) 0 0
\(289\) 2082.53 3607.05i 0.423882 0.734184i
\(290\) 0 0
\(291\) 2427.45 + 4204.46i 0.489002 + 0.846976i
\(292\) 0 0
\(293\) −2176.53 −0.433974 −0.216987 0.976174i \(-0.569623\pi\)
−0.216987 + 0.976174i \(0.569623\pi\)
\(294\) 0 0
\(295\) −7315.61 −1.44383
\(296\) 0 0
\(297\) −699.801 1212.09i −0.136722 0.236810i
\(298\) 0 0
\(299\) 2861.30 4955.91i 0.553421 0.958554i
\(300\) 0 0
\(301\) −6024.79 853.616i −1.15370 0.163460i
\(302\) 0 0
\(303\) 1078.11 1867.35i 0.204409 0.354047i
\(304\) 0 0
\(305\) 1467.69 + 2542.12i 0.275541 + 0.477250i
\(306\) 0 0
\(307\) −623.504 −0.115913 −0.0579564 0.998319i \(-0.518458\pi\)
−0.0579564 + 0.998319i \(0.518458\pi\)
\(308\) 0 0
\(309\) −4834.74 −0.890093
\(310\) 0 0
\(311\) 233.996 + 405.293i 0.0426647 + 0.0738973i 0.886569 0.462596i \(-0.153082\pi\)
−0.843905 + 0.536493i \(0.819749\pi\)
\(312\) 0 0
\(313\) −1806.41 + 3128.79i −0.326211 + 0.565014i −0.981757 0.190141i \(-0.939105\pi\)
0.655546 + 0.755156i \(0.272439\pi\)
\(314\) 0 0
\(315\) −986.131 2448.66i −0.176388 0.437988i
\(316\) 0 0
\(317\) −2265.87 + 3924.60i −0.401463 + 0.695355i −0.993903 0.110260i \(-0.964832\pi\)
0.592439 + 0.805615i \(0.298165\pi\)
\(318\) 0 0
\(319\) 6225.85 + 10783.5i 1.09273 + 1.89266i
\(320\) 0 0
\(321\) 2804.01 0.487553
\(322\) 0 0
\(323\) −2092.47 −0.360459
\(324\) 0 0
\(325\) −2443.13 4231.63i −0.416987 0.722242i
\(326\) 0 0
\(327\) −1795.53 + 3109.95i −0.303648 + 0.525934i
\(328\) 0 0
\(329\) −775.943 + 990.871i −0.130028 + 0.166044i
\(330\) 0 0
\(331\) −618.528 + 1071.32i −0.102711 + 0.177901i −0.912801 0.408405i \(-0.866085\pi\)
0.810090 + 0.586306i \(0.199418\pi\)
\(332\) 0 0
\(333\) 726.903 + 1259.03i 0.119622 + 0.207191i
\(334\) 0 0
\(335\) 8634.53 1.40822
\(336\) 0 0
\(337\) −1867.83 −0.301921 −0.150960 0.988540i \(-0.548237\pi\)
−0.150960 + 0.988540i \(0.548237\pi\)
\(338\) 0 0
\(339\) −3576.97 6195.49i −0.573080 0.992604i
\(340\) 0 0
\(341\) 7689.37 13318.4i 1.22112 2.11505i
\(342\) 0 0
\(343\) −5794.53 2603.27i −0.912173 0.409806i
\(344\) 0 0
\(345\) 3500.36 6062.81i 0.546241 0.946118i
\(346\) 0 0
\(347\) −31.6819 54.8746i −0.00490136 0.00848940i 0.863564 0.504239i \(-0.168227\pi\)
−0.868466 + 0.495749i \(0.834893\pi\)
\(348\) 0 0
\(349\) 1223.79 0.187702 0.0938508 0.995586i \(-0.470082\pi\)
0.0938508 + 0.995586i \(0.470082\pi\)
\(350\) 0 0
\(351\) −1048.60 −0.159459
\(352\) 0 0
\(353\) 2257.81 + 3910.64i 0.340428 + 0.589638i 0.984512 0.175316i \(-0.0560949\pi\)
−0.644085 + 0.764954i \(0.722762\pi\)
\(354\) 0 0
\(355\) 1035.29 1793.18i 0.154782 0.268090i
\(356\) 0 0
\(357\) −936.841 + 1196.34i −0.138888 + 0.177358i
\(358\) 0 0
\(359\) 1114.25 1929.93i 0.163810 0.283727i −0.772422 0.635109i \(-0.780955\pi\)
0.936232 + 0.351383i \(0.114288\pi\)
\(360\) 0 0
\(361\) 502.506 + 870.365i 0.0732622 + 0.126894i
\(362\) 0 0
\(363\) −4068.26 −0.588232
\(364\) 0 0
\(365\) −2871.26 −0.411749
\(366\) 0 0
\(367\) −718.670 1244.77i −0.102219 0.177048i 0.810380 0.585905i \(-0.199261\pi\)
−0.912598 + 0.408857i \(0.865928\pi\)
\(368\) 0 0
\(369\) 463.398 802.628i 0.0653754 0.113234i
\(370\) 0 0
\(371\) −460.006 1142.24i −0.0643728 0.159844i
\(372\) 0 0
\(373\) 6118.71 10597.9i 0.849370 1.47115i −0.0324014 0.999475i \(-0.510315\pi\)
0.881771 0.471677i \(-0.156351\pi\)
\(374\) 0 0
\(375\) −19.3465 33.5092i −0.00266413 0.00461442i
\(376\) 0 0
\(377\) 9329.00 1.27445
\(378\) 0 0
\(379\) 10647.0 1.44301 0.721503 0.692411i \(-0.243451\pi\)
0.721503 + 0.692411i \(0.243451\pi\)
\(380\) 0 0
\(381\) 4010.89 + 6947.06i 0.539328 + 0.934143i
\(382\) 0 0
\(383\) −3357.41 + 5815.20i −0.447925 + 0.775829i −0.998251 0.0591208i \(-0.981170\pi\)
0.550326 + 0.834950i \(0.314504\pi\)
\(384\) 0 0
\(385\) −15053.9 2132.89i −1.99277 0.282344i
\(386\) 0 0
\(387\) −1478.51 + 2560.85i −0.194203 + 0.336370i
\(388\) 0 0
\(389\) 5326.54 + 9225.83i 0.694258 + 1.20249i 0.970430 + 0.241381i \(0.0776005\pi\)
−0.276173 + 0.961108i \(0.589066\pi\)
\(390\) 0 0
\(391\) −4029.76 −0.521211
\(392\) 0 0
\(393\) −116.580 −0.0149635
\(394\) 0 0
\(395\) 3244.21 + 5619.14i 0.413250 + 0.715771i
\(396\) 0 0
\(397\) −1610.52 + 2789.50i −0.203601 + 0.352648i −0.949686 0.313203i \(-0.898598\pi\)
0.746085 + 0.665851i \(0.231931\pi\)
\(398\) 0 0
\(399\) −4208.99 596.347i −0.528103 0.0748238i
\(400\) 0 0
\(401\) −6242.50 + 10812.3i −0.777395 + 1.34649i 0.156043 + 0.987750i \(0.450126\pi\)
−0.933438 + 0.358738i \(0.883207\pi\)
\(402\) 0 0
\(403\) −5760.99 9978.32i −0.712097 1.23339i
\(404\) 0 0
\(405\) −1282.81 −0.157391
\(406\) 0 0
\(407\) 8373.46 1.01980
\(408\) 0 0
\(409\) −3518.69 6094.56i −0.425399 0.736813i 0.571059 0.820909i \(-0.306533\pi\)
−0.996458 + 0.0840967i \(0.973200\pi\)
\(410\) 0 0
\(411\) −1152.22 + 1995.70i −0.138284 + 0.239514i
\(412\) 0 0
\(413\) 3195.88 + 7935.67i 0.380772 + 0.945493i
\(414\) 0 0
\(415\) −2755.09 + 4771.95i −0.325884 + 0.564448i
\(416\) 0 0
\(417\) −1578.82 2734.60i −0.185408 0.321137i
\(418\) 0 0
\(419\) 1549.66 0.180682 0.0903410 0.995911i \(-0.471204\pi\)
0.0903410 + 0.995911i \(0.471204\pi\)
\(420\) 0 0
\(421\) 5531.63 0.640369 0.320184 0.947355i \(-0.396255\pi\)
0.320184 + 0.947355i \(0.396255\pi\)
\(422\) 0 0
\(423\) 305.795 + 529.653i 0.0351496 + 0.0608809i
\(424\) 0 0
\(425\) −1720.42 + 2979.85i −0.196359 + 0.340103i
\(426\) 0 0
\(427\) 2116.41 2702.64i 0.239860 0.306299i
\(428\) 0 0
\(429\) −3019.81 + 5230.46i −0.339855 + 0.588646i
\(430\) 0 0
\(431\) −1014.97 1757.97i −0.113432 0.196470i 0.803720 0.595008i \(-0.202851\pi\)
−0.917152 + 0.398538i \(0.869518\pi\)
\(432\) 0 0
\(433\) −327.739 −0.0363744 −0.0181872 0.999835i \(-0.505789\pi\)
−0.0181872 + 0.999835i \(0.505789\pi\)
\(434\) 0 0
\(435\) 11412.6 1.25792
\(436\) 0 0
\(437\) −5636.92 9763.43i −0.617049 1.06876i
\(438\) 0 0
\(439\) 3954.34 6849.12i 0.429910 0.744625i −0.566955 0.823749i \(-0.691879\pi\)
0.996865 + 0.0791234i \(0.0252121\pi\)
\(440\) 0 0
\(441\) −2225.40 + 2139.43i −0.240298 + 0.231015i
\(442\) 0 0
\(443\) −1460.41 + 2529.51i −0.156628 + 0.271288i −0.933651 0.358185i \(-0.883396\pi\)
0.777023 + 0.629473i \(0.216729\pi\)
\(444\) 0 0
\(445\) 9163.03 + 15870.8i 0.976111 + 1.69067i
\(446\) 0 0
\(447\) −1082.93 −0.114588
\(448\) 0 0
\(449\) −10240.2 −1.07631 −0.538156 0.842845i \(-0.680879\pi\)
−0.538156 + 0.842845i \(0.680879\pi\)
\(450\) 0 0
\(451\) −2669.02 4622.88i −0.278668 0.482668i
\(452\) 0 0
\(453\) −2322.59 + 4022.84i −0.240893 + 0.417239i
\(454\) 0 0
\(455\) −7023.19 + 8968.54i −0.723632 + 0.924069i
\(456\) 0 0
\(457\) −2946.31 + 5103.17i −0.301582 + 0.522355i −0.976494 0.215543i \(-0.930848\pi\)
0.674913 + 0.737897i \(0.264181\pi\)
\(458\) 0 0
\(459\) 369.205 + 639.481i 0.0375446 + 0.0650292i
\(460\) 0 0
\(461\) −12643.4 −1.27735 −0.638677 0.769475i \(-0.720518\pi\)
−0.638677 + 0.769475i \(0.720518\pi\)
\(462\) 0 0
\(463\) −15093.2 −1.51499 −0.757494 0.652842i \(-0.773577\pi\)
−0.757494 + 0.652842i \(0.773577\pi\)
\(464\) 0 0
\(465\) −7047.70 12207.0i −0.702858 1.21739i
\(466\) 0 0
\(467\) −1410.12 + 2442.39i −0.139727 + 0.242014i −0.927393 0.374088i \(-0.877956\pi\)
0.787666 + 0.616102i \(0.211289\pi\)
\(468\) 0 0
\(469\) −3772.06 9366.38i −0.371380 0.922173i
\(470\) 0 0
\(471\) −1450.60 + 2512.52i −0.141911 + 0.245798i
\(472\) 0 0
\(473\) 8515.72 + 14749.7i 0.827808 + 1.43381i
\(474\) 0 0
\(475\) −9626.23 −0.929856
\(476\) 0 0
\(477\) −598.398 −0.0574397
\(478\) 0 0
\(479\) −8224.25 14244.8i −0.784500 1.35879i −0.929297 0.369332i \(-0.879586\pi\)
0.144798 0.989461i \(-0.453747\pi\)
\(480\) 0 0
\(481\) 3136.76 5433.03i 0.297347 0.515020i
\(482\) 0 0
\(483\) −8105.84 1148.47i −0.763620 0.108193i
\(484\) 0 0
\(485\) 12814.6 22195.5i 1.19975 2.07804i
\(486\) 0 0
\(487\) 3165.53 + 5482.87i 0.294546 + 0.510169i 0.974879 0.222734i \(-0.0714982\pi\)
−0.680333 + 0.732903i \(0.738165\pi\)
\(488\) 0 0
\(489\) −3979.50 −0.368015
\(490\) 0 0
\(491\) 9286.90 0.853588 0.426794 0.904349i \(-0.359643\pi\)
0.426794 + 0.904349i \(0.359643\pi\)
\(492\) 0 0
\(493\) −3284.67 5689.21i −0.300069 0.519735i
\(494\) 0 0
\(495\) −3694.28 + 6398.68i −0.335445 + 0.581008i
\(496\) 0 0
\(497\) −2397.44 339.679i −0.216378 0.0306573i
\(498\) 0 0
\(499\) −121.725 + 210.835i −0.0109202 + 0.0189143i −0.871434 0.490513i \(-0.836809\pi\)
0.860514 + 0.509427i \(0.170143\pi\)
\(500\) 0 0
\(501\) −2125.05 3680.69i −0.189501 0.328225i
\(502\) 0 0
\(503\) −8499.30 −0.753409 −0.376705 0.926333i \(-0.622943\pi\)
−0.376705 + 0.926333i \(0.622943\pi\)
\(504\) 0 0
\(505\) −11382.8 −1.00303
\(506\) 0 0
\(507\) −1033.02 1789.24i −0.0904890 0.156731i
\(508\) 0 0
\(509\) 3841.55 6653.76i 0.334526 0.579416i −0.648868 0.760901i \(-0.724757\pi\)
0.983394 + 0.181485i \(0.0580904\pi\)
\(510\) 0 0
\(511\) 1254.33 + 3114.62i 0.108588 + 0.269634i
\(512\) 0 0
\(513\) −1032.90 + 1789.04i −0.0888963 + 0.153973i
\(514\) 0 0
\(515\) 12761.4 + 22103.4i 1.09191 + 1.89124i
\(516\) 0 0
\(517\) 3522.57 0.299656
\(518\) 0 0
\(519\) 3109.80 0.263015
\(520\) 0 0
\(521\) 10765.3 + 18646.1i 0.905253 + 1.56794i 0.820578 + 0.571535i \(0.193652\pi\)
0.0846750 + 0.996409i \(0.473015\pi\)
\(522\) 0 0
\(523\) −8423.53 + 14590.0i −0.704274 + 1.21984i 0.262679 + 0.964883i \(0.415394\pi\)
−0.966953 + 0.254955i \(0.917939\pi\)
\(524\) 0 0
\(525\) −4309.86 + 5503.64i −0.358281 + 0.457521i
\(526\) 0 0
\(527\) −4056.80 + 7026.58i −0.335326 + 0.580802i
\(528\) 0 0
\(529\) −4772.29 8265.84i −0.392232 0.679366i
\(530\) 0 0
\(531\) 4157.35 0.339762
\(532\) 0 0
\(533\) −3999.34 −0.325011
\(534\) 0 0
\(535\) −7401.24 12819.3i −0.598100 1.03594i
\(536\) 0 0
\(537\) 1151.15 1993.85i 0.0925059 0.160225i
\(538\) 0 0
\(539\) 4262.72 + 17261.6i 0.340646 + 1.37942i
\(540\) 0 0
\(541\) −8720.02 + 15103.5i −0.692981 + 1.20028i 0.277875 + 0.960617i \(0.410370\pi\)
−0.970856 + 0.239662i \(0.922963\pi\)
\(542\) 0 0
\(543\) −5936.56 10282.4i −0.469175 0.812636i
\(544\) 0 0
\(545\) 18957.3 1.48999
\(546\) 0 0
\(547\) −11520.7 −0.900530 −0.450265 0.892895i \(-0.648671\pi\)
−0.450265 + 0.892895i \(0.648671\pi\)
\(548\) 0 0
\(549\) −834.068 1444.65i −0.0648400 0.112306i
\(550\) 0 0
\(551\) 9189.33 15916.4i 0.710488 1.23060i
\(552\) 0 0
\(553\) 4678.15 5973.94i 0.359738 0.459382i
\(554\) 0 0
\(555\) 3837.35 6646.49i 0.293489 0.508338i
\(556\) 0 0
\(557\) −5746.51 9953.25i −0.437141 0.757151i 0.560327 0.828272i \(-0.310676\pi\)
−0.997468 + 0.0711212i \(0.977342\pi\)
\(558\) 0 0
\(559\) 12760.2 0.965472
\(560\) 0 0
\(561\) 4253.00 0.320075
\(562\) 0 0
\(563\) 9055.65 + 15684.8i 0.677886 + 1.17413i 0.975616 + 0.219483i \(0.0704372\pi\)
−0.297730 + 0.954650i \(0.596230\pi\)
\(564\) 0 0
\(565\) −18882.9 + 32706.2i −1.40604 + 2.43533i
\(566\) 0 0
\(567\) 560.403 + 1391.54i 0.0415075 + 0.103067i
\(568\) 0 0
\(569\) −2208.81 + 3825.77i −0.162738 + 0.281871i −0.935850 0.352399i \(-0.885366\pi\)
0.773112 + 0.634270i \(0.218699\pi\)
\(570\) 0 0
\(571\) 6609.87 + 11448.6i 0.484439 + 0.839073i 0.999840 0.0178762i \(-0.00569048\pi\)
−0.515401 + 0.856949i \(0.672357\pi\)
\(572\) 0 0
\(573\) −5415.89 −0.394855
\(574\) 0 0
\(575\) −18538.6 −1.34454
\(576\) 0 0
\(577\) 8748.20 + 15152.3i 0.631182 + 1.09324i 0.987310 + 0.158803i \(0.0507634\pi\)
−0.356128 + 0.934437i \(0.615903\pi\)
\(578\) 0 0
\(579\) 5056.26 8757.70i 0.362921 0.628597i
\(580\) 0 0
\(581\) 6380.00 + 903.944i 0.455571 + 0.0645472i
\(582\) 0 0
\(583\) −1723.29 + 2984.83i −0.122421 + 0.212039i
\(584\) 0 0
\(585\) 2767.81 + 4793.98i 0.195615 + 0.338815i
\(586\) 0 0
\(587\) 4280.53 0.300982 0.150491 0.988611i \(-0.451915\pi\)
0.150491 + 0.988611i \(0.451915\pi\)
\(588\) 0 0
\(589\) −22699.0 −1.58794
\(590\) 0 0
\(591\) −6918.47 11983.1i −0.481536 0.834044i
\(592\) 0 0
\(593\) 795.466 1377.79i 0.0550858 0.0954114i −0.837168 0.546946i \(-0.815790\pi\)
0.892253 + 0.451535i \(0.149123\pi\)
\(594\) 0 0
\(595\) 7942.20 + 1125.28i 0.547224 + 0.0775329i
\(596\) 0 0
\(597\) 3344.80 5793.36i 0.229302 0.397163i
\(598\) 0 0
\(599\) −6961.42 12057.5i −0.474851 0.822467i 0.524734 0.851266i \(-0.324165\pi\)
−0.999585 + 0.0287997i \(0.990831\pi\)
\(600\) 0 0
\(601\) 12559.7 0.852446 0.426223 0.904618i \(-0.359844\pi\)
0.426223 + 0.904618i \(0.359844\pi\)
\(602\) 0 0
\(603\) −4906.87 −0.331382
\(604\) 0 0
\(605\) 10738.3 + 18599.2i 0.721607 + 1.24986i
\(606\) 0 0
\(607\) 3839.19 6649.66i 0.256718 0.444648i −0.708643 0.705567i \(-0.750692\pi\)
0.965361 + 0.260919i \(0.0840256\pi\)
\(608\) 0 0
\(609\) −4985.69 12379.9i −0.331741 0.823745i
\(610\) 0 0
\(611\) 1319.58 2285.58i 0.0873723 0.151333i
\(612\) 0 0
\(613\) −3079.19 5333.31i −0.202883 0.351403i 0.746573 0.665303i \(-0.231698\pi\)
−0.949456 + 0.313900i \(0.898364\pi\)
\(614\) 0 0
\(615\) −4892.59 −0.320794
\(616\) 0 0
\(617\) 8813.12 0.575045 0.287523 0.957774i \(-0.407168\pi\)
0.287523 + 0.957774i \(0.407168\pi\)
\(618\) 0 0
\(619\) 11595.0 + 20083.1i 0.752894 + 1.30405i 0.946415 + 0.322954i \(0.104676\pi\)
−0.193521 + 0.981096i \(0.561991\pi\)
\(620\) 0 0
\(621\) −1989.20 + 3445.40i −0.128541 + 0.222640i
\(622\) 0 0
\(623\) 13213.1 16873.0i 0.849713 1.08507i
\(624\) 0 0
\(625\) 7761.27 13442.9i 0.496721 0.860346i
\(626\) 0 0
\(627\) 5949.19 + 10304.3i 0.378928 + 0.656323i
\(628\) 0 0
\(629\) −4417.71 −0.280041
\(630\) 0 0
\(631\) −7936.94 −0.500736 −0.250368 0.968151i \(-0.580552\pi\)
−0.250368 + 0.968151i \(0.580552\pi\)
\(632\) 0 0
\(633\) −1368.92 2371.04i −0.0859553 0.148879i
\(634\) 0 0
\(635\) 21173.6 36673.8i 1.32323 2.29190i
\(636\) 0 0
\(637\) 12796.8 + 3700.50i 0.795964 + 0.230171i
\(638\) 0 0
\(639\) −588.341 + 1019.04i −0.0364232 + 0.0630868i
\(640\) 0 0
\(641\) −16057.3 27812.1i −0.989432 1.71375i −0.620286 0.784376i \(-0.712984\pi\)
−0.369146 0.929371i \(-0.620350\pi\)
\(642\) 0 0
\(643\) 24786.7 1.52021 0.760104 0.649802i \(-0.225148\pi\)
0.760104 + 0.649802i \(0.225148\pi\)
\(644\) 0 0
\(645\) 15610.2 0.952946
\(646\) 0 0
\(647\) 3772.80 + 6534.67i 0.229249 + 0.397070i 0.957586 0.288149i \(-0.0930398\pi\)
−0.728337 + 0.685219i \(0.759706\pi\)
\(648\) 0 0
\(649\) 11972.5 20737.0i 0.724133 1.25423i
\(650\) 0 0
\(651\) −10162.8 + 12977.8i −0.611844 + 0.781318i
\(652\) 0 0
\(653\) 2444.49 4233.99i 0.146494 0.253735i −0.783435 0.621473i \(-0.786534\pi\)
0.929929 + 0.367738i \(0.119868\pi\)
\(654\) 0 0
\(655\) 307.714 + 532.976i 0.0183563 + 0.0317941i
\(656\) 0 0
\(657\) 1631.69 0.0968926
\(658\) 0 0
\(659\) −25895.9 −1.53075 −0.765374 0.643586i \(-0.777446\pi\)
−0.765374 + 0.643586i \(0.777446\pi\)
\(660\) 0 0
\(661\) −4091.68 7087.00i −0.240769 0.417023i 0.720165 0.693803i \(-0.244066\pi\)
−0.960933 + 0.276780i \(0.910733\pi\)
\(662\) 0 0
\(663\) 1593.20 2759.51i 0.0933257 0.161645i
\(664\) 0 0
\(665\) 8383.36 + 20816.7i 0.488861 + 1.21389i
\(666\) 0 0
\(667\) 17697.2 30652.4i 1.02734 1.77941i
\(668\) 0 0
\(669\) 6479.20 + 11222.3i 0.374440 + 0.648549i
\(670\) 0 0
\(671\) −9607.93 −0.552772
\(672\) 0 0
\(673\) −4635.02 −0.265478 −0.132739 0.991151i \(-0.542377\pi\)
−0.132739 + 0.991151i \(0.542377\pi\)
\(674\) 0 0
\(675\) 1698.49 + 2941.88i 0.0968520 + 0.167753i
\(676\) 0 0
\(677\) 12192.9 21118.7i 0.692187 1.19890i −0.278932 0.960311i \(-0.589980\pi\)
0.971120 0.238593i \(-0.0766862\pi\)
\(678\) 0 0
\(679\) −29674.9 4204.46i −1.67720 0.237633i
\(680\) 0 0
\(681\) −3091.93 + 5355.37i −0.173984 + 0.301349i
\(682\) 0 0
\(683\) −9196.71 15929.2i −0.515230 0.892405i −0.999844 0.0176767i \(-0.994373\pi\)
0.484613 0.874728i \(-0.338960\pi\)
\(684\) 0 0
\(685\) 12165.2 0.678552
\(686\) 0 0
\(687\) 10423.9 0.578889
\(688\) 0 0
\(689\) 1291.11 + 2236.27i 0.0713897 + 0.123651i
\(690\) 0 0
\(691\) −7449.44 + 12902.8i −0.410116 + 0.710341i −0.994902 0.100846i \(-0.967845\pi\)
0.584786 + 0.811187i \(0.301178\pi\)
\(692\) 0 0
\(693\) 8554.89 + 1212.09i 0.468937 + 0.0664409i
\(694\) 0 0
\(695\) −8334.67 + 14436.1i −0.454895 + 0.787902i
\(696\) 0 0
\(697\) 1408.14 + 2438.96i 0.0765236 + 0.132543i
\(698\) 0 0
\(699\) −2328.30 −0.125986
\(700\) 0 0
\(701\) −5725.70 −0.308497 −0.154249 0.988032i \(-0.549296\pi\)
−0.154249 + 0.988032i \(0.549296\pi\)
\(702\) 0 0
\(703\) −6179.60 10703.4i −0.331533 0.574232i
\(704\) 0 0
\(705\) 1614.31 2796.06i 0.0862387 0.149370i
\(706\) 0 0
\(707\) 4972.66 + 12347.6i 0.264521 + 0.656831i
\(708\) 0 0
\(709\) 11728.4 20314.2i 0.621255 1.07604i −0.367998 0.929827i \(-0.619957\pi\)
0.989252 0.146218i \(-0.0467101\pi\)
\(710\) 0 0
\(711\) −1843.64 3193.27i −0.0972458 0.168435i
\(712\) 0 0
\(713\) −43714.5 −2.29610
\(714\) 0 0
\(715\) 31883.4 1.66765
\(716\) 0 0
\(717\) −3010.19 5213.81i −0.156789 0.271567i
\(718\) 0 0
\(719\) −4229.50 + 7325.71i −0.219379 + 0.379976i −0.954618 0.297832i \(-0.903737\pi\)
0.735239 + 0.677808i \(0.237070\pi\)
\(720\) 0 0
\(721\) 18401.9 23499.0i 0.950518 1.21380i
\(722\) 0 0
\(723\) 1208.47 2093.13i 0.0621626 0.107669i
\(724\) 0 0
\(725\) −15110.8 26172.7i −0.774072 1.34073i
\(726\) 0 0
\(727\) 11822.2 0.603111 0.301555 0.953449i \(-0.402494\pi\)
0.301555 + 0.953449i \(0.402494\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −4492.77 7781.70i −0.227320 0.393730i
\(732\) 0 0
\(733\) −2514.48 + 4355.20i −0.126704 + 0.219458i −0.922398 0.386241i \(-0.873773\pi\)
0.795694 + 0.605699i \(0.207107\pi\)
\(734\) 0 0
\(735\) 15655.0 + 4527.00i 0.785637 + 0.227185i
\(736\) 0 0
\(737\) −14131.0 + 24475.6i −0.706272 + 1.22330i
\(738\) 0 0
\(739\) −8871.95 15366.7i −0.441624 0.764914i 0.556187 0.831057i \(-0.312264\pi\)
−0.997810 + 0.0661431i \(0.978931\pi\)
\(740\) 0 0
\(741\) 8914.44 0.441944
\(742\) 0 0
\(743\) 13202.3 0.651877 0.325938 0.945391i \(-0.394320\pi\)
0.325938 + 0.945391i \(0.394320\pi\)
\(744\) 0 0
\(745\) 2858.42 + 4950.93i 0.140570 + 0.243474i
\(746\) 0 0
\(747\) 1565.68 2711.83i 0.0766869 0.132826i
\(748\) 0 0
\(749\) −10672.6 + 13628.8i −0.520652 + 0.664866i
\(750\) 0 0
\(751\) 7800.49 13510.8i 0.379020 0.656482i −0.611900 0.790935i \(-0.709594\pi\)
0.990920 + 0.134453i \(0.0429278\pi\)
\(752\) 0 0
\(753\) −2132.68 3693.90i −0.103213 0.178769i
\(754\) 0 0
\(755\) 24522.0 1.18205
\(756\) 0 0
\(757\) 2948.08 0.141545 0.0707725 0.997492i \(-0.477454\pi\)
0.0707725 + 0.997492i \(0.477454\pi\)
\(758\) 0 0
\(759\) 11457.2 + 19844.4i 0.547917 + 0.949021i
\(760\) 0 0
\(761\) −848.515 + 1469.67i −0.0404187 + 0.0700073i −0.885527 0.464588i \(-0.846203\pi\)
0.845108 + 0.534595i \(0.179536\pi\)
\(762\) 0 0
\(763\) −8281.65 20564.1i −0.392943 0.975716i
\(764\) 0 0
\(765\) 1949.05 3375.85i 0.0921149 0.159548i
\(766\) 0 0
\(767\) −8969.98 15536.5i −0.422278 0.731407i
\(768\) 0 0
\(769\) −96.7799 −0.00453833 −0.00226916 0.999997i \(-0.500722\pi\)
−0.00226916 + 0.999997i \(0.500722\pi\)
\(770\) 0 0
\(771\) 4397.45 0.205409
\(772\) 0 0
\(773\) −18163.4 31459.9i −0.845138 1.46382i −0.885501 0.464637i \(-0.846185\pi\)
0.0403629 0.999185i \(-0.487149\pi\)
\(774\) 0 0
\(775\) −18662.9 + 32325.2i −0.865023 + 1.49826i
\(776\) 0 0
\(777\) −8886.21 1259.03i −0.410284 0.0581307i
\(778\) 0 0
\(779\) −3939.47 + 6823.35i −0.181189 + 0.313828i
\(780\) 0 0
\(781\) 3388.66 + 5869.32i 0.155257 + 0.268913i
\(782\) 0 0
\(783\) −6485.62 −0.296012
\(784\) 0 0
\(785\) 15315.6 0.696352
\(786\) 0 0
\(787\) 3548.23 + 6145.72i 0.160713 + 0.278362i 0.935124 0.354319i \(-0.115287\pi\)
−0.774412 + 0.632682i \(0.781954\pi\)
\(788\) 0 0
\(789\) −10487.1 + 18164.2i −0.473194 + 0.819596i
\(790\) 0 0
\(791\) 43727.5 + 6195.49i 1.96558 + 0.278491i
\(792\) 0 0
\(793\) −3599.20 + 6234.00i −0.161174 + 0.279162i