Properties

Label 288.3.u.a.163.5
Level $288$
Weight $3$
Character 288.163
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 163.5
Character \(\chi\) \(=\) 288.163
Dual form 288.3.u.a.235.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.44490 + 1.38284i) q^{2} +(0.175499 + 3.99615i) q^{4} +(3.18221 + 7.68254i) q^{5} +(3.67370 + 3.67370i) q^{7} +(-5.27246 + 6.01674i) q^{8} +O(q^{10})\) \(q+(1.44490 + 1.38284i) q^{2} +(0.175499 + 3.99615i) q^{4} +(3.18221 + 7.68254i) q^{5} +(3.67370 + 3.67370i) q^{7} +(-5.27246 + 6.01674i) q^{8} +(-6.02574 + 15.5010i) q^{10} +(-6.10089 - 14.7288i) q^{11} +(2.82075 - 6.80990i) q^{13} +(0.228001 + 10.3883i) q^{14} +(-15.9384 + 1.40264i) q^{16} +3.67152i q^{17} +(-1.65751 - 0.686564i) q^{19} +(-30.1421 + 14.0649i) q^{20} +(11.5525 - 29.7183i) q^{22} +(8.31529 - 8.31529i) q^{23} +(-31.2172 + 31.2172i) q^{25} +(13.4927 - 5.93900i) q^{26} +(-14.0359 + 15.3254i) q^{28} +(38.8592 + 16.0960i) q^{29} +4.11293i q^{31} +(-24.9691 - 20.0136i) q^{32} +(-5.07713 + 5.30499i) q^{34} +(-16.5328 + 39.9138i) q^{35} +(19.8759 + 47.9847i) q^{37} +(-1.44554 - 3.28410i) q^{38} +(-63.0019 - 21.3593i) q^{40} +(-21.1187 - 21.1187i) q^{41} +(-0.102495 - 0.247444i) q^{43} +(57.7879 - 26.9649i) q^{44} +(23.5135 - 0.516073i) q^{46} +39.3838 q^{47} -22.0079i q^{49} +(-88.2745 + 1.93744i) q^{50} +(27.7084 + 10.0770i) q^{52} +(-22.6154 + 9.36759i) q^{53} +(93.7406 - 93.7406i) q^{55} +(-41.4731 + 2.73426i) q^{56} +(33.8896 + 76.9933i) q^{58} +(101.380 - 41.9931i) q^{59} +(-14.0475 - 5.81867i) q^{61} +(-5.68753 + 5.94279i) q^{62} +(-8.40232 - 63.4460i) q^{64} +61.2936 q^{65} +(3.67448 - 8.87098i) q^{67} +(-14.6719 + 0.644346i) q^{68} +(-79.0828 + 34.8093i) q^{70} +(-75.7712 - 75.7712i) q^{71} +(-29.0378 - 29.0378i) q^{73} +(-37.6364 + 96.8185i) q^{74} +(2.45272 - 6.74415i) q^{76} +(31.6965 - 76.5221i) q^{77} +2.76556 q^{79} +(-61.4952 - 117.984i) q^{80} +(-1.31069 - 59.7184i) q^{82} +(79.1972 + 32.8045i) q^{83} +(-28.2066 + 11.6835i) q^{85} +(0.194081 - 0.499267i) q^{86} +(120.786 + 40.9498i) q^{88} +(-72.4200 + 72.4200i) q^{89} +(35.3801 - 14.6549i) q^{91} +(34.6885 + 31.7698i) q^{92} +(56.9058 + 54.4615i) q^{94} -14.9187i q^{95} +66.0511 q^{97} +(30.4335 - 31.7993i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.44490 + 1.38284i 0.722452 + 0.691421i
\(3\) 0 0
\(4\) 0.175499 + 3.99615i 0.0438747 + 0.999037i
\(5\) 3.18221 + 7.68254i 0.636442 + 1.53651i 0.831387 + 0.555693i \(0.187547\pi\)
−0.194945 + 0.980814i \(0.562453\pi\)
\(6\) 0 0
\(7\) 3.67370 + 3.67370i 0.524814 + 0.524814i 0.919021 0.394208i \(-0.128981\pi\)
−0.394208 + 0.919021i \(0.628981\pi\)
\(8\) −5.27246 + 6.01674i −0.659058 + 0.752092i
\(9\) 0 0
\(10\) −6.02574 + 15.5010i −0.602574 + 1.55010i
\(11\) −6.10089 14.7288i −0.554626 1.33899i −0.913971 0.405781i \(-0.867000\pi\)
0.359345 0.933205i \(-0.383000\pi\)
\(12\) 0 0
\(13\) 2.82075 6.80990i 0.216981 0.523839i −0.777484 0.628902i \(-0.783505\pi\)
0.994466 + 0.105063i \(0.0335046\pi\)
\(14\) 0.228001 + 10.3883i 0.0162858 + 0.742020i
\(15\) 0 0
\(16\) −15.9384 + 1.40264i −0.996150 + 0.0876648i
\(17\) 3.67152i 0.215972i 0.994152 + 0.107986i \(0.0344401\pi\)
−0.994152 + 0.107986i \(0.965560\pi\)
\(18\) 0 0
\(19\) −1.65751 0.686564i −0.0872375 0.0361349i 0.338638 0.940917i \(-0.390034\pi\)
−0.425875 + 0.904782i \(0.640034\pi\)
\(20\) −30.1421 + 14.0649i −1.50710 + 0.703243i
\(21\) 0 0
\(22\) 11.5525 29.7183i 0.525112 1.35083i
\(23\) 8.31529 8.31529i 0.361534 0.361534i −0.502843 0.864378i \(-0.667713\pi\)
0.864378 + 0.502843i \(0.167713\pi\)
\(24\) 0 0
\(25\) −31.2172 + 31.2172i −1.24869 + 1.24869i
\(26\) 13.4927 5.93900i 0.518951 0.228423i
\(27\) 0 0
\(28\) −14.0359 + 15.3254i −0.501282 + 0.547334i
\(29\) 38.8592 + 16.0960i 1.33997 + 0.555035i 0.933483 0.358621i \(-0.116753\pi\)
0.406489 + 0.913656i \(0.366753\pi\)
\(30\) 0 0
\(31\) 4.11293i 0.132675i 0.997797 + 0.0663376i \(0.0211314\pi\)
−0.997797 + 0.0663376i \(0.978869\pi\)
\(32\) −24.9691 20.0136i −0.780284 0.625425i
\(33\) 0 0
\(34\) −5.07713 + 5.30499i −0.149327 + 0.156029i
\(35\) −16.5328 + 39.9138i −0.472367 + 1.14039i
\(36\) 0 0
\(37\) 19.8759 + 47.9847i 0.537186 + 1.29688i 0.926679 + 0.375853i \(0.122650\pi\)
−0.389493 + 0.921030i \(0.627350\pi\)
\(38\) −1.44554 3.28410i −0.0380405 0.0864236i
\(39\) 0 0
\(40\) −63.0019 21.3593i −1.57505 0.533984i
\(41\) −21.1187 21.1187i −0.515091 0.515091i 0.400991 0.916082i \(-0.368666\pi\)
−0.916082 + 0.400991i \(0.868666\pi\)
\(42\) 0 0
\(43\) −0.102495 0.247444i −0.00238360 0.00575451i 0.922683 0.385559i \(-0.125991\pi\)
−0.925067 + 0.379804i \(0.875991\pi\)
\(44\) 57.7879 26.9649i 1.31336 0.612839i
\(45\) 0 0
\(46\) 23.5135 0.516073i 0.511164 0.0112190i
\(47\) 39.3838 0.837952 0.418976 0.907997i \(-0.362389\pi\)
0.418976 + 0.907997i \(0.362389\pi\)
\(48\) 0 0
\(49\) 22.0079i 0.449141i
\(50\) −88.2745 + 1.93744i −1.76549 + 0.0387488i
\(51\) 0 0
\(52\) 27.7084 + 10.0770i 0.532854 + 0.193789i
\(53\) −22.6154 + 9.36759i −0.426705 + 0.176747i −0.585692 0.810534i \(-0.699177\pi\)
0.158987 + 0.987281i \(0.449177\pi\)
\(54\) 0 0
\(55\) 93.7406 93.7406i 1.70437 1.70437i
\(56\) −41.4731 + 2.73426i −0.740591 + 0.0488260i
\(57\) 0 0
\(58\) 33.8896 + 76.9933i 0.584304 + 1.32747i
\(59\) 101.380 41.9931i 1.71831 0.711747i 0.718441 0.695588i \(-0.244856\pi\)
0.999869 0.0161592i \(-0.00514387\pi\)
\(60\) 0 0
\(61\) −14.0475 5.81867i −0.230287 0.0953880i 0.264556 0.964370i \(-0.414775\pi\)
−0.494843 + 0.868982i \(0.664775\pi\)
\(62\) −5.68753 + 5.94279i −0.0917344 + 0.0958515i
\(63\) 0 0
\(64\) −8.40232 63.4460i −0.131286 0.991345i
\(65\) 61.2936 0.942978
\(66\) 0 0
\(67\) 3.67448 8.87098i 0.0548430 0.132403i −0.894083 0.447901i \(-0.852172\pi\)
0.948926 + 0.315498i \(0.102172\pi\)
\(68\) −14.6719 + 0.644346i −0.215764 + 0.00947568i
\(69\) 0 0
\(70\) −79.0828 + 34.8093i −1.12975 + 0.497276i
\(71\) −75.7712 75.7712i −1.06720 1.06720i −0.997573 0.0696271i \(-0.977819\pi\)
−0.0696271 0.997573i \(-0.522181\pi\)
\(72\) 0 0
\(73\) −29.0378 29.0378i −0.397779 0.397779i 0.479670 0.877449i \(-0.340756\pi\)
−0.877449 + 0.479670i \(0.840756\pi\)
\(74\) −37.6364 + 96.8185i −0.508600 + 1.30836i
\(75\) 0 0
\(76\) 2.45272 6.74415i 0.0322726 0.0887389i
\(77\) 31.6965 76.5221i 0.411643 0.993793i
\(78\) 0 0
\(79\) 2.76556 0.0350072 0.0175036 0.999847i \(-0.494428\pi\)
0.0175036 + 0.999847i \(0.494428\pi\)
\(80\) −61.4952 117.984i −0.768690 1.47480i
\(81\) 0 0
\(82\) −1.31069 59.7184i −0.0159841 0.728273i
\(83\) 79.1972 + 32.8045i 0.954183 + 0.395235i 0.804801 0.593544i \(-0.202272\pi\)
0.149381 + 0.988780i \(0.452272\pi\)
\(84\) 0 0
\(85\) −28.2066 + 11.6835i −0.331842 + 0.137453i
\(86\) 0.194081 0.499267i 0.00225675 0.00580543i
\(87\) 0 0
\(88\) 120.786 + 40.9498i 1.37257 + 0.465339i
\(89\) −72.4200 + 72.4200i −0.813708 + 0.813708i −0.985188 0.171480i \(-0.945145\pi\)
0.171480 + 0.985188i \(0.445145\pi\)
\(90\) 0 0
\(91\) 35.3801 14.6549i 0.388792 0.161043i
\(92\) 34.6885 + 31.7698i 0.377048 + 0.345324i
\(93\) 0 0
\(94\) 56.9058 + 54.4615i 0.605380 + 0.579378i
\(95\) 14.9187i 0.157039i
\(96\) 0 0
\(97\) 66.0511 0.680940 0.340470 0.940255i \(-0.389414\pi\)
0.340470 + 0.940255i \(0.389414\pi\)
\(98\) 30.4335 31.7993i 0.310545 0.324483i
\(99\) 0 0
\(100\) −130.227 119.270i −1.30227 1.19270i
\(101\) 7.51179 + 18.1351i 0.0743742 + 0.179555i 0.956694 0.291095i \(-0.0940195\pi\)
−0.882320 + 0.470650i \(0.844019\pi\)
\(102\) 0 0
\(103\) 0.589180 + 0.589180i 0.00572020 + 0.00572020i 0.709961 0.704241i \(-0.248712\pi\)
−0.704241 + 0.709961i \(0.748712\pi\)
\(104\) 26.1011 + 52.8767i 0.250972 + 0.508430i
\(105\) 0 0
\(106\) −45.6309 17.7382i −0.430480 0.167341i
\(107\) 55.4567 + 133.884i 0.518287 + 1.25126i 0.938955 + 0.344041i \(0.111796\pi\)
−0.420668 + 0.907215i \(0.638204\pi\)
\(108\) 0 0
\(109\) 29.4015 70.9815i 0.269739 0.651207i −0.729732 0.683733i \(-0.760355\pi\)
0.999471 + 0.0325264i \(0.0103553\pi\)
\(110\) 265.075 5.81783i 2.40977 0.0528894i
\(111\) 0 0
\(112\) −63.7057 53.4000i −0.568801 0.476786i
\(113\) 134.274i 1.18826i 0.804368 + 0.594131i \(0.202504\pi\)
−0.804368 + 0.594131i \(0.797496\pi\)
\(114\) 0 0
\(115\) 90.3436 + 37.4215i 0.785596 + 0.325405i
\(116\) −57.5023 + 158.112i −0.495709 + 1.36303i
\(117\) 0 0
\(118\) 204.555 + 79.5169i 1.73351 + 0.673872i
\(119\) −13.4880 + 13.4880i −0.113345 + 0.113345i
\(120\) 0 0
\(121\) −94.1580 + 94.1580i −0.778166 + 0.778166i
\(122\) −12.2510 27.8329i −0.100418 0.228138i
\(123\) 0 0
\(124\) −16.4359 + 0.721814i −0.132547 + 0.00582108i
\(125\) −147.104 60.9325i −1.17683 0.487460i
\(126\) 0 0
\(127\) 95.5030i 0.751992i −0.926621 0.375996i \(-0.877301\pi\)
0.926621 0.375996i \(-0.122699\pi\)
\(128\) 75.5953 103.293i 0.590588 0.806973i
\(129\) 0 0
\(130\) 88.5634 + 84.7593i 0.681257 + 0.651995i
\(131\) 67.1188 162.039i 0.512357 1.23694i −0.430151 0.902757i \(-0.641540\pi\)
0.942508 0.334183i \(-0.108460\pi\)
\(132\) 0 0
\(133\) −3.56697 8.61142i −0.0268193 0.0647475i
\(134\) 17.5764 7.73649i 0.131167 0.0577350i
\(135\) 0 0
\(136\) −22.0906 19.3579i −0.162431 0.142338i
\(137\) −88.7244 88.7244i −0.647624 0.647624i 0.304794 0.952418i \(-0.401412\pi\)
−0.952418 + 0.304794i \(0.901412\pi\)
\(138\) 0 0
\(139\) −27.6838 66.8346i −0.199164 0.480824i 0.792469 0.609912i \(-0.208795\pi\)
−0.991633 + 0.129087i \(0.958795\pi\)
\(140\) −162.403 59.0628i −1.16002 0.421877i
\(141\) 0 0
\(142\) −4.70260 214.262i −0.0331169 1.50889i
\(143\) −117.511 −0.821756
\(144\) 0 0
\(145\) 349.758i 2.41213i
\(146\) −1.80218 82.1116i −0.0123437 0.562409i
\(147\) 0 0
\(148\) −188.266 + 87.8483i −1.27207 + 0.593569i
\(149\) 100.536 41.6433i 0.674737 0.279485i −0.0188878 0.999822i \(-0.506013\pi\)
0.693625 + 0.720336i \(0.256013\pi\)
\(150\) 0 0
\(151\) −134.706 + 134.706i −0.892096 + 0.892096i −0.994720 0.102624i \(-0.967276\pi\)
0.102624 + 0.994720i \(0.467276\pi\)
\(152\) 12.8700 6.35294i 0.0846713 0.0417956i
\(153\) 0 0
\(154\) 151.616 66.7359i 0.984522 0.433350i
\(155\) −31.5977 + 13.0882i −0.203856 + 0.0844401i
\(156\) 0 0
\(157\) −56.0501 23.2167i −0.357007 0.147877i 0.196969 0.980410i \(-0.436890\pi\)
−0.553976 + 0.832533i \(0.686890\pi\)
\(158\) 3.99598 + 3.82434i 0.0252910 + 0.0242047i
\(159\) 0 0
\(160\) 74.2983 255.514i 0.464365 1.59696i
\(161\) 61.0957 0.379476
\(162\) 0 0
\(163\) 85.7621 207.048i 0.526148 1.27023i −0.407881 0.913035i \(-0.633732\pi\)
0.934029 0.357198i \(-0.116268\pi\)
\(164\) 80.6872 88.0998i 0.491995 0.537194i
\(165\) 0 0
\(166\) 69.0689 + 156.917i 0.416077 + 0.945280i
\(167\) −72.6395 72.6395i −0.434967 0.434967i 0.455347 0.890314i \(-0.349515\pi\)
−0.890314 + 0.455347i \(0.849515\pi\)
\(168\) 0 0
\(169\) 81.0829 + 81.0829i 0.479781 + 0.479781i
\(170\) −56.9123 22.1236i −0.334778 0.130139i
\(171\) 0 0
\(172\) 0.970835 0.453010i 0.00564439 0.00263378i
\(173\) 4.05480 9.78916i 0.0234382 0.0565847i −0.911727 0.410796i \(-0.865251\pi\)
0.935165 + 0.354212i \(0.115251\pi\)
\(174\) 0 0
\(175\) −229.365 −1.31066
\(176\) 117.898 + 226.197i 0.669873 + 1.28521i
\(177\) 0 0
\(178\) −204.785 + 4.49461i −1.15048 + 0.0252506i
\(179\) −214.146 88.7024i −1.19635 0.495544i −0.306531 0.951861i \(-0.599168\pi\)
−0.889817 + 0.456317i \(0.849168\pi\)
\(180\) 0 0
\(181\) −98.2125 + 40.6810i −0.542611 + 0.224757i −0.637116 0.770768i \(-0.719873\pi\)
0.0945057 + 0.995524i \(0.469873\pi\)
\(182\) 71.3863 + 27.7501i 0.392233 + 0.152473i
\(183\) 0 0
\(184\) 6.18890 + 93.8730i 0.0336353 + 0.510179i
\(185\) −305.395 + 305.395i −1.65078 + 1.65078i
\(186\) 0 0
\(187\) 54.0772 22.3995i 0.289183 0.119783i
\(188\) 6.91180 + 157.383i 0.0367649 + 0.837145i
\(189\) 0 0
\(190\) 20.6302 21.5561i 0.108580 0.113453i
\(191\) 181.842i 0.952052i −0.879431 0.476026i \(-0.842077\pi\)
0.879431 0.476026i \(-0.157923\pi\)
\(192\) 0 0
\(193\) −221.267 −1.14646 −0.573230 0.819394i \(-0.694310\pi\)
−0.573230 + 0.819394i \(0.694310\pi\)
\(194\) 95.4376 + 91.3383i 0.491946 + 0.470816i
\(195\) 0 0
\(196\) 87.9469 3.86236i 0.448709 0.0197059i
\(197\) 15.4361 + 37.2660i 0.0783556 + 0.189167i 0.958203 0.286089i \(-0.0923553\pi\)
−0.879847 + 0.475256i \(0.842355\pi\)
\(198\) 0 0
\(199\) −135.618 135.618i −0.681498 0.681498i 0.278840 0.960338i \(-0.410050\pi\)
−0.960338 + 0.278840i \(0.910050\pi\)
\(200\) −23.2343 352.418i −0.116172 1.76209i
\(201\) 0 0
\(202\) −14.2241 + 36.5911i −0.0704164 + 0.181144i
\(203\) 83.6250 + 201.889i 0.411946 + 0.994526i
\(204\) 0 0
\(205\) 95.0411 229.450i 0.463615 1.11927i
\(206\) 0.0365664 + 1.66605i 0.000177507 + 0.00808763i
\(207\) 0 0
\(208\) −35.4065 + 112.495i −0.170223 + 0.540844i
\(209\) 28.6019i 0.136851i
\(210\) 0 0
\(211\) 138.015 + 57.1678i 0.654100 + 0.270937i 0.684954 0.728587i \(-0.259822\pi\)
−0.0308532 + 0.999524i \(0.509822\pi\)
\(212\) −41.4032 88.7303i −0.195298 0.418539i
\(213\) 0 0
\(214\) −105.011 + 270.138i −0.490706 + 1.26233i
\(215\) 1.57484 1.57484i 0.00732483 0.00732483i
\(216\) 0 0
\(217\) −15.1097 + 15.1097i −0.0696298 + 0.0696298i
\(218\) 140.639 61.9039i 0.645131 0.283963i
\(219\) 0 0
\(220\) 391.053 + 358.150i 1.77751 + 1.62795i
\(221\) 25.0027 + 10.3564i 0.113134 + 0.0468618i
\(222\) 0 0
\(223\) 30.6228i 0.137322i −0.997640 0.0686609i \(-0.978127\pi\)
0.997640 0.0686609i \(-0.0218727\pi\)
\(224\) −18.2050 165.253i −0.0812721 0.737736i
\(225\) 0 0
\(226\) −185.679 + 194.013i −0.821589 + 0.858463i
\(227\) −8.41171 + 20.3077i −0.0370560 + 0.0894611i −0.941324 0.337504i \(-0.890417\pi\)
0.904268 + 0.426965i \(0.140417\pi\)
\(228\) 0 0
\(229\) 76.6532 + 185.057i 0.334730 + 0.808110i 0.998204 + 0.0599101i \(0.0190814\pi\)
−0.663474 + 0.748199i \(0.730919\pi\)
\(230\) 78.7898 + 179.001i 0.342564 + 0.778267i
\(231\) 0 0
\(232\) −301.729 + 148.940i −1.30056 + 0.641983i
\(233\) 127.558 + 127.558i 0.547461 + 0.547461i 0.925706 0.378245i \(-0.123472\pi\)
−0.378245 + 0.925706i \(0.623472\pi\)
\(234\) 0 0
\(235\) 125.327 + 302.567i 0.533308 + 1.28752i
\(236\) 185.603 + 397.761i 0.786452 + 1.68543i
\(237\) 0 0
\(238\) −38.1408 + 0.837110i −0.160255 + 0.00351727i
\(239\) −397.241 −1.66210 −0.831048 0.556200i \(-0.812259\pi\)
−0.831048 + 0.556200i \(0.812259\pi\)
\(240\) 0 0
\(241\) 401.128i 1.66443i −0.554451 0.832216i \(-0.687072\pi\)
0.554451 0.832216i \(-0.312928\pi\)
\(242\) −266.255 + 5.84374i −1.10023 + 0.0241477i
\(243\) 0 0
\(244\) 20.7869 57.1571i 0.0851924 0.234250i
\(245\) 169.077 70.0338i 0.690109 0.285852i
\(246\) 0 0
\(247\) −9.35087 + 9.35087i −0.0378578 + 0.0378578i
\(248\) −24.7464 21.6853i −0.0997840 0.0874406i
\(249\) 0 0
\(250\) −128.291 291.463i −0.513166 1.16585i
\(251\) −220.193 + 91.2070i −0.877264 + 0.363375i −0.775435 0.631427i \(-0.782469\pi\)
−0.101829 + 0.994802i \(0.532469\pi\)
\(252\) 0 0
\(253\) −173.205 71.7440i −0.684606 0.283573i
\(254\) 132.066 137.993i 0.519943 0.543279i
\(255\) 0 0
\(256\) 252.065 44.7116i 0.984630 0.174655i
\(257\) −436.624 −1.69893 −0.849463 0.527648i \(-0.823074\pi\)
−0.849463 + 0.527648i \(0.823074\pi\)
\(258\) 0 0
\(259\) −103.263 + 249.299i −0.398699 + 0.962545i
\(260\) 10.7569 + 244.938i 0.0413729 + 0.942070i
\(261\) 0 0
\(262\) 321.055 141.316i 1.22540 0.539376i
\(263\) 324.662 + 324.662i 1.23445 + 1.23445i 0.962235 + 0.272219i \(0.0877576\pi\)
0.272219 + 0.962235i \(0.412242\pi\)
\(264\) 0 0
\(265\) −143.934 143.934i −0.543146 0.543146i
\(266\) 6.75430 17.3752i 0.0253921 0.0653204i
\(267\) 0 0
\(268\) 36.0946 + 13.1269i 0.134681 + 0.0489810i
\(269\) 98.7998 238.524i 0.367286 0.886706i −0.626907 0.779094i \(-0.715680\pi\)
0.994193 0.107612i \(-0.0343205\pi\)
\(270\) 0 0
\(271\) −91.7678 −0.338627 −0.169313 0.985562i \(-0.554155\pi\)
−0.169313 + 0.985562i \(0.554155\pi\)
\(272\) −5.14981 58.5181i −0.0189331 0.215140i
\(273\) 0 0
\(274\) −5.50651 250.890i −0.0200968 0.915658i
\(275\) 650.247 + 269.341i 2.36453 + 0.979422i
\(276\) 0 0
\(277\) 42.7749 17.7179i 0.154422 0.0639636i −0.304134 0.952629i \(-0.598367\pi\)
0.458556 + 0.888666i \(0.348367\pi\)
\(278\) 52.4212 134.852i 0.188566 0.485079i
\(279\) 0 0
\(280\) −152.982 309.918i −0.546365 1.10685i
\(281\) 167.424 167.424i 0.595813 0.595813i −0.343382 0.939196i \(-0.611573\pi\)
0.939196 + 0.343382i \(0.111573\pi\)
\(282\) 0 0
\(283\) −494.380 + 204.779i −1.74693 + 0.723601i −0.748775 + 0.662824i \(0.769358\pi\)
−0.998151 + 0.0607762i \(0.980642\pi\)
\(284\) 289.495 316.091i 1.01935 1.11300i
\(285\) 0 0
\(286\) −169.792 162.499i −0.593679 0.568179i
\(287\) 155.168i 0.540653i
\(288\) 0 0
\(289\) 275.520 0.953356
\(290\) −483.660 + 505.367i −1.66779 + 1.74265i
\(291\) 0 0
\(292\) 110.943 121.136i 0.379943 0.414848i
\(293\) −146.767 354.328i −0.500913 1.20931i −0.948987 0.315314i \(-0.897890\pi\)
0.448075 0.893996i \(-0.352110\pi\)
\(294\) 0 0
\(295\) 645.227 + 645.227i 2.18721 + 2.18721i
\(296\) −393.506 133.409i −1.32941 0.450707i
\(297\) 0 0
\(298\) 202.851 + 78.8545i 0.680707 + 0.264613i
\(299\) −33.1709 80.0817i −0.110940 0.267832i
\(300\) 0 0
\(301\) 0.532500 1.28557i 0.00176910 0.00427099i
\(302\) −380.916 + 8.36030i −1.26131 + 0.0276831i
\(303\) 0 0
\(304\) 27.3811 + 8.61784i 0.0900694 + 0.0283482i
\(305\) 126.437i 0.414547i
\(306\) 0 0
\(307\) −53.4306 22.1317i −0.174041 0.0720902i 0.293962 0.955817i \(-0.405026\pi\)
−0.468003 + 0.883727i \(0.655026\pi\)
\(308\) 311.356 + 113.234i 1.01090 + 0.367644i
\(309\) 0 0
\(310\) −63.7547 24.7835i −0.205660 0.0799466i
\(311\) −274.515 + 274.515i −0.882685 + 0.882685i −0.993807 0.111122i \(-0.964556\pi\)
0.111122 + 0.993807i \(0.464556\pi\)
\(312\) 0 0
\(313\) −78.4013 + 78.4013i −0.250483 + 0.250483i −0.821169 0.570685i \(-0.806678\pi\)
0.570685 + 0.821169i \(0.306678\pi\)
\(314\) −48.8820 111.054i −0.155675 0.353676i
\(315\) 0 0
\(316\) 0.485353 + 11.0516i 0.00153593 + 0.0349734i
\(317\) 136.520 + 56.5483i 0.430661 + 0.178386i 0.587475 0.809243i \(-0.300122\pi\)
−0.156814 + 0.987628i \(0.550122\pi\)
\(318\) 0 0
\(319\) 670.551i 2.10204i
\(320\) 460.689 266.450i 1.43965 0.832656i
\(321\) 0 0
\(322\) 88.2775 + 84.4857i 0.274154 + 0.262378i
\(323\) 2.52073 6.08558i 0.00780412 0.0188408i
\(324\) 0 0
\(325\) 124.530 + 300.643i 0.383170 + 0.925054i
\(326\) 410.232 180.569i 1.25838 0.553893i
\(327\) 0 0
\(328\) 238.413 15.7182i 0.726870 0.0479214i
\(329\) 144.684 + 144.684i 0.439769 + 0.439769i
\(330\) 0 0
\(331\) 143.690 + 346.898i 0.434109 + 1.04803i 0.977949 + 0.208843i \(0.0669696\pi\)
−0.543841 + 0.839189i \(0.683030\pi\)
\(332\) −117.193 + 322.241i −0.352990 + 0.970605i
\(333\) 0 0
\(334\) −4.50823 205.406i −0.0134977 0.614988i
\(335\) 79.8446 0.238342
\(336\) 0 0
\(337\) 479.136i 1.42177i −0.703310 0.710884i \(-0.748295\pi\)
0.703310 0.710884i \(-0.251705\pi\)
\(338\) 5.03226 + 229.282i 0.0148883 + 0.678349i
\(339\) 0 0
\(340\) −51.6394 110.667i −0.151881 0.325492i
\(341\) 60.5787 25.0925i 0.177650 0.0735851i
\(342\) 0 0
\(343\) 260.861 260.861i 0.760529 0.760529i
\(344\) 2.02920 + 0.687955i 0.00589885 + 0.00199987i
\(345\) 0 0
\(346\) 19.3957 8.53725i 0.0560568 0.0246741i
\(347\) −172.145 + 71.3048i −0.496095 + 0.205489i −0.616680 0.787214i \(-0.711523\pi\)
0.120585 + 0.992703i \(0.461523\pi\)
\(348\) 0 0
\(349\) 388.120 + 160.765i 1.11209 + 0.460644i 0.861658 0.507490i \(-0.169427\pi\)
0.250434 + 0.968134i \(0.419427\pi\)
\(350\) −331.411 317.176i −0.946889 0.906217i
\(351\) 0 0
\(352\) −142.444 + 489.867i −0.404669 + 1.39167i
\(353\) 165.952 0.470120 0.235060 0.971981i \(-0.424471\pi\)
0.235060 + 0.971981i \(0.424471\pi\)
\(354\) 0 0
\(355\) 340.995 823.235i 0.960550 2.31897i
\(356\) −302.111 276.691i −0.848626 0.777223i
\(357\) 0 0
\(358\) −186.760 424.297i −0.521676 1.18519i
\(359\) −100.971 100.971i −0.281257 0.281257i 0.552353 0.833610i \(-0.313730\pi\)
−0.833610 + 0.552353i \(0.813730\pi\)
\(360\) 0 0
\(361\) −252.990 252.990i −0.700802 0.700802i
\(362\) −198.163 77.0322i −0.547412 0.212796i
\(363\) 0 0
\(364\) 64.7724 + 138.812i 0.177946 + 0.381352i
\(365\) 130.680 315.489i 0.358027 0.864353i
\(366\) 0 0
\(367\) −651.959 −1.77645 −0.888227 0.459405i \(-0.848063\pi\)
−0.888227 + 0.459405i \(0.848063\pi\)
\(368\) −120.869 + 144.196i −0.328449 + 0.391836i
\(369\) 0 0
\(370\) −863.579 + 18.9537i −2.33400 + 0.0512263i
\(371\) −117.496 48.6683i −0.316700 0.131181i
\(372\) 0 0
\(373\) 605.919 250.980i 1.62445 0.672868i 0.629854 0.776713i \(-0.283115\pi\)
0.994593 + 0.103845i \(0.0331146\pi\)
\(374\) 109.111 + 42.4150i 0.291742 + 0.113409i
\(375\) 0 0
\(376\) −207.649 + 236.962i −0.552259 + 0.630218i
\(377\) 219.224 219.224i 0.581497 0.581497i
\(378\) 0 0
\(379\) −431.591 + 178.771i −1.13876 + 0.471691i −0.870750 0.491725i \(-0.836366\pi\)
−0.268011 + 0.963416i \(0.586366\pi\)
\(380\) 59.6173 2.61821i 0.156888 0.00689003i
\(381\) 0 0
\(382\) 251.459 262.744i 0.658269 0.687812i
\(383\) 583.987i 1.52477i −0.647124 0.762385i \(-0.724028\pi\)
0.647124 0.762385i \(-0.275972\pi\)
\(384\) 0 0
\(385\) 688.749 1.78896
\(386\) −319.710 305.977i −0.828263 0.792687i
\(387\) 0 0
\(388\) 11.5919 + 263.950i 0.0298760 + 0.680284i
\(389\) 57.9070 + 139.800i 0.148861 + 0.359383i 0.980667 0.195684i \(-0.0626927\pi\)
−0.831806 + 0.555067i \(0.812693\pi\)
\(390\) 0 0
\(391\) 30.5297 + 30.5297i 0.0780812 + 0.0780812i
\(392\) 132.416 + 116.036i 0.337796 + 0.296010i
\(393\) 0 0
\(394\) −29.2293 + 75.1914i −0.0741860 + 0.190841i
\(395\) 8.80061 + 21.2466i 0.0222800 + 0.0537888i
\(396\) 0 0
\(397\) 216.482 522.634i 0.545295 1.31646i −0.375649 0.926762i \(-0.622580\pi\)
0.920944 0.389696i \(-0.127420\pi\)
\(398\) −8.41688 383.493i −0.0211479 0.963551i
\(399\) 0 0
\(400\) 453.767 541.340i 1.13442 1.35335i
\(401\) 271.900i 0.678055i 0.940776 + 0.339028i \(0.110098\pi\)
−0.940776 + 0.339028i \(0.889902\pi\)
\(402\) 0 0
\(403\) 28.0087 + 11.6016i 0.0695004 + 0.0287880i
\(404\) −71.1521 + 33.2009i −0.176119 + 0.0821805i
\(405\) 0 0
\(406\) −158.350 + 407.350i −0.390024 + 1.00333i
\(407\) 585.498 585.498i 1.43857 1.43857i
\(408\) 0 0
\(409\) −181.723 + 181.723i −0.444310 + 0.444310i −0.893458 0.449147i \(-0.851728\pi\)
0.449147 + 0.893458i \(0.351728\pi\)
\(410\) 454.618 200.106i 1.10882 0.488063i
\(411\) 0 0
\(412\) −2.25105 + 2.45785i −0.00546372 + 0.00596566i
\(413\) 526.710 + 218.171i 1.27533 + 0.528258i
\(414\) 0 0
\(415\) 712.826i 1.71765i
\(416\) −206.722 + 113.584i −0.496929 + 0.273038i
\(417\) 0 0
\(418\) −39.5519 + 41.3270i −0.0946217 + 0.0988684i
\(419\) 84.5458 204.112i 0.201780 0.487140i −0.790304 0.612715i \(-0.790077\pi\)
0.992084 + 0.125575i \(0.0400775\pi\)
\(420\) 0 0
\(421\) 13.1417 + 31.7269i 0.0312155 + 0.0753608i 0.938719 0.344685i \(-0.112014\pi\)
−0.907503 + 0.420045i \(0.862014\pi\)
\(422\) 120.365 + 273.455i 0.285225 + 0.647998i
\(423\) 0 0
\(424\) 62.8762 185.461i 0.148293 0.437408i
\(425\) −114.615 114.615i −0.269682 0.269682i
\(426\) 0 0
\(427\) −30.2302 72.9823i −0.0707968 0.170919i
\(428\) −525.289 + 245.110i −1.22731 + 0.572686i
\(429\) 0 0
\(430\) 4.45324 0.0977393i 0.0103564 0.000227301i
\(431\) −18.4839 −0.0428861 −0.0214431 0.999770i \(-0.506826\pi\)
−0.0214431 + 0.999770i \(0.506826\pi\)
\(432\) 0 0
\(433\) 370.297i 0.855190i 0.903970 + 0.427595i \(0.140639\pi\)
−0.903970 + 0.427595i \(0.859361\pi\)
\(434\) −42.7263 + 0.937752i −0.0984476 + 0.00216072i
\(435\) 0 0
\(436\) 288.813 + 105.036i 0.662414 + 0.240907i
\(437\) −19.4917 + 8.07372i −0.0446034 + 0.0184753i
\(438\) 0 0
\(439\) −1.47108 + 1.47108i −0.00335099 + 0.00335099i −0.708780 0.705429i \(-0.750754\pi\)
0.705429 + 0.708780i \(0.250754\pi\)
\(440\) 69.7691 + 1058.26i 0.158566 + 2.40513i
\(441\) 0 0
\(442\) 21.8052 + 49.5388i 0.0493329 + 0.112079i
\(443\) −15.4970 + 6.41908i −0.0349820 + 0.0144900i −0.400106 0.916469i \(-0.631027\pi\)
0.365124 + 0.930959i \(0.381027\pi\)
\(444\) 0 0
\(445\) −786.825 325.914i −1.76815 0.732390i
\(446\) 42.3464 44.2470i 0.0949472 0.0992085i
\(447\) 0 0
\(448\) 202.214 263.949i 0.451370 0.589172i
\(449\) 349.645 0.778719 0.389359 0.921086i \(-0.372696\pi\)
0.389359 + 0.921086i \(0.372696\pi\)
\(450\) 0 0
\(451\) −182.211 + 439.897i −0.404016 + 0.975382i
\(452\) −536.577 + 23.5648i −1.18712 + 0.0521346i
\(453\) 0 0
\(454\) −40.2364 + 17.7106i −0.0886264 + 0.0390101i
\(455\) 225.174 + 225.174i 0.494888 + 0.494888i
\(456\) 0 0
\(457\) 167.442 + 167.442i 0.366393 + 0.366393i 0.866160 0.499767i \(-0.166581\pi\)
−0.499767 + 0.866160i \(0.666581\pi\)
\(458\) −145.148 + 373.389i −0.316917 + 0.815260i
\(459\) 0 0
\(460\) −133.687 + 367.594i −0.290623 + 0.799117i
\(461\) −299.864 + 723.935i −0.650463 + 1.57036i 0.161644 + 0.986849i \(0.448320\pi\)
−0.812107 + 0.583508i \(0.801680\pi\)
\(462\) 0 0
\(463\) −70.4485 −0.152157 −0.0760783 0.997102i \(-0.524240\pi\)
−0.0760783 + 0.997102i \(0.524240\pi\)
\(464\) −641.930 202.039i −1.38347 0.435429i
\(465\) 0 0
\(466\) 7.91667 + 360.703i 0.0169886 + 0.774040i
\(467\) 89.8391 + 37.2126i 0.192375 + 0.0796843i 0.476791 0.879017i \(-0.341800\pi\)
−0.284416 + 0.958701i \(0.591800\pi\)
\(468\) 0 0
\(469\) 46.0882 19.0904i 0.0982691 0.0407044i
\(470\) −237.316 + 610.489i −0.504928 + 1.29891i
\(471\) 0 0
\(472\) −281.862 + 831.386i −0.597166 + 1.76141i
\(473\) −3.01925 + 3.01925i −0.00638320 + 0.00638320i
\(474\) 0 0
\(475\) 73.1756 30.3103i 0.154054 0.0638112i
\(476\) −56.2673 51.5331i −0.118209 0.108263i
\(477\) 0 0
\(478\) −573.975 549.321i −1.20079 1.14921i
\(479\) 900.546i 1.88005i 0.341101 + 0.940027i \(0.389200\pi\)
−0.341101 + 0.940027i \(0.610800\pi\)
\(480\) 0 0
\(481\) 382.836 0.795917
\(482\) 554.697 579.592i 1.15082 1.20247i
\(483\) 0 0
\(484\) −392.794 359.745i −0.811558 0.743274i
\(485\) 210.189 + 507.440i 0.433379 + 1.04627i
\(486\) 0 0
\(487\) −175.466 175.466i −0.360301 0.360301i 0.503623 0.863924i \(-0.332000\pi\)
−0.863924 + 0.503623i \(0.832000\pi\)
\(488\) 109.074 53.8415i 0.223513 0.110331i
\(489\) 0 0
\(490\) 341.145 + 132.614i 0.696215 + 0.270641i
\(491\) 111.990 + 270.368i 0.228086 + 0.550648i 0.995944 0.0899713i \(-0.0286775\pi\)
−0.767858 + 0.640620i \(0.778678\pi\)
\(492\) 0 0
\(493\) −59.0968 + 142.672i −0.119872 + 0.289396i
\(494\) −26.4419 + 0.580344i −0.0535261 + 0.00117478i
\(495\) 0 0
\(496\) −5.76895 65.5535i −0.0116309 0.132164i
\(497\) 556.721i 1.12016i
\(498\) 0 0
\(499\) 96.4128 + 39.9355i 0.193212 + 0.0800310i 0.477192 0.878799i \(-0.341655\pi\)
−0.283980 + 0.958830i \(0.591655\pi\)
\(500\) 217.679 598.544i 0.435358 1.19709i
\(501\) 0 0
\(502\) −444.283 172.707i −0.885026 0.344038i
\(503\) −491.151 + 491.151i −0.976442 + 0.976442i −0.999729 0.0232864i \(-0.992587\pi\)
0.0232864 + 0.999729i \(0.492587\pi\)
\(504\) 0 0
\(505\) −115.419 + 115.419i −0.228553 + 0.228553i
\(506\) −151.055 343.179i −0.298527 0.678219i
\(507\) 0 0
\(508\) 381.644 16.7607i 0.751268 0.0329934i
\(509\) −891.336 369.204i −1.75115 0.725351i −0.997695 0.0678534i \(-0.978385\pi\)
−0.753457 0.657498i \(-0.771615\pi\)
\(510\) 0 0
\(511\) 213.352i 0.417519i
\(512\) 426.039 + 283.962i 0.832108 + 0.554614i
\(513\) 0 0
\(514\) −630.880 603.782i −1.22739 1.17467i
\(515\) −2.65150 + 6.40130i −0.00514855 + 0.0124297i
\(516\) 0 0
\(517\) −240.276 580.077i −0.464750 1.12201i
\(518\) −493.946 + 217.417i −0.953564 + 0.419724i
\(519\) 0 0
\(520\) −323.168 + 368.787i −0.621477 + 0.709207i
\(521\) −285.723 285.723i −0.548413 0.548413i 0.377569 0.925982i \(-0.376760\pi\)
−0.925982 + 0.377569i \(0.876760\pi\)
\(522\) 0 0
\(523\) 260.696 + 629.375i 0.498462 + 1.20339i 0.950312 + 0.311300i \(0.100764\pi\)
−0.451849 + 0.892094i \(0.649236\pi\)
\(524\) 659.312 + 239.779i 1.25823 + 0.457594i
\(525\) 0 0
\(526\) 20.1495 + 918.060i 0.0383070 + 1.74536i
\(527\) −15.1007 −0.0286541
\(528\) 0 0
\(529\) 390.712i 0.738586i
\(530\) −8.93297 407.008i −0.0168547 0.767939i
\(531\) 0 0
\(532\) 33.7865 15.7654i 0.0635085 0.0296343i
\(533\) −203.387 + 84.2457i −0.381589 + 0.158059i
\(534\) 0 0
\(535\) −852.096 + 852.096i −1.59270 + 1.59270i
\(536\) 34.0008 + 68.8802i 0.0634343 + 0.128508i
\(537\) 0 0
\(538\) 472.597 208.020i 0.878433 0.386654i
\(539\) −324.151 + 134.268i −0.601393 + 0.249105i
\(540\) 0 0
\(541\) 355.077 + 147.078i 0.656335 + 0.271863i 0.685895 0.727700i \(-0.259411\pi\)
−0.0295603 + 0.999563i \(0.509411\pi\)
\(542\) −132.596 126.900i −0.244642 0.234134i
\(543\) 0 0
\(544\) 73.4803 91.6745i 0.135074 0.168519i
\(545\) 638.880 1.17226
\(546\) 0 0
\(547\) 404.897 977.508i 0.740214 1.78704i 0.135204 0.990818i \(-0.456831\pi\)
0.605010 0.796218i \(-0.293169\pi\)
\(548\) 338.985 370.127i 0.618586 0.675414i
\(549\) 0 0
\(550\) 567.089 + 1288.36i 1.03107 + 2.34247i
\(551\) −53.3586 53.3586i −0.0968396 0.0968396i
\(552\) 0 0
\(553\) 10.1598 + 10.1598i 0.0183722 + 0.0183722i
\(554\) 86.3067 + 33.5501i 0.155788 + 0.0605598i
\(555\) 0 0
\(556\) 262.222 122.358i 0.471623 0.220068i
\(557\) 296.952 716.907i 0.533128 1.28709i −0.396313 0.918115i \(-0.629711\pi\)
0.929441 0.368970i \(-0.120289\pi\)
\(558\) 0 0
\(559\) −1.97418 −0.00353163
\(560\) 207.522 659.352i 0.370576 1.17741i
\(561\) 0 0
\(562\) 473.431 10.3908i 0.842405 0.0184890i
\(563\) 44.6869 + 18.5099i 0.0793728 + 0.0328773i 0.422017 0.906588i \(-0.361322\pi\)
−0.342644 + 0.939465i \(0.611322\pi\)
\(564\) 0 0
\(565\) −1031.56 + 427.287i −1.82577 + 0.756260i
\(566\) −997.509 387.763i −1.76238 0.685094i
\(567\) 0 0
\(568\) 855.396 56.3949i 1.50598 0.0992868i
\(569\) −487.094 + 487.094i −0.856053 + 0.856053i −0.990870 0.134818i \(-0.956955\pi\)
0.134818 + 0.990870i \(0.456955\pi\)
\(570\) 0 0
\(571\) −252.561 + 104.614i −0.442313 + 0.183212i −0.592714 0.805413i \(-0.701944\pi\)
0.150401 + 0.988625i \(0.451944\pi\)
\(572\) −20.6230 469.592i −0.0360543 0.820964i
\(573\) 0 0
\(574\) 214.572 224.202i 0.373819 0.390596i
\(575\) 519.161i 0.902889i
\(576\) 0 0
\(577\) 460.004 0.797234 0.398617 0.917118i \(-0.369490\pi\)
0.398617 + 0.917118i \(0.369490\pi\)
\(578\) 398.100 + 381.000i 0.688754 + 0.659170i
\(579\) 0 0
\(580\) −1397.69 + 61.3821i −2.40980 + 0.105831i
\(581\) 170.432 + 411.460i 0.293343 + 0.708193i
\(582\) 0 0
\(583\) 275.947 + 275.947i 0.473323 + 0.473323i
\(584\) 327.814 21.6123i 0.561325 0.0370073i
\(585\) 0 0
\(586\) 277.914 714.926i 0.474257 1.22001i
\(587\) −68.3015 164.895i −0.116357 0.280911i 0.854962 0.518690i \(-0.173580\pi\)
−0.971319 + 0.237780i \(0.923580\pi\)
\(588\) 0 0
\(589\) 2.82379 6.81723i 0.00479421 0.0115742i
\(590\) 40.0448 + 1824.54i 0.0678725 + 3.09244i
\(591\) 0 0
\(592\) −384.095 736.920i −0.648809 1.24480i
\(593\) 167.545i 0.282538i −0.989971 0.141269i \(-0.954882\pi\)
0.989971 0.141269i \(-0.0451182\pi\)
\(594\) 0 0
\(595\) −146.544 60.7006i −0.246293 0.102018i
\(596\) 184.057 + 394.448i 0.308820 + 0.661825i
\(597\) 0 0
\(598\) 62.8115 161.581i 0.105036 0.270202i
\(599\) 316.998 316.998i 0.529213 0.529213i −0.391125 0.920338i \(-0.627914\pi\)
0.920338 + 0.391125i \(0.127914\pi\)
\(600\) 0 0
\(601\) −224.198 + 224.198i −0.373042 + 0.373042i −0.868584 0.495542i \(-0.834970\pi\)
0.495542 + 0.868584i \(0.334970\pi\)
\(602\) 2.54715 1.12116i 0.00423114 0.00186239i
\(603\) 0 0
\(604\) −561.948 514.666i −0.930377 0.852096i
\(605\) −1023.00 423.742i −1.69091 0.700400i
\(606\) 0 0
\(607\) 89.2468i 0.147029i −0.997294 0.0735146i \(-0.976578\pi\)
0.997294 0.0735146i \(-0.0234216\pi\)
\(608\) 27.6459 + 50.3157i 0.0454703 + 0.0827560i
\(609\) 0 0
\(610\) 174.842 182.689i 0.286626 0.299490i
\(611\) 111.092 268.200i 0.181820 0.438952i
\(612\) 0 0
\(613\) 202.134 + 487.995i 0.329746 + 0.796076i 0.998611 + 0.0526926i \(0.0167803\pi\)
−0.668865 + 0.743384i \(0.733220\pi\)
\(614\) −46.5975 105.864i −0.0758918 0.172417i
\(615\) 0 0
\(616\) 293.295 + 594.169i 0.476128 + 0.964560i
\(617\) −380.984 380.984i −0.617479 0.617479i 0.327405 0.944884i \(-0.393826\pi\)
−0.944884 + 0.327405i \(0.893826\pi\)
\(618\) 0 0
\(619\) −371.320 896.447i −0.599871 1.44822i −0.873712 0.486443i \(-0.838294\pi\)
0.273841 0.961775i \(-0.411706\pi\)
\(620\) −57.8478 123.972i −0.0933029 0.199955i
\(621\) 0 0
\(622\) −776.259 + 17.0373i −1.24800 + 0.0273911i
\(623\) −532.098 −0.854090
\(624\) 0 0
\(625\) 220.337i 0.352539i
\(626\) −221.699 + 4.86583i −0.354152 + 0.00777289i
\(627\) 0 0
\(628\) 82.9407 228.059i 0.132071 0.363151i
\(629\) −176.177 + 72.9747i −0.280090 + 0.116017i
\(630\) 0 0
\(631\) 384.726 384.726i 0.609708 0.609708i −0.333162 0.942870i \(-0.608115\pi\)
0.942870 + 0.333162i \(0.108115\pi\)
\(632\) −14.5813 + 16.6397i −0.0230717 + 0.0263286i
\(633\) 0 0
\(634\) 119.061 + 270.492i 0.187793 + 0.426643i
\(635\) 733.706 303.911i 1.15544 0.478600i
\(636\) 0 0
\(637\) −149.872 62.0789i −0.235277 0.0974551i
\(638\) 927.266 968.882i 1.45339 1.51862i
\(639\) 0 0
\(640\) 1034.11 + 252.065i 1.61580 + 0.393851i
\(641\) 407.931 0.636398 0.318199 0.948024i \(-0.396922\pi\)
0.318199 + 0.948024i \(0.396922\pi\)
\(642\) 0 0
\(643\) −319.302 + 770.863i −0.496582 + 1.19885i 0.454732 + 0.890629i \(0.349735\pi\)
−0.951313 + 0.308226i \(0.900265\pi\)
\(644\) 10.7222 + 244.148i 0.0166494 + 0.379111i
\(645\) 0 0
\(646\) 12.0576 5.30732i 0.0186650 0.00821566i
\(647\) 48.6565 + 48.6565i 0.0752033 + 0.0752033i 0.743708 0.668505i \(-0.233065\pi\)
−0.668505 + 0.743708i \(0.733065\pi\)
\(648\) 0 0
\(649\) −1237.02 1237.02i −1.90604 1.90604i
\(650\) −235.807 + 606.606i −0.362780 + 0.933239i
\(651\) 0 0
\(652\) 842.445 + 306.381i 1.29209 + 0.469910i
\(653\) 290.106 700.378i 0.444267 1.07255i −0.530170 0.847892i \(-0.677872\pi\)
0.974436 0.224663i \(-0.0721282\pi\)
\(654\) 0 0
\(655\) 1458.46 2.22665
\(656\) 366.220 + 306.977i 0.558263 + 0.467952i
\(657\) 0 0
\(658\) 8.97953 + 409.129i 0.0136467 + 0.621777i
\(659\) −818.045 338.845i −1.24134 0.514181i −0.337209 0.941430i \(-0.609483\pi\)
−0.904134 + 0.427248i \(0.859483\pi\)
\(660\) 0 0
\(661\) −35.2123 + 14.5854i −0.0532712 + 0.0220657i −0.409160 0.912463i \(-0.634178\pi\)
0.355889 + 0.934528i \(0.384178\pi\)
\(662\) −272.087 + 699.936i −0.411008 + 1.05730i
\(663\) 0 0
\(664\) −614.940 + 303.548i −0.926115 + 0.457151i
\(665\) 54.8067 54.8067i 0.0824161 0.0824161i
\(666\) 0 0
\(667\) 456.969 189.283i 0.685110 0.283782i
\(668\) 277.530 303.026i 0.415464 0.453632i
\(669\) 0 0
\(670\) 115.368 + 110.412i 0.172191 + 0.164795i
\(671\) 242.402i 0.361256i
\(672\) 0 0
\(673\) 114.199 0.169687 0.0848434 0.996394i \(-0.472961\pi\)
0.0848434 + 0.996394i \(0.472961\pi\)
\(674\) 662.569 692.305i 0.983039 1.02716i
\(675\) 0 0
\(676\) −309.789 + 338.249i −0.458268 + 0.500369i
\(677\) 212.733 + 513.583i 0.314229 + 0.758617i 0.999539 + 0.0303647i \(0.00966689\pi\)
−0.685310 + 0.728252i \(0.740333\pi\)
\(678\) 0 0
\(679\) 242.652 + 242.652i 0.357366 + 0.357366i
\(680\) 78.4212 231.313i 0.115325 0.340166i
\(681\) 0 0
\(682\) 122.229 + 47.5144i 0.179222 + 0.0696693i
\(683\) −363.453 877.454i −0.532142 1.28471i −0.930102 0.367302i \(-0.880281\pi\)
0.397959 0.917403i \(-0.369719\pi\)
\(684\) 0 0
\(685\) 399.289 963.969i 0.582904 1.40725i
\(686\) 737.650 16.1899i 1.07529 0.0236004i
\(687\) 0 0
\(688\) 1.98067 + 3.80010i 0.00287889 + 0.00552340i
\(689\) 180.432i 0.261875i
\(690\) 0 0
\(691\) −682.306 282.620i −0.987418 0.409002i −0.170249 0.985401i \(-0.554457\pi\)
−0.817168 + 0.576399i \(0.804457\pi\)
\(692\) 39.8306 + 14.4856i 0.0575586 + 0.0209330i
\(693\) 0 0
\(694\) −347.336 135.021i −0.500485 0.194554i
\(695\) 425.364 425.364i 0.612034 0.612034i
\(696\) 0 0
\(697\) 77.5377 77.5377i 0.111245 0.111245i
\(698\) 338.485 + 768.998i 0.484935 + 1.10172i
\(699\) 0 0
\(700\) −40.2533 916.578i −0.0575047 1.30940i
\(701\) 565.621 + 234.288i 0.806878 + 0.334220i 0.747708 0.664028i \(-0.231154\pi\)
0.0591703 + 0.998248i \(0.481154\pi\)
\(702\) 0 0
\(703\) 93.1812i 0.132548i
\(704\) −883.225 + 510.833i −1.25458 + 0.725616i
\(705\) 0 0
\(706\) 239.785 + 229.486i 0.339639 + 0.325051i
\(707\) −39.0267 + 94.2188i −0.0552004 + 0.133266i
\(708\) 0 0
\(709\) 447.695 + 1080.83i 0.631446 + 1.52444i 0.837806 + 0.545968i \(0.183838\pi\)
−0.206360 + 0.978476i \(0.566162\pi\)
\(710\) 1631.11 717.954i 2.29734 1.01120i
\(711\) 0 0
\(712\) −53.9007 817.564i −0.0757032 1.14826i
\(713\) 34.2002 + 34.2002i 0.0479666 + 0.0479666i
\(714\) 0 0
\(715\) −373.945 902.783i −0.523000 1.26263i
\(716\) 316.885 871.328i 0.442577 1.21694i
\(717\) 0 0
\(718\) −6.26658 285.521i −0.00872783 0.397661i
\(719\) −122.001 −0.169681 −0.0848406 0.996395i \(-0.527038\pi\)
−0.0848406 + 0.996395i \(0.527038\pi\)
\(720\) 0 0
\(721\) 4.32894i 0.00600408i
\(722\) −15.7013 715.390i −0.0217470 0.990845i
\(723\) 0 0
\(724\) −179.803 385.332i −0.248347 0.532227i
\(725\) −1715.55 + 710.604i −2.36628 + 0.980144i
\(726\) 0 0
\(727\) 438.189 438.189i 0.602736 0.602736i −0.338301 0.941038i \(-0.609852\pi\)
0.941038 + 0.338301i \(0.109852\pi\)
\(728\) −98.3654 + 290.140i −0.135117 + 0.398545i
\(729\) 0 0
\(730\) 625.091 275.142i 0.856289 0.376907i
\(731\) 0.908495 0.376311i 0.00124281 0.000514789i
\(732\) 0 0
\(733\) −629.241 260.640i −0.858446 0.355580i −0.0903463 0.995910i \(-0.528797\pi\)
−0.768099 + 0.640331i \(0.778797\pi\)
\(734\) −942.018 901.555i −1.28340 1.22828i
\(735\) 0 0
\(736\) −374.044 + 41.2063i −0.508212 + 0.0559869i
\(737\) −153.077 −0.207703
\(738\) 0 0
\(739\) 55.5902 134.207i 0.0752235 0.181606i −0.881795 0.471633i \(-0.843665\pi\)
0.957018 + 0.290028i \(0.0936646\pi\)
\(740\) −1274.00 1166.81i −1.72162 1.57676i
\(741\) 0 0
\(742\) −102.469 232.799i −0.138099 0.313745i
\(743\) 180.295 + 180.295i 0.242658 + 0.242658i 0.817949 0.575291i \(-0.195111\pi\)
−0.575291 + 0.817949i \(0.695111\pi\)
\(744\) 0 0
\(745\) 639.853 + 639.853i 0.858863 + 0.858863i
\(746\) 1222.56 + 475.248i 1.63882 + 0.637062i
\(747\) 0 0
\(748\) 99.0022 + 212.169i 0.132356 + 0.283649i
\(749\) −288.119 + 695.581i −0.384672 + 0.928680i
\(750\) 0 0
\(751\) −264.213 −0.351815 −0.175908 0.984407i \(-0.556286\pi\)
−0.175908 + 0.984407i \(0.556286\pi\)
\(752\) −627.714 + 55.2411i −0.834726 + 0.0734589i
\(753\) 0 0
\(754\) 619.911 13.6057i 0.822163 0.0180448i
\(755\) −1463.55 606.223i −1.93848 0.802945i
\(756\) 0 0
\(757\) −691.098 + 286.262i −0.912944 + 0.378154i −0.789183 0.614158i \(-0.789496\pi\)
−0.123761 + 0.992312i \(0.539496\pi\)
\(758\) −870.819 338.515i −1.14884 0.446590i
\(759\) 0 0
\(760\) 89.7619 + 78.6582i 0.118108 + 0.103498i
\(761\) −287.342 + 287.342i −0.377585 + 0.377585i −0.870230 0.492645i \(-0.836030\pi\)
0.492645 + 0.870230i \(0.336030\pi\)
\(762\) 0 0
\(763\) 368.777 152.752i 0.483325 0.200200i
\(764\) 726.667 31.9130i 0.951135 0.0417710i
\(765\) 0 0
\(766\) 807.561 843.805i 1.05426 1.10157i
\(767\) 808.842i 1.05455i
\(768\) 0 0
\(769\) −1240.31 −1.61289 −0.806446 0.591308i \(-0.798612\pi\)
−0.806446 + 0.591308i \(0.798612\pi\)
\(770\) 995.176 + 952.430i 1.29244 + 1.23692i
\(771\) 0 0
\(772\) −38.8321 884.215i −0.0503006 1.14536i
\(773\) 318.633 + 769.248i 0.412203 + 0.995146i 0.984545 + 0.175131i \(0.0560350\pi\)
−0.572342 + 0.820015i \(0.693965\pi\)
\(774\) 0 0
\(775\) −128.394 128.394i −0.165670 0.165670i
\(776\) −348.252 + 397.413i −0.448778 + 0.512130i
\(777\) 0 0
\(778\) −109.651 + 282.074i −0.140940 + 0.362563i
\(779\) 20.5052 + 49.5039i 0.0263224 + 0.0635480i
\(780\) 0 0
\(781\) −653.751 + 1578.29i −0.837069 + 2.02086i
\(782\) 1.89477 + 86.3304i 0.00242298 + 0.110397i
\(783\) 0 0
\(784\) 30.8691 + 350.771i 0.0393739 + 0.447412i
\(785\) 504.487i 0.642659i
\(786\) 0 0
\(787\) 584.664 + 242.176i 0.742902 + 0.307720i 0.721842 0.692058i \(-0.243296\pi\)
0.0210600 + 0.999778i \(0.493296\pi\)