Properties

Label 288.3.u.a.19.1
Level $288$
Weight $3$
Character 288.19
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 19.1
Character \(\chi\) \(=\) 288.19
Dual form 288.3.u.a.91.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.82416 + 0.820030i) q^{2} +(2.65510 - 2.99173i) q^{4} +(7.60625 - 3.15061i) q^{5} +(6.84161 + 6.84161i) q^{7} +(-2.39002 + 7.63465i) q^{8} +O(q^{10})\) \(q+(-1.82416 + 0.820030i) q^{2} +(2.65510 - 2.99173i) q^{4} +(7.60625 - 3.15061i) q^{5} +(6.84161 + 6.84161i) q^{7} +(-2.39002 + 7.63465i) q^{8} +(-11.2914 + 11.9846i) q^{10} +(2.23818 - 0.927086i) q^{11} +(1.40964 + 0.583890i) q^{13} +(-18.0905 - 6.86984i) q^{14} +(-1.90088 - 15.8867i) q^{16} -2.67812i q^{17} +(5.38908 - 13.0104i) q^{19} +(10.7696 - 31.1210i) q^{20} +(-3.32256 + 3.52653i) q^{22} +(-18.8388 + 18.8388i) q^{23} +(30.2510 - 30.2510i) q^{25} +(-3.05020 + 0.0908360i) q^{26} +(38.6334 - 2.30307i) q^{28} +(10.0298 - 24.2140i) q^{29} +47.5858i q^{31} +(16.4951 + 27.4210i) q^{32} +(2.19614 + 4.88532i) q^{34} +(73.5942 + 30.4837i) q^{35} +(-28.2682 + 11.7091i) q^{37} +(0.838382 + 28.1522i) q^{38} +(5.87475 + 65.6010i) q^{40} +(-6.93962 - 6.93962i) q^{41} +(8.48982 - 3.51660i) q^{43} +(3.16902 - 9.15755i) q^{44} +(18.9165 - 49.8132i) q^{46} +67.0112 q^{47} +44.6152i q^{49} +(-30.3759 + 79.9893i) q^{50} +(5.48956 - 2.66696i) q^{52} +(10.5006 + 25.3507i) q^{53} +(14.1033 - 14.1033i) q^{55} +(-68.5848 + 35.8817i) q^{56} +(1.56034 + 52.3950i) q^{58} +(-27.9364 - 67.4445i) q^{59} +(31.5752 - 76.2294i) q^{61} +(-39.0218 - 86.8040i) q^{62} +(-52.5757 - 36.4938i) q^{64} +12.5616 q^{65} +(90.1903 + 37.3580i) q^{67} +(-8.01222 - 7.11069i) q^{68} +(-159.245 + 4.74236i) q^{70} +(-1.98379 - 1.98379i) q^{71} +(-55.5273 - 55.5273i) q^{73} +(41.9639 - 44.5400i) q^{74} +(-24.6150 - 50.6666i) q^{76} +(21.6555 + 8.97002i) q^{77} +10.9856 q^{79} +(-64.5113 - 114.849i) q^{80} +(18.3496 + 6.96826i) q^{82} +(-34.1779 + 82.5128i) q^{83} +(-8.43772 - 20.3705i) q^{85} +(-12.6031 + 13.3767i) q^{86} +(1.72868 + 19.3035i) q^{88} +(16.1705 - 16.1705i) q^{89} +(5.64942 + 13.6389i) q^{91} +(6.34164 + 106.379i) q^{92} +(-122.239 + 54.9512i) q^{94} -115.939i q^{95} -62.6434 q^{97} +(-36.5858 - 81.3851i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82416 + 0.820030i −0.912079 + 0.410015i
\(3\) 0 0
\(4\) 2.65510 2.99173i 0.663775 0.747932i
\(5\) 7.60625 3.15061i 1.52125 0.630122i 0.543408 0.839469i \(-0.317134\pi\)
0.977842 + 0.209346i \(0.0671336\pi\)
\(6\) 0 0
\(7\) 6.84161 + 6.84161i 0.977372 + 0.977372i 0.999750 0.0223772i \(-0.00712349\pi\)
−0.0223772 + 0.999750i \(0.507123\pi\)
\(8\) −2.39002 + 7.63465i −0.298752 + 0.954331i
\(9\) 0 0
\(10\) −11.2914 + 11.9846i −1.12914 + 1.19846i
\(11\) 2.23818 0.927086i 0.203471 0.0842806i −0.278621 0.960401i \(-0.589877\pi\)
0.482092 + 0.876121i \(0.339877\pi\)
\(12\) 0 0
\(13\) 1.40964 + 0.583890i 0.108433 + 0.0449146i 0.436241 0.899830i \(-0.356310\pi\)
−0.327807 + 0.944745i \(0.606310\pi\)
\(14\) −18.0905 6.86984i −1.29218 0.490703i
\(15\) 0 0
\(16\) −1.90088 15.8867i −0.118805 0.992918i
\(17\) 2.67812i 0.157537i −0.996893 0.0787683i \(-0.974901\pi\)
0.996893 0.0787683i \(-0.0250987\pi\)
\(18\) 0 0
\(19\) 5.38908 13.0104i 0.283636 0.684757i −0.716279 0.697814i \(-0.754156\pi\)
0.999915 + 0.0130566i \(0.00415616\pi\)
\(20\) 10.7696 31.1210i 0.538479 1.55605i
\(21\) 0 0
\(22\) −3.32256 + 3.52653i −0.151026 + 0.160297i
\(23\) −18.8388 + 18.8388i −0.819076 + 0.819076i −0.985974 0.166898i \(-0.946625\pi\)
0.166898 + 0.985974i \(0.446625\pi\)
\(24\) 0 0
\(25\) 30.2510 30.2510i 1.21004 1.21004i
\(26\) −3.05020 + 0.0908360i −0.117316 + 0.00349369i
\(27\) 0 0
\(28\) 38.6334 2.30307i 1.37976 0.0822525i
\(29\) 10.0298 24.2140i 0.345855 0.834967i −0.651245 0.758867i \(-0.725753\pi\)
0.997100 0.0761000i \(-0.0242468\pi\)
\(30\) 0 0
\(31\) 47.5858i 1.53503i 0.641033 + 0.767513i \(0.278506\pi\)
−0.641033 + 0.767513i \(0.721494\pi\)
\(32\) 16.4951 + 27.4210i 0.515470 + 0.856907i
\(33\) 0 0
\(34\) 2.19614 + 4.88532i 0.0645924 + 0.143686i
\(35\) 73.5942 + 30.4837i 2.10269 + 0.870963i
\(36\) 0 0
\(37\) −28.2682 + 11.7091i −0.764006 + 0.316462i −0.730442 0.682975i \(-0.760686\pi\)
−0.0335642 + 0.999437i \(0.510686\pi\)
\(38\) 0.838382 + 28.1522i 0.0220627 + 0.740848i
\(39\) 0 0
\(40\) 5.87475 + 65.6010i 0.146869 + 1.64003i
\(41\) −6.93962 6.93962i −0.169259 0.169259i 0.617395 0.786654i \(-0.288188\pi\)
−0.786654 + 0.617395i \(0.788188\pi\)
\(42\) 0 0
\(43\) 8.48982 3.51660i 0.197438 0.0817814i −0.281774 0.959481i \(-0.590923\pi\)
0.479211 + 0.877700i \(0.340923\pi\)
\(44\) 3.16902 9.15755i 0.0720231 0.208126i
\(45\) 0 0
\(46\) 18.9165 49.8132i 0.411228 1.08290i
\(47\) 67.0112 1.42577 0.712885 0.701281i \(-0.247388\pi\)
0.712885 + 0.701281i \(0.247388\pi\)
\(48\) 0 0
\(49\) 44.6152i 0.910513i
\(50\) −30.3759 + 79.9893i −0.607517 + 1.59979i
\(51\) 0 0
\(52\) 5.48956 2.66696i 0.105569 0.0512877i
\(53\) 10.5006 + 25.3507i 0.198124 + 0.478315i 0.991451 0.130482i \(-0.0416525\pi\)
−0.793326 + 0.608797i \(0.791653\pi\)
\(54\) 0 0
\(55\) 14.1033 14.1033i 0.256424 0.256424i
\(56\) −68.5848 + 35.8817i −1.22473 + 0.640745i
\(57\) 0 0
\(58\) 1.56034 + 52.3950i 0.0269024 + 0.903361i
\(59\) −27.9364 67.4445i −0.473499 1.14313i −0.962606 0.270904i \(-0.912677\pi\)
0.489107 0.872224i \(-0.337323\pi\)
\(60\) 0 0
\(61\) 31.5752 76.2294i 0.517627 1.24966i −0.421730 0.906721i \(-0.638577\pi\)
0.939357 0.342941i \(-0.111423\pi\)
\(62\) −39.0218 86.8040i −0.629384 1.40006i
\(63\) 0 0
\(64\) −52.5757 36.4938i −0.821495 0.570216i
\(65\) 12.5616 0.193256
\(66\) 0 0
\(67\) 90.1903 + 37.3580i 1.34612 + 0.557583i 0.935211 0.354092i \(-0.115210\pi\)
0.410913 + 0.911674i \(0.365210\pi\)
\(68\) −8.01222 7.11069i −0.117827 0.104569i
\(69\) 0 0
\(70\) −159.245 + 4.74236i −2.27493 + 0.0677481i
\(71\) −1.98379 1.98379i −0.0279407 0.0279407i 0.692998 0.720939i \(-0.256289\pi\)
−0.720939 + 0.692998i \(0.756289\pi\)
\(72\) 0 0
\(73\) −55.5273 55.5273i −0.760648 0.760648i 0.215792 0.976439i \(-0.430767\pi\)
−0.976439 + 0.215792i \(0.930767\pi\)
\(74\) 41.9639 44.5400i 0.567080 0.601892i
\(75\) 0 0
\(76\) −24.6150 50.6666i −0.323882 0.666665i
\(77\) 21.6555 + 8.97002i 0.281241 + 0.116494i
\(78\) 0 0
\(79\) 10.9856 0.139058 0.0695292 0.997580i \(-0.477850\pi\)
0.0695292 + 0.997580i \(0.477850\pi\)
\(80\) −64.5113 114.849i −0.806391 1.43561i
\(81\) 0 0
\(82\) 18.3496 + 6.96826i 0.223776 + 0.0849788i
\(83\) −34.1779 + 82.5128i −0.411782 + 0.994130i 0.572877 + 0.819641i \(0.305827\pi\)
−0.984659 + 0.174489i \(0.944173\pi\)
\(84\) 0 0
\(85\) −8.43772 20.3705i −0.0992674 0.239653i
\(86\) −12.6031 + 13.3767i −0.146547 + 0.155543i
\(87\) 0 0
\(88\) 1.72868 + 19.3035i 0.0196441 + 0.219358i
\(89\) 16.1705 16.1705i 0.181691 0.181691i −0.610401 0.792093i \(-0.708992\pi\)
0.792093 + 0.610401i \(0.208992\pi\)
\(90\) 0 0
\(91\) 5.64942 + 13.6389i 0.0620816 + 0.149878i
\(92\) 6.34164 + 106.379i 0.0689308 + 1.15630i
\(93\) 0 0
\(94\) −122.239 + 54.9512i −1.30042 + 0.584587i
\(95\) 115.939i 1.22041i
\(96\) 0 0
\(97\) −62.6434 −0.645808 −0.322904 0.946432i \(-0.604659\pi\)
−0.322904 + 0.946432i \(0.604659\pi\)
\(98\) −36.5858 81.3851i −0.373324 0.830460i
\(99\) 0 0
\(100\) −10.1833 170.822i −0.101833 1.70822i
\(101\) −39.7340 + 16.4584i −0.393406 + 0.162954i −0.570612 0.821220i \(-0.693294\pi\)
0.177206 + 0.984174i \(0.443294\pi\)
\(102\) 0 0
\(103\) −36.3254 36.3254i −0.352674 0.352674i 0.508430 0.861104i \(-0.330226\pi\)
−0.861104 + 0.508430i \(0.830226\pi\)
\(104\) −7.82684 + 9.36656i −0.0752581 + 0.0900631i
\(105\) 0 0
\(106\) −39.9431 37.6328i −0.376821 0.355027i
\(107\) −111.798 + 46.3084i −1.04484 + 0.432789i −0.838049 0.545596i \(-0.816304\pi\)
−0.206796 + 0.978384i \(0.566304\pi\)
\(108\) 0 0
\(109\) −55.7631 23.0978i −0.511588 0.211907i 0.111929 0.993716i \(-0.464297\pi\)
−0.623517 + 0.781809i \(0.714297\pi\)
\(110\) −14.1615 + 37.2918i −0.128741 + 0.339016i
\(111\) 0 0
\(112\) 95.6854 121.695i 0.854334 1.08657i
\(113\) 80.7753i 0.714825i 0.933947 + 0.357413i \(0.116341\pi\)
−0.933947 + 0.357413i \(0.883659\pi\)
\(114\) 0 0
\(115\) −83.9387 + 202.646i −0.729901 + 1.76214i
\(116\) −45.8118 94.2971i −0.394929 0.812906i
\(117\) 0 0
\(118\) 106.267 + 100.121i 0.900568 + 0.848481i
\(119\) 18.3227 18.3227i 0.153972 0.153972i
\(120\) 0 0
\(121\) −81.4099 + 81.4099i −0.672809 + 0.672809i
\(122\) 4.91217 + 164.947i 0.0402637 + 1.35203i
\(123\) 0 0
\(124\) 142.364 + 126.345i 1.14810 + 1.01891i
\(125\) 56.0222 135.250i 0.448178 1.08200i
\(126\) 0 0
\(127\) 143.036i 1.12627i −0.826365 0.563135i \(-0.809595\pi\)
0.826365 0.563135i \(-0.190405\pi\)
\(128\) 125.832 + 23.4569i 0.983065 + 0.183257i
\(129\) 0 0
\(130\) −22.9144 + 10.3009i −0.176265 + 0.0792379i
\(131\) 56.1430 + 23.2552i 0.428573 + 0.177521i 0.586534 0.809925i \(-0.300492\pi\)
−0.157961 + 0.987445i \(0.550492\pi\)
\(132\) 0 0
\(133\) 125.882 52.1420i 0.946481 0.392045i
\(134\) −195.156 + 5.81181i −1.45639 + 0.0433717i
\(135\) 0 0
\(136\) 20.4465 + 6.40075i 0.150342 + 0.0470644i
\(137\) −168.165 168.165i −1.22748 1.22748i −0.964915 0.262563i \(-0.915432\pi\)
−0.262563 0.964915i \(-0.584568\pi\)
\(138\) 0 0
\(139\) −97.5768 + 40.4176i −0.701991 + 0.290774i −0.704986 0.709221i \(-0.749047\pi\)
0.00299484 + 0.999996i \(0.499047\pi\)
\(140\) 286.599 139.237i 2.04714 0.994547i
\(141\) 0 0
\(142\) 5.24551 + 1.99198i 0.0369402 + 0.0140280i
\(143\) 3.69634 0.0258485
\(144\) 0 0
\(145\) 215.778i 1.48812i
\(146\) 146.825 + 55.7565i 1.00565 + 0.381894i
\(147\) 0 0
\(148\) −40.0246 + 115.660i −0.270437 + 0.781484i
\(149\) −44.3735 107.127i −0.297809 0.718974i −0.999976 0.00696156i \(-0.997784\pi\)
0.702167 0.712012i \(-0.252216\pi\)
\(150\) 0 0
\(151\) −128.078 + 128.078i −0.848200 + 0.848200i −0.989908 0.141708i \(-0.954741\pi\)
0.141708 + 0.989908i \(0.454741\pi\)
\(152\) 86.4498 + 72.2388i 0.568748 + 0.475255i
\(153\) 0 0
\(154\) −46.8588 + 1.39547i −0.304278 + 0.00906149i
\(155\) 149.924 + 361.950i 0.967254 + 2.33516i
\(156\) 0 0
\(157\) 20.1590 48.6682i 0.128401 0.309988i −0.846585 0.532254i \(-0.821345\pi\)
0.974986 + 0.222265i \(0.0713452\pi\)
\(158\) −20.0395 + 9.00854i −0.126832 + 0.0570161i
\(159\) 0 0
\(160\) 211.859 + 156.602i 1.32412 + 0.978761i
\(161\) −257.775 −1.60109
\(162\) 0 0
\(163\) 68.6749 + 28.4461i 0.421319 + 0.174516i 0.583262 0.812284i \(-0.301776\pi\)
−0.161943 + 0.986800i \(0.551776\pi\)
\(164\) −39.1868 + 2.33606i −0.238944 + 0.0142443i
\(165\) 0 0
\(166\) −5.31707 178.543i −0.0320306 1.07556i
\(167\) −131.350 131.350i −0.786527 0.786527i 0.194396 0.980923i \(-0.437725\pi\)
−0.980923 + 0.194396i \(0.937725\pi\)
\(168\) 0 0
\(169\) −117.855 117.855i −0.697366 0.697366i
\(170\) 32.0961 + 30.2398i 0.188801 + 0.177881i
\(171\) 0 0
\(172\) 12.0206 34.7362i 0.0698873 0.201954i
\(173\) 206.045 + 85.3465i 1.19101 + 0.493333i 0.888084 0.459681i \(-0.152036\pi\)
0.302926 + 0.953014i \(0.402036\pi\)
\(174\) 0 0
\(175\) 413.931 2.36532
\(176\) −18.9828 33.7950i −0.107857 0.192017i
\(177\) 0 0
\(178\) −16.2373 + 42.7579i −0.0912207 + 0.240213i
\(179\) −80.2014 + 193.623i −0.448053 + 1.08169i 0.524998 + 0.851104i \(0.324066\pi\)
−0.973051 + 0.230591i \(0.925934\pi\)
\(180\) 0 0
\(181\) 93.4345 + 225.571i 0.516213 + 1.24625i 0.940213 + 0.340586i \(0.110626\pi\)
−0.424000 + 0.905662i \(0.639374\pi\)
\(182\) −21.4898 20.2468i −0.118076 0.111246i
\(183\) 0 0
\(184\) −98.8023 188.852i −0.536969 1.02637i
\(185\) −178.124 + 178.124i −0.962835 + 0.962835i
\(186\) 0 0
\(187\) −2.48285 5.99413i −0.0132773 0.0320542i
\(188\) 177.922 200.479i 0.946391 1.06638i
\(189\) 0 0
\(190\) 95.0736 + 211.491i 0.500388 + 1.11311i
\(191\) 20.1639i 0.105570i 0.998606 + 0.0527851i \(0.0168098\pi\)
−0.998606 + 0.0527851i \(0.983190\pi\)
\(192\) 0 0
\(193\) 115.896 0.600497 0.300248 0.953861i \(-0.402930\pi\)
0.300248 + 0.953861i \(0.402930\pi\)
\(194\) 114.271 51.3694i 0.589028 0.264791i
\(195\) 0 0
\(196\) 133.476 + 118.458i 0.681002 + 0.604376i
\(197\) 177.705 73.6077i 0.902055 0.373643i 0.117045 0.993127i \(-0.462658\pi\)
0.785010 + 0.619483i \(0.212658\pi\)
\(198\) 0 0
\(199\) −22.1763 22.1763i −0.111439 0.111439i 0.649189 0.760627i \(-0.275109\pi\)
−0.760627 + 0.649189i \(0.775109\pi\)
\(200\) 158.655 + 303.256i 0.793277 + 1.51628i
\(201\) 0 0
\(202\) 58.9847 62.6057i 0.292003 0.309929i
\(203\) 234.283 97.0431i 1.15410 0.478045i
\(204\) 0 0
\(205\) −74.6485 30.9204i −0.364139 0.150831i
\(206\) 96.0512 + 36.4753i 0.466268 + 0.177065i
\(207\) 0 0
\(208\) 6.59653 23.5043i 0.0317141 0.113002i
\(209\) 34.1158i 0.163233i
\(210\) 0 0
\(211\) −116.936 + 282.308i −0.554197 + 1.33795i 0.360103 + 0.932913i \(0.382742\pi\)
−0.914300 + 0.405038i \(0.867258\pi\)
\(212\) 103.722 + 35.8937i 0.489257 + 0.169310i
\(213\) 0 0
\(214\) 165.963 176.152i 0.775530 0.823139i
\(215\) 53.4962 53.4962i 0.248820 0.248820i
\(216\) 0 0
\(217\) −325.563 + 325.563i −1.50029 + 1.50029i
\(218\) 120.662 3.59334i 0.553493 0.0164832i
\(219\) 0 0
\(220\) −4.74755 79.6389i −0.0215798 0.361995i
\(221\) 1.56373 3.77518i 0.00707570 0.0170822i
\(222\) 0 0
\(223\) 12.1409i 0.0544434i 0.999629 + 0.0272217i \(0.00866601\pi\)
−0.999629 + 0.0272217i \(0.991334\pi\)
\(224\) −74.7512 + 300.457i −0.333711 + 1.34132i
\(225\) 0 0
\(226\) −66.2381 147.347i −0.293089 0.651977i
\(227\) −215.118 89.1048i −0.947656 0.392532i −0.145307 0.989387i \(-0.546417\pi\)
−0.802350 + 0.596854i \(0.796417\pi\)
\(228\) 0 0
\(229\) 85.4872 35.4100i 0.373307 0.154629i −0.188139 0.982142i \(-0.560245\pi\)
0.561445 + 0.827514i \(0.310245\pi\)
\(230\) −13.0584 438.490i −0.0567755 1.90648i
\(231\) 0 0
\(232\) 160.894 + 134.446i 0.693510 + 0.579508i
\(233\) −33.1162 33.1162i −0.142129 0.142129i 0.632462 0.774591i \(-0.282044\pi\)
−0.774591 + 0.632462i \(0.782044\pi\)
\(234\) 0 0
\(235\) 509.704 211.126i 2.16895 0.898410i
\(236\) −275.950 95.4938i −1.16928 0.404635i
\(237\) 0 0
\(238\) −18.3983 + 48.4486i −0.0773037 + 0.203565i
\(239\) −332.992 −1.39327 −0.696636 0.717425i \(-0.745321\pi\)
−0.696636 + 0.717425i \(0.745321\pi\)
\(240\) 0 0
\(241\) 218.867i 0.908160i −0.890961 0.454080i \(-0.849968\pi\)
0.890961 0.454080i \(-0.150032\pi\)
\(242\) 81.7459 215.263i 0.337793 0.889517i
\(243\) 0 0
\(244\) −144.222 296.861i −0.591074 1.21664i
\(245\) 140.565 + 339.354i 0.573735 + 1.38512i
\(246\) 0 0
\(247\) 15.1933 15.1933i 0.0615112 0.0615112i
\(248\) −363.301 113.731i −1.46492 0.458592i
\(249\) 0 0
\(250\) 8.71540 + 292.657i 0.0348616 + 1.17063i
\(251\) −92.6681 223.721i −0.369196 0.891318i −0.993883 0.110442i \(-0.964773\pi\)
0.624687 0.780875i \(-0.285227\pi\)
\(252\) 0 0
\(253\) −24.6995 + 59.6298i −0.0976263 + 0.235691i
\(254\) 117.294 + 260.921i 0.461788 + 1.02725i
\(255\) 0 0
\(256\) −248.773 + 60.3972i −0.971771 + 0.235927i
\(257\) 138.514 0.538966 0.269483 0.963005i \(-0.413147\pi\)
0.269483 + 0.963005i \(0.413147\pi\)
\(258\) 0 0
\(259\) −273.509 113.291i −1.05602 0.437418i
\(260\) 33.3524 37.5810i 0.128279 0.144542i
\(261\) 0 0
\(262\) −121.484 + 3.61782i −0.463678 + 0.0138085i
\(263\) −91.6940 91.6940i −0.348647 0.348647i 0.510959 0.859605i \(-0.329290\pi\)
−0.859605 + 0.510959i \(0.829290\pi\)
\(264\) 0 0
\(265\) 159.740 + 159.740i 0.602793 + 0.602793i
\(266\) −186.870 + 198.342i −0.702521 + 0.745648i
\(267\) 0 0
\(268\) 351.230 170.636i 1.31056 0.636700i
\(269\) −179.504 74.3530i −0.667301 0.276405i 0.0232059 0.999731i \(-0.492613\pi\)
−0.690507 + 0.723325i \(0.742613\pi\)
\(270\) 0 0
\(271\) −454.375 −1.67666 −0.838331 0.545161i \(-0.816468\pi\)
−0.838331 + 0.545161i \(0.816468\pi\)
\(272\) −42.5465 + 5.09078i −0.156421 + 0.0187161i
\(273\) 0 0
\(274\) 444.659 + 168.859i 1.62284 + 0.616272i
\(275\) 39.6620 95.7526i 0.144226 0.348191i
\(276\) 0 0
\(277\) −12.5345 30.2610i −0.0452510 0.109246i 0.899638 0.436637i \(-0.143830\pi\)
−0.944889 + 0.327391i \(0.893830\pi\)
\(278\) 144.852 153.744i 0.521049 0.553036i
\(279\) 0 0
\(280\) −408.624 + 489.009i −1.45937 + 1.74646i
\(281\) −312.777 + 312.777i −1.11308 + 1.11308i −0.120353 + 0.992731i \(0.538403\pi\)
−0.992731 + 0.120353i \(0.961597\pi\)
\(282\) 0 0
\(283\) −74.2838 179.337i −0.262487 0.633700i 0.736604 0.676324i \(-0.236428\pi\)
−0.999091 + 0.0426244i \(0.986428\pi\)
\(284\) −11.2021 + 0.667798i −0.0394441 + 0.00235140i
\(285\) 0 0
\(286\) −6.74271 + 3.03111i −0.0235759 + 0.0105983i
\(287\) 94.9562i 0.330858i
\(288\) 0 0
\(289\) 281.828 0.975182
\(290\) 176.944 + 393.613i 0.610153 + 1.35729i
\(291\) 0 0
\(292\) −313.553 + 18.6920i −1.07381 + 0.0640137i
\(293\) 156.211 64.7046i 0.533143 0.220835i −0.0998364 0.995004i \(-0.531832\pi\)
0.632979 + 0.774169i \(0.281832\pi\)
\(294\) 0 0
\(295\) −424.983 424.983i −1.44062 1.44062i
\(296\) −21.8332 243.803i −0.0737609 0.823658i
\(297\) 0 0
\(298\) 168.792 + 159.029i 0.566415 + 0.533655i
\(299\) −37.5555 + 15.5560i −0.125604 + 0.0520268i
\(300\) 0 0
\(301\) 82.1432 + 34.0248i 0.272901 + 0.113039i
\(302\) 128.607 338.663i 0.425851 1.12140i
\(303\) 0 0
\(304\) −216.936 60.8835i −0.713605 0.200275i
\(305\) 679.301i 2.22722i
\(306\) 0 0
\(307\) 111.488 269.157i 0.363155 0.876733i −0.631681 0.775229i \(-0.717635\pi\)
0.994835 0.101504i \(-0.0323654\pi\)
\(308\) 84.3335 40.9712i 0.273810 0.133023i
\(309\) 0 0
\(310\) −570.295 537.311i −1.83966 1.73326i
\(311\) 74.0508 74.0508i 0.238105 0.238105i −0.577960 0.816065i \(-0.696151\pi\)
0.816065 + 0.577960i \(0.196151\pi\)
\(312\) 0 0
\(313\) −119.709 + 119.709i −0.382458 + 0.382458i −0.871987 0.489529i \(-0.837169\pi\)
0.489529 + 0.871987i \(0.337169\pi\)
\(314\) 3.13615 + 105.309i 0.00998773 + 0.335380i
\(315\) 0 0
\(316\) 29.1679 32.8660i 0.0923036 0.104006i
\(317\) −154.558 + 373.135i −0.487563 + 1.17708i 0.468379 + 0.883528i \(0.344838\pi\)
−0.955942 + 0.293554i \(0.905162\pi\)
\(318\) 0 0
\(319\) 63.4940i 0.199041i
\(320\) −514.881 111.936i −1.60900 0.349799i
\(321\) 0 0
\(322\) 470.222 211.383i 1.46032 0.656469i
\(323\) −34.8434 14.4326i −0.107874 0.0446830i
\(324\) 0 0
\(325\) 60.3061 24.9796i 0.185557 0.0768604i
\(326\) −148.601 + 4.42537i −0.455830 + 0.0135748i
\(327\) 0 0
\(328\) 69.5673 36.3957i 0.212095 0.110963i
\(329\) 458.464 + 458.464i 1.39351 + 1.39351i
\(330\) 0 0
\(331\) −376.019 + 155.752i −1.13601 + 0.470551i −0.869820 0.493370i \(-0.835765\pi\)
−0.266190 + 0.963921i \(0.585765\pi\)
\(332\) 156.110 + 321.331i 0.470211 + 0.967864i
\(333\) 0 0
\(334\) 347.314 + 131.892i 1.03986 + 0.394887i
\(335\) 803.711 2.39914
\(336\) 0 0
\(337\) 584.284i 1.73378i 0.498499 + 0.866890i \(0.333885\pi\)
−0.498499 + 0.866890i \(0.666115\pi\)
\(338\) 311.630 + 118.341i 0.921984 + 0.350122i
\(339\) 0 0
\(340\) −83.3459 28.8423i −0.245135 0.0848302i
\(341\) 44.1162 + 106.506i 0.129373 + 0.312334i
\(342\) 0 0
\(343\) 29.9994 29.9994i 0.0874617 0.0874617i
\(344\) 6.55719 + 73.2215i 0.0190616 + 0.212853i
\(345\) 0 0
\(346\) −445.845 + 13.2774i −1.28857 + 0.0383740i
\(347\) 15.0226 + 36.2679i 0.0432929 + 0.104518i 0.944047 0.329812i \(-0.106985\pi\)
−0.900754 + 0.434330i \(0.856985\pi\)
\(348\) 0 0
\(349\) 82.9090 200.160i 0.237562 0.573525i −0.759468 0.650545i \(-0.774541\pi\)
0.997030 + 0.0770202i \(0.0245406\pi\)
\(350\) −755.075 + 339.436i −2.15736 + 0.969817i
\(351\) 0 0
\(352\) 62.3406 + 46.0810i 0.177104 + 0.130912i
\(353\) 213.926 0.606022 0.303011 0.952987i \(-0.402008\pi\)
0.303011 + 0.952987i \(0.402008\pi\)
\(354\) 0 0
\(355\) −21.3394 8.83905i −0.0601109 0.0248987i
\(356\) −5.44344 91.3123i −0.0152906 0.256495i
\(357\) 0 0
\(358\) −12.4770 418.967i −0.0348519 1.17030i
\(359\) −235.583 235.583i −0.656219 0.656219i 0.298264 0.954483i \(-0.403592\pi\)
−0.954483 + 0.298264i \(0.903592\pi\)
\(360\) 0 0
\(361\) 115.037 + 115.037i 0.318663 + 0.318663i
\(362\) −355.414 334.858i −0.981807 0.925021i
\(363\) 0 0
\(364\) 55.8037 + 19.3112i 0.153307 + 0.0530526i
\(365\) −597.299 247.410i −1.63644 0.677834i
\(366\) 0 0
\(367\) 266.252 0.725482 0.362741 0.931890i \(-0.381841\pi\)
0.362741 + 0.931890i \(0.381841\pi\)
\(368\) 335.095 + 263.475i 0.910585 + 0.715965i
\(369\) 0 0
\(370\) 178.860 470.994i 0.483404 1.27296i
\(371\) −101.598 + 245.280i −0.273850 + 0.661133i
\(372\) 0 0
\(373\) 133.648 + 322.655i 0.358306 + 0.865028i 0.995539 + 0.0943560i \(0.0300792\pi\)
−0.637232 + 0.770672i \(0.719921\pi\)
\(374\) 9.44448 + 8.89823i 0.0252526 + 0.0237921i
\(375\) 0 0
\(376\) −160.158 + 511.607i −0.425952 + 1.36066i
\(377\) 28.2767 28.2767i 0.0750045 0.0750045i
\(378\) 0 0
\(379\) 1.26349 + 3.05034i 0.00333376 + 0.00804840i 0.925538 0.378656i \(-0.123614\pi\)
−0.922204 + 0.386704i \(0.873614\pi\)
\(380\) −346.859 307.830i −0.912786 0.810080i
\(381\) 0 0
\(382\) −16.5350 36.7822i −0.0432854 0.0962884i
\(383\) 310.584i 0.810923i 0.914112 + 0.405462i \(0.132889\pi\)
−0.914112 + 0.405462i \(0.867111\pi\)
\(384\) 0 0
\(385\) 192.978 0.501243
\(386\) −211.412 + 95.0381i −0.547700 + 0.246213i
\(387\) 0 0
\(388\) −166.324 + 187.412i −0.428671 + 0.483020i
\(389\) 677.246 280.524i 1.74099 0.721142i 0.742296 0.670072i \(-0.233737\pi\)
0.998695 0.0510705i \(-0.0162633\pi\)
\(390\) 0 0
\(391\) 50.4525 + 50.4525i 0.129035 + 0.129035i
\(392\) −340.621 106.631i −0.868931 0.272018i
\(393\) 0 0
\(394\) −263.801 + 279.995i −0.669545 + 0.710648i
\(395\) 83.5594 34.6114i 0.211543 0.0876239i
\(396\) 0 0
\(397\) −467.679 193.719i −1.17803 0.487957i −0.294192 0.955746i \(-0.595051\pi\)
−0.883840 + 0.467789i \(0.845051\pi\)
\(398\) 58.6383 + 22.2678i 0.147332 + 0.0559493i
\(399\) 0 0
\(400\) −538.092 423.085i −1.34523 1.05771i
\(401\) 447.783i 1.11667i 0.829617 + 0.558333i \(0.188559\pi\)
−0.829617 + 0.558333i \(0.811441\pi\)
\(402\) 0 0
\(403\) −27.7849 + 67.0786i −0.0689451 + 0.166448i
\(404\) −56.2588 + 162.572i −0.139255 + 0.402406i
\(405\) 0 0
\(406\) −347.790 + 369.141i −0.856627 + 0.909214i
\(407\) −52.4142 + 52.4142i −0.128782 + 0.128782i
\(408\) 0 0
\(409\) 266.640 266.640i 0.651931 0.651931i −0.301527 0.953458i \(-0.597496\pi\)
0.953458 + 0.301527i \(0.0974962\pi\)
\(410\) 161.526 4.81030i 0.393966 0.0117324i
\(411\) 0 0
\(412\) −205.123 + 12.2281i −0.497872 + 0.0296799i
\(413\) 270.299 652.559i 0.654477 1.58005i
\(414\) 0 0
\(415\) 735.294i 1.77179i
\(416\) 7.24114 + 48.2850i 0.0174066 + 0.116070i
\(417\) 0 0
\(418\) 27.9760 + 62.2326i 0.0669282 + 0.148882i
\(419\) 565.518 + 234.245i 1.34969 + 0.559058i 0.936205 0.351455i \(-0.114313\pi\)
0.413481 + 0.910513i \(0.364313\pi\)
\(420\) 0 0
\(421\) −184.538 + 76.4382i −0.438333 + 0.181564i −0.590926 0.806726i \(-0.701238\pi\)
0.152593 + 0.988289i \(0.451238\pi\)
\(422\) −18.1917 610.864i −0.0431084 1.44755i
\(423\) 0 0
\(424\) −218.640 + 19.5798i −0.515660 + 0.0461788i
\(425\) −81.0159 81.0159i −0.190626 0.190626i
\(426\) 0 0
\(427\) 737.557 305.506i 1.72730 0.715471i
\(428\) −158.294 + 457.424i −0.369845 + 1.06875i
\(429\) 0 0
\(430\) −53.7170 + 141.454i −0.124923 + 0.328963i
\(431\) −329.019 −0.763385 −0.381692 0.924289i \(-0.624659\pi\)
−0.381692 + 0.924289i \(0.624659\pi\)
\(432\) 0 0
\(433\) 403.449i 0.931753i −0.884850 0.465877i \(-0.845739\pi\)
0.884850 0.465877i \(-0.154261\pi\)
\(434\) 326.907 860.851i 0.753242 1.98353i
\(435\) 0 0
\(436\) −217.159 + 105.501i −0.498071 + 0.241975i
\(437\) 143.576 + 346.623i 0.328549 + 0.793188i
\(438\) 0 0
\(439\) 432.214 432.214i 0.984542 0.984542i −0.0153402 0.999882i \(-0.504883\pi\)
0.999882 + 0.0153402i \(0.00488314\pi\)
\(440\) 73.9666 + 141.381i 0.168106 + 0.321320i
\(441\) 0 0
\(442\) 0.243270 + 8.16882i 0.000550385 + 0.0184815i
\(443\) −138.144 333.509i −0.311838 0.752843i −0.999637 0.0269419i \(-0.991423\pi\)
0.687799 0.725901i \(-0.258577\pi\)
\(444\) 0 0
\(445\) 72.0501 173.944i 0.161910 0.390886i
\(446\) −9.95589 22.1469i −0.0223226 0.0496567i
\(447\) 0 0
\(448\) −110.025 609.378i −0.245592 1.36022i
\(449\) 320.009 0.712715 0.356358 0.934350i \(-0.384019\pi\)
0.356358 + 0.934350i \(0.384019\pi\)
\(450\) 0 0
\(451\) −21.9658 9.09852i −0.0487046 0.0201741i
\(452\) 241.658 + 214.466i 0.534641 + 0.474483i
\(453\) 0 0
\(454\) 465.478 13.8621i 1.02528 0.0305332i
\(455\) 85.9419 + 85.9419i 0.188883 + 0.188883i
\(456\) 0 0
\(457\) −148.390 148.390i −0.324705 0.324705i 0.525864 0.850569i \(-0.323742\pi\)
−0.850569 + 0.525864i \(0.823742\pi\)
\(458\) −126.905 + 134.695i −0.277085 + 0.294095i
\(459\) 0 0
\(460\) 383.396 + 789.167i 0.833469 + 1.71558i
\(461\) 224.303 + 92.9092i 0.486557 + 0.201538i 0.612456 0.790505i \(-0.290182\pi\)
−0.125899 + 0.992043i \(0.540182\pi\)
\(462\) 0 0
\(463\) 675.592 1.45916 0.729581 0.683894i \(-0.239715\pi\)
0.729581 + 0.683894i \(0.239715\pi\)
\(464\) −403.746 113.312i −0.870143 0.244207i
\(465\) 0 0
\(466\) 87.5654 + 33.2529i 0.187909 + 0.0713581i
\(467\) −190.920 + 460.923i −0.408823 + 0.986987i 0.576625 + 0.817009i \(0.304369\pi\)
−0.985448 + 0.169977i \(0.945631\pi\)
\(468\) 0 0
\(469\) 361.458 + 872.636i 0.770698 + 1.86063i
\(470\) −756.651 + 803.100i −1.60989 + 1.70872i
\(471\) 0 0
\(472\) 581.684 52.0914i 1.23238 0.110363i
\(473\) 15.7416 15.7416i 0.0332803 0.0332803i
\(474\) 0 0
\(475\) −230.552 556.603i −0.485373 1.17179i
\(476\) −6.16791 103.465i −0.0129578 0.217363i
\(477\) 0 0
\(478\) 607.430 273.063i 1.27077 0.571262i
\(479\) 775.709i 1.61943i −0.586821 0.809717i \(-0.699621\pi\)
0.586821 0.809717i \(-0.300379\pi\)
\(480\) 0 0
\(481\) −46.6847 −0.0970576
\(482\) 179.477 + 399.247i 0.372359 + 0.828314i
\(483\) 0 0
\(484\) 27.4048 + 459.708i 0.0566215 + 0.949810i
\(485\) −476.481 + 197.365i −0.982435 + 0.406938i
\(486\) 0 0
\(487\) −422.101 422.101i −0.866738 0.866738i 0.125372 0.992110i \(-0.459988\pi\)
−0.992110 + 0.125372i \(0.959988\pi\)
\(488\) 506.519 + 423.255i 1.03795 + 0.867326i
\(489\) 0 0
\(490\) −534.693 503.768i −1.09121 1.02810i
\(491\) 277.565 114.971i 0.565306 0.234157i −0.0816809 0.996659i \(-0.526029\pi\)
0.646987 + 0.762501i \(0.276029\pi\)
\(492\) 0 0
\(493\) −64.8482 26.8610i −0.131538 0.0544848i
\(494\) −15.2560 + 40.1739i −0.0308826 + 0.0813236i
\(495\) 0 0
\(496\) 755.981 90.4548i 1.52415 0.182368i
\(497\) 27.1446i 0.0546170i
\(498\) 0 0
\(499\) −328.498 + 793.063i −0.658312 + 1.58930i 0.142099 + 0.989852i \(0.454615\pi\)
−0.800410 + 0.599452i \(0.795385\pi\)
\(500\) −255.885 526.705i −0.511771 1.05341i
\(501\) 0 0
\(502\) 352.499 + 332.111i 0.702189 + 0.661576i
\(503\) 115.459 115.459i 0.229540 0.229540i −0.582960 0.812501i \(-0.698106\pi\)
0.812501 + 0.582960i \(0.198106\pi\)
\(504\) 0 0
\(505\) −250.373 + 250.373i −0.495788 + 0.495788i
\(506\) −3.84250 129.028i −0.00759388 0.254997i
\(507\) 0 0
\(508\) −427.926 379.776i −0.842374 0.747590i
\(509\) 97.7110 235.895i 0.191967 0.463449i −0.798364 0.602175i \(-0.794301\pi\)
0.990331 + 0.138727i \(0.0443009\pi\)
\(510\) 0 0
\(511\) 759.792i 1.48687i
\(512\) 404.274 314.176i 0.789598 0.613624i
\(513\) 0 0
\(514\) −252.672 + 113.586i −0.491579 + 0.220984i
\(515\) −390.747 161.853i −0.758733 0.314277i
\(516\) 0 0
\(517\) 149.983 62.1252i 0.290103 0.120165i
\(518\) 591.826 17.6248i 1.14252 0.0340246i
\(519\) 0 0
\(520\) −30.0225 + 95.9037i −0.0577356 + 0.184430i
\(521\) −229.899 229.899i −0.441264 0.441264i 0.451173 0.892437i \(-0.351006\pi\)
−0.892437 + 0.451173i \(0.851006\pi\)
\(522\) 0 0
\(523\) −900.921 + 373.174i −1.72260 + 0.713525i −0.722856 + 0.690999i \(0.757171\pi\)
−0.999746 + 0.0225265i \(0.992829\pi\)
\(524\) 218.639 106.220i 0.417249 0.202709i
\(525\) 0 0
\(526\) 242.456 + 92.0725i 0.460943 + 0.175043i
\(527\) 127.441 0.241823
\(528\) 0 0
\(529\) 180.797i 0.341772i
\(530\) −422.383 160.400i −0.796950 0.302641i
\(531\) 0 0
\(532\) 178.235 515.047i 0.335027 0.968133i
\(533\) −5.73035 13.8343i −0.0107511 0.0259555i
\(534\) 0 0
\(535\) −704.466 + 704.466i −1.31676 + 1.31676i
\(536\) −500.772 + 599.285i −0.934276 + 1.11807i
\(537\) 0 0
\(538\) 388.415 11.5671i 0.721962 0.0215002i
\(539\) 41.3621 + 99.8569i 0.0767386 + 0.185263i
\(540\) 0 0
\(541\) 86.3781 208.535i 0.159664 0.385462i −0.823721 0.566995i \(-0.808106\pi\)
0.983385 + 0.181533i \(0.0581058\pi\)
\(542\) 828.852 372.602i 1.52925 0.687457i
\(543\) 0 0
\(544\) 73.4369 44.1758i 0.134994 0.0812055i
\(545\) −496.920 −0.911780
\(546\) 0 0
\(547\) 497.491 + 206.067i 0.909489 + 0.376723i 0.787861 0.615853i \(-0.211188\pi\)
0.121628 + 0.992576i \(0.461188\pi\)
\(548\) −949.596 + 56.6087i −1.73284 + 0.103301i
\(549\) 0 0
\(550\) 6.17024 + 207.192i 0.0112186 + 0.376713i
\(551\) −260.983 260.983i −0.473653 0.473653i
\(552\) 0 0
\(553\) 75.1593 + 75.1593i 0.135912 + 0.135912i
\(554\) 47.6799 + 44.9222i 0.0860648 + 0.0810869i
\(555\) 0 0
\(556\) −138.158 + 399.236i −0.248485 + 0.718050i
\(557\) 527.914 + 218.669i 0.947782 + 0.392584i 0.802397 0.596791i \(-0.203558\pi\)
0.145385 + 0.989375i \(0.453558\pi\)
\(558\) 0 0
\(559\) 14.0209 0.0250820
\(560\) 344.392 1227.11i 0.614985 2.19127i
\(561\) 0 0
\(562\) 314.068 827.040i 0.558839 1.47160i
\(563\) 303.900 733.680i 0.539788 1.30316i −0.385084 0.922882i \(-0.625827\pi\)
0.924871 0.380281i \(-0.124173\pi\)
\(564\) 0 0
\(565\) 254.491 + 614.397i 0.450427 + 1.08743i
\(566\) 282.567 + 266.224i 0.499235 + 0.470360i
\(567\) 0 0
\(568\) 19.8868 10.4042i 0.0350120 0.0183173i
\(569\) 143.631 143.631i 0.252426 0.252426i −0.569538 0.821965i \(-0.692878\pi\)
0.821965 + 0.569538i \(0.192878\pi\)
\(570\) 0 0
\(571\) −371.018 895.717i −0.649769 1.56868i −0.813109 0.582112i \(-0.802227\pi\)
0.163339 0.986570i \(-0.447773\pi\)
\(572\) 9.81416 11.0584i 0.0171576 0.0193329i
\(573\) 0 0
\(574\) 77.8670 + 173.215i 0.135657 + 0.301769i
\(575\) 1139.78i 1.98223i
\(576\) 0 0
\(577\) 706.702 1.22479 0.612393 0.790553i \(-0.290207\pi\)
0.612393 + 0.790553i \(0.290207\pi\)
\(578\) −514.098 + 231.107i −0.889443 + 0.399839i
\(579\) 0 0
\(580\) −645.549 572.912i −1.11302 0.987780i
\(581\) −798.352 + 330.688i −1.37410 + 0.569171i
\(582\) 0 0
\(583\) 47.0045 + 47.0045i 0.0806253 + 0.0806253i
\(584\) 556.642 291.220i 0.953155 0.498665i
\(585\) 0 0
\(586\) −231.893 + 246.129i −0.395722 + 0.420015i
\(587\) −293.599 + 121.613i −0.500169 + 0.207177i −0.618481 0.785800i \(-0.712252\pi\)
0.118312 + 0.992976i \(0.462252\pi\)
\(588\) 0 0
\(589\) 619.110 + 256.444i 1.05112 + 0.435389i
\(590\) 1123.74 + 426.737i 1.90464 + 0.723283i
\(591\) 0 0
\(592\) 239.753 + 426.831i 0.404988 + 0.720998i
\(593\) 674.627i 1.13765i 0.822458 + 0.568825i \(0.192602\pi\)
−0.822458 + 0.568825i \(0.807398\pi\)
\(594\) 0 0
\(595\) 81.6391 197.094i 0.137209 0.331251i
\(596\) −438.311 151.680i −0.735422 0.254496i
\(597\) 0 0
\(598\) 55.7508 59.1733i 0.0932288 0.0989520i
\(599\) −379.725 + 379.725i −0.633932 + 0.633932i −0.949052 0.315120i \(-0.897955\pi\)
0.315120 + 0.949052i \(0.397955\pi\)
\(600\) 0 0
\(601\) −548.542 + 548.542i −0.912715 + 0.912715i −0.996485 0.0837700i \(-0.973304\pi\)
0.0837700 + 0.996485i \(0.473304\pi\)
\(602\) −177.743 + 5.29326i −0.295255 + 0.00879278i
\(603\) 0 0
\(604\) 43.1146 + 723.236i 0.0713818 + 1.19741i
\(605\) −362.733 + 875.715i −0.599559 + 1.44746i
\(606\) 0 0
\(607\) 1.05067i 0.00173092i −1.00000 0.000865460i \(-0.999725\pi\)
1.00000 0.000865460i \(-0.000275484\pi\)
\(608\) 445.652 66.8330i 0.732980 0.109923i
\(609\) 0 0
\(610\) 557.047 + 1239.15i 0.913192 + 2.03140i
\(611\) 94.4614 + 39.1272i 0.154601 + 0.0640379i
\(612\) 0 0
\(613\) 625.826 259.226i 1.02092 0.422881i 0.191495 0.981494i \(-0.438666\pi\)
0.829428 + 0.558613i \(0.188666\pi\)
\(614\) 17.3443 + 582.408i 0.0282481 + 0.948548i
\(615\) 0 0
\(616\) −120.240 + 143.894i −0.195195 + 0.233594i
\(617\) −180.644 180.644i −0.292779 0.292779i 0.545398 0.838177i \(-0.316378\pi\)
−0.838177 + 0.545398i \(0.816378\pi\)
\(618\) 0 0
\(619\) 555.651 230.158i 0.897658 0.371822i 0.114339 0.993442i \(-0.463525\pi\)
0.783319 + 0.621620i \(0.213525\pi\)
\(620\) 1480.92 + 512.480i 2.38858 + 0.826580i
\(621\) 0 0
\(622\) −74.3564 + 195.804i −0.119544 + 0.314798i
\(623\) 221.265 0.355160
\(624\) 0 0
\(625\) 135.712i 0.217139i
\(626\) 120.203 316.534i 0.192018 0.505645i
\(627\) 0 0
\(628\) −92.0778 189.529i −0.146621 0.301798i
\(629\) 31.3584 + 75.7058i 0.0498543 + 0.120359i
\(630\) 0 0
\(631\) −267.583 + 267.583i −0.424062 + 0.424062i −0.886600 0.462537i \(-0.846939\pi\)
0.462537 + 0.886600i \(0.346939\pi\)
\(632\) −26.2558 + 83.8713i −0.0415440 + 0.132708i
\(633\) 0 0
\(634\) −24.0446 807.399i −0.0379252 1.27350i
\(635\) −450.652 1087.97i −0.709688 1.71334i
\(636\) 0 0
\(637\) −26.0503 + 62.8911i −0.0408954 + 0.0987301i
\(638\) 52.0670 + 115.823i 0.0816097 + 0.181541i
\(639\) 0 0
\(640\) 1031.02 218.030i 1.61096 0.340672i
\(641\) 834.869 1.30245 0.651224 0.758886i \(-0.274256\pi\)
0.651224 + 0.758886i \(0.274256\pi\)
\(642\) 0 0
\(643\) 1006.71 + 416.995i 1.56565 + 0.648514i 0.986060 0.166393i \(-0.0532119\pi\)
0.579592 + 0.814907i \(0.303212\pi\)
\(644\) −684.418 + 771.192i −1.06276 + 1.19750i
\(645\) 0 0
\(646\) 75.3951 2.24529i 0.116711 0.00347568i
\(647\) 857.194 + 857.194i 1.32488 + 1.32488i 0.909776 + 0.415099i \(0.136253\pi\)
0.415099 + 0.909776i \(0.363747\pi\)
\(648\) 0 0
\(649\) −125.054 125.054i −0.192687 0.192687i
\(650\) −89.5239 + 95.0196i −0.137729 + 0.146184i
\(651\) 0 0
\(652\) 267.442 129.930i 0.410187 0.199278i
\(653\) 105.248 + 43.5953i 0.161177 + 0.0667616i 0.461813 0.886977i \(-0.347199\pi\)
−0.300636 + 0.953739i \(0.597199\pi\)
\(654\) 0 0
\(655\) 500.306 0.763826
\(656\) −97.0561 + 123.439i −0.147951 + 0.188169i
\(657\) 0 0
\(658\) −1212.27 460.357i −1.84235 0.699630i
\(659\) 222.875 538.067i 0.338201 0.816490i −0.659687 0.751540i \(-0.729311\pi\)
0.997889 0.0649499i \(-0.0206888\pi\)
\(660\) 0 0
\(661\) −396.971 958.372i −0.600561 1.44988i −0.873005 0.487711i \(-0.837832\pi\)
0.272445 0.962171i \(-0.412168\pi\)
\(662\) 558.197 592.464i 0.843197 0.894960i
\(663\) 0 0
\(664\) −548.270 458.143i −0.825708 0.689974i
\(665\) 793.210 793.210i 1.19280 1.19280i
\(666\) 0 0
\(667\) 267.214 + 645.111i 0.400620 + 0.967183i
\(668\) −741.711 + 44.2160i −1.11035 + 0.0661916i
\(669\) 0 0
\(670\) −1466.09 + 659.067i −2.18820 + 0.983682i
\(671\) 199.888i 0.297896i
\(672\) 0 0
\(673\) −908.805 −1.35038 −0.675190 0.737644i \(-0.735938\pi\)
−0.675190 + 0.737644i \(0.735938\pi\)
\(674\) −479.131 1065.83i −0.710876 1.58134i
\(675\) 0 0
\(676\) −665.507 + 39.6732i −0.984477 + 0.0586881i
\(677\) −963.142 + 398.947i −1.42266 + 0.589286i −0.955528 0.294900i \(-0.904713\pi\)
−0.467134 + 0.884186i \(0.654713\pi\)
\(678\) 0 0
\(679\) −428.581 428.581i −0.631195 0.631195i
\(680\) 175.688 15.7333i 0.258364 0.0231372i
\(681\) 0 0
\(682\) −167.813 158.107i −0.246060 0.231828i
\(683\) −248.963 + 103.124i −0.364515 + 0.150987i −0.557420 0.830230i \(-0.688209\pi\)
0.192906 + 0.981217i \(0.438209\pi\)
\(684\) 0 0
\(685\) −1808.92 749.280i −2.64076 1.09384i
\(686\) −30.1232 + 79.3239i −0.0439113 + 0.115633i
\(687\) 0 0
\(688\) −72.0052 128.190i −0.104659 0.186323i
\(689\) 41.8664i 0.0607640i
\(690\) 0 0
\(691\) −222.756 + 537.780i −0.322367 + 0.778263i 0.676748 + 0.736214i \(0.263388\pi\)
−0.999116 + 0.0420488i \(0.986612\pi\)
\(692\) 802.403 389.826i 1.15954 0.563333i
\(693\) 0 0
\(694\) −57.1444 53.8393i −0.0823407 0.0775782i
\(695\) −614.853 + 614.853i −0.884681 + 0.884681i
\(696\) 0 0
\(697\) −18.5851 + 18.5851i −0.0266645 + 0.0266645i
\(698\) 12.8982 + 433.111i 0.0184788 + 0.620504i
\(699\) 0 0
\(700\) 1099.03 1238.37i 1.57004 1.76910i
\(701\) 236.347 570.592i 0.337157 0.813969i −0.660829 0.750536i \(-0.729795\pi\)
0.997986 0.0634324i \(-0.0202047\pi\)
\(702\) 0 0
\(703\) 430.882i 0.612919i
\(704\) −151.507 32.9378i −0.215209 0.0467866i
\(705\) 0 0
\(706\) −390.234 + 175.426i −0.552740 + 0.248478i
\(707\) −384.446 159.243i −0.543771 0.225237i
\(708\) 0 0
\(709\) −599.630 + 248.375i −0.845740 + 0.350317i −0.763114 0.646264i \(-0.776331\pi\)
−0.0826257 + 0.996581i \(0.526331\pi\)
\(710\) 46.1746 1.37509i 0.0650347 0.00193675i
\(711\) 0 0
\(712\) 84.8085 + 162.104i 0.119113 + 0.227674i
\(713\) −896.458 896.458i −1.25730 1.25730i
\(714\) 0 0
\(715\) 28.1153 11.6457i 0.0393221 0.0162877i
\(716\) 366.326 + 754.031i 0.511628 + 1.05312i
\(717\) 0 0
\(718\) 622.925 + 236.555i 0.867583 + 0.329464i
\(719\) −96.4410 −0.134132 −0.0670661 0.997749i \(-0.521364\pi\)
−0.0670661 + 0.997749i \(0.521364\pi\)
\(720\) 0 0
\(721\) 497.048i 0.689388i
\(722\) −304.181 115.512i −0.421303 0.159989i
\(723\) 0 0
\(724\) 922.925 + 319.383i 1.27476 + 0.441137i
\(725\) −429.088 1035.91i −0.591846 1.42884i
\(726\) 0 0
\(727\) −708.402 + 708.402i −0.974418 + 0.974418i −0.999681 0.0252626i \(-0.991958\pi\)
0.0252626 + 0.999681i \(0.491958\pi\)
\(728\) −117.631 + 10.5341i −0.161580 + 0.0144700i
\(729\) 0 0
\(730\) 1292.45 38.4896i 1.77048 0.0527255i
\(731\) −9.41788 22.7368i −0.0128836 0.0311037i
\(732\) 0 0
\(733\) −149.531 + 361.000i −0.203999 + 0.492497i −0.992457 0.122591i \(-0.960880\pi\)
0.788458 + 0.615088i \(0.210880\pi\)
\(734\) −485.686 + 218.335i −0.661697 + 0.297459i
\(735\) 0 0
\(736\) −827.324 205.832i −1.12408 0.279663i
\(737\) 236.497 0.320891
\(738\) 0 0
\(739\) −971.442 402.384i −1.31454 0.544499i −0.388331 0.921520i \(-0.626948\pi\)
−0.926205 + 0.377021i \(0.876948\pi\)
\(740\) 59.9615 + 1005.84i 0.0810291 + 1.35924i
\(741\) 0 0
\(742\) −15.8057 530.744i −0.0213015 0.715288i
\(743\) −117.181 117.181i −0.157714 0.157714i 0.623839 0.781553i \(-0.285572\pi\)
−0.781553 + 0.623839i \(0.785572\pi\)
\(744\) 0 0
\(745\) −675.032 675.032i −0.906083 0.906083i
\(746\) −508.383 478.979i −0.681478 0.642063i
\(747\) 0 0
\(748\) −24.5250 8.48701i −0.0327875 0.0113463i
\(749\) −1081.70 448.056i −1.44420 0.598206i
\(750\) 0 0
\(751\) 604.910 0.805473 0.402736 0.915316i \(-0.368059\pi\)
0.402736 + 0.915316i \(0.368059\pi\)
\(752\) −127.380 1064.59i −0.169388 1.41567i
\(753\) 0 0
\(754\) −28.3934 + 74.7689i −0.0376570 + 0.0991629i
\(755\) −570.670 + 1377.72i −0.755855 + 1.82479i
\(756\) 0 0
\(757\) −459.899 1110.29i −0.607528 1.46670i −0.865680 0.500598i \(-0.833113\pi\)
0.258152 0.966104i \(-0.416887\pi\)
\(758\) −4.80619 4.52820i −0.00634061 0.00597388i
\(759\) 0 0
\(760\) 885.155 + 277.096i 1.16468 + 0.364601i
\(761\) −202.753 + 202.753i −0.266430 + 0.266430i −0.827660 0.561230i \(-0.810328\pi\)
0.561230 + 0.827660i \(0.310328\pi\)
\(762\) 0 0
\(763\) −223.483 539.535i −0.292900 0.707124i
\(764\) 60.3250 + 53.5372i 0.0789594 + 0.0700749i
\(765\) 0 0
\(766\) −254.688 566.553i −0.332491 0.739626i
\(767\) 111.384i 0.145220i
\(768\) 0 0
\(769\) 954.072 1.24067 0.620333 0.784338i \(-0.286997\pi\)
0.620333 + 0.784338i \(0.286997\pi\)
\(770\) −352.023 + 158.248i −0.457173 + 0.205517i
\(771\) 0 0
\(772\) 307.715 346.729i 0.398595 0.449131i
\(773\) −244.204 + 101.153i −0.315918 + 0.130857i −0.535007 0.844847i \(-0.679691\pi\)
0.219090 + 0.975705i \(0.429691\pi\)
\(774\) 0 0
\(775\) 1439.52 + 1439.52i 1.85744 + 1.85744i
\(776\) 149.719 478.260i 0.192936 0.616314i
\(777\) 0 0
\(778\) −1005.36 + 1067.08i −1.29224 + 1.37157i
\(779\) −127.685 + 52.8890i −0.163909 + 0.0678934i
\(780\) 0 0
\(781\) −6.27923 2.60094i −0.00803999 0.00333027i
\(782\) −133.406 50.6607i −0.170596 0.0647835i
\(783\) 0 0
\(784\) 708.787 84.8079i 0.904065 0.108173i
\(785\) 433.696i 0.552479i
\(786\) 0 0
\(787\) −19.8368 + 47.8903i −0.0252056 + 0.0608518i −0.935981 0.352050i \(-0.885485\pi\)
0.910776 + 0.412902i \(0.13