Properties

Label 288.3.u.a.91.1
Level $288$
Weight $3$
Character 288.91
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 91.1
Character \(\chi\) \(=\) 288.91
Dual form 288.3.u.a.19.1

$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

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

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 0.977842 0.209346i \(-0.0671336\pi\)
0.543408 + 0.839469i \(0.317134\pi\)
\(6\) 0 0
\(7\) 6.84161 6.84161i 0.977372 0.977372i −0.0223772 0.999750i \(-0.507123\pi\)
0.999750 + 0.0223772i \(0.00712349\pi\)
\(8\) −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 0.482092 0.876121i \(-0.339877\pi\)
−0.278621 + 0.960401i \(0.589877\pi\)
\(12\) 0 0
\(13\) 1.40964 0.583890i 0.108433 0.0449146i −0.327807 0.944745i \(-0.606310\pi\)
0.436241 + 0.899830i \(0.356310\pi\)
\(14\) −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 \(0.0250987\pi\)
−0.996893 + 0.0787683i \(0.974901\pi\)
\(18\) 0 0
\(19\) 5.38908 + 13.0104i 0.283636 + 0.684757i 0.999915 0.0130566i \(-0.00415616\pi\)
−0.716279 + 0.697814i \(0.754156\pi\)
\(20\) 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 0.166898 0.985974i \(-0.446625\pi\)
−0.985974 + 0.166898i \(0.946625\pi\)
\(24\) 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 0.997100 + 0.0761000i \(0.0242468\pi\)
−0.651245 + 0.758867i \(0.725753\pi\)
\(30\) 0 0
\(31\) 47.5858i 1.53503i −0.641033 0.767513i \(-0.721494\pi\)
0.641033 0.767513i \(-0.278506\pi\)
\(32\) 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 −0.0335642 0.999437i \(-0.510686\pi\)
−0.730442 + 0.682975i \(0.760686\pi\)
\(38\) 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 −0.786654 0.617395i \(-0.788188\pi\)
0.617395 + 0.786654i \(0.288188\pi\)
\(42\) 0 0
\(43\) 8.48982 + 3.51660i 0.197438 + 0.0817814i 0.479211 0.877700i \(-0.340923\pi\)
−0.281774 + 0.959481i \(0.590923\pi\)
\(44\) 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 −0.793326 0.608797i \(-0.791653\pi\)
0.991451 + 0.130482i \(0.0416525\pi\)
\(54\) 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 0.489107 + 0.872224i \(0.337323\pi\)
−0.962606 + 0.270904i \(0.912677\pi\)
\(60\) 0 0
\(61\) 31.5752 + 76.2294i 0.517627 + 1.24966i 0.939357 + 0.342941i \(0.111423\pi\)
−0.421730 + 0.906721i \(0.638577\pi\)
\(62\) −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 0.410913 0.911674i \(-0.365210\pi\)
0.935211 + 0.354092i \(0.115210\pi\)
\(68\) −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 −0.720939 0.692998i \(-0.756289\pi\)
0.692998 + 0.720939i \(0.256289\pi\)
\(72\) 0 0
\(73\) −55.5273 + 55.5273i −0.760648 + 0.760648i −0.976439 0.215792i \(-0.930767\pi\)
0.215792 + 0.976439i \(0.430767\pi\)
\(74\) 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 −0.984659 0.174489i \(-0.944173\pi\)
0.572877 0.819641i \(-0.305827\pi\)
\(84\) 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 0.792093 0.610401i \(-0.208992\pi\)
−0.610401 + 0.792093i \(0.708992\pi\)
\(90\) 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 0.177206 0.984174i \(-0.443294\pi\)
−0.570612 + 0.821220i \(0.693294\pi\)
\(102\) 0 0
\(103\) −36.3254 + 36.3254i −0.352674 + 0.352674i −0.861104 0.508430i \(-0.830226\pi\)
0.508430 + 0.861104i \(0.330226\pi\)
\(104\) −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 −0.206796 0.978384i \(-0.566304\pi\)
−0.838049 + 0.545596i \(0.816304\pi\)
\(108\) 0 0
\(109\) −55.7631 + 23.0978i −0.511588 + 0.211907i −0.623517 0.781809i \(-0.714297\pi\)
0.111929 + 0.993716i \(0.464297\pi\)
\(110\) −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 \(-0.883659\pi\)
0.933947 0.357413i \(-0.116341\pi\)
\(114\) 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 \(0.190405\pi\)
−0.826365 + 0.563135i \(0.809595\pi\)
\(128\) 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 −0.157961 0.987445i \(-0.550492\pi\)
0.586534 + 0.809925i \(0.300492\pi\)
\(132\) 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 −0.262563 + 0.964915i \(0.584568\pi\)
−0.964915 + 0.262563i \(0.915432\pi\)
\(138\) 0 0
\(139\) −97.5768 40.4176i −0.701991 0.290774i 0.00299484 0.999996i \(-0.499047\pi\)
−0.704986 + 0.709221i \(0.749047\pi\)
\(140\) 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 0.702167 + 0.712012i \(0.252216\pi\)
−0.999976 + 0.00696156i \(0.997784\pi\)
\(150\) 0 0
\(151\) −128.078 128.078i −0.848200 0.848200i 0.141708 0.989908i \(-0.454741\pi\)
−0.989908 + 0.141708i \(0.954741\pi\)
\(152\) 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 0.974986 0.222265i \(-0.0713452\pi\)
−0.846585 + 0.532254i \(0.821345\pi\)
\(158\) −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 −0.161943 0.986800i \(-0.551776\pi\)
0.583262 + 0.812284i \(0.301776\pi\)
\(164\) −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 −0.980923 0.194396i \(-0.937725\pi\)
0.194396 + 0.980923i \(0.437725\pi\)
\(168\) 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 0.302926 0.953014i \(-0.402036\pi\)
0.888084 + 0.459681i \(0.152036\pi\)
\(174\) 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 −0.973051 0.230591i \(-0.925934\pi\)
0.524998 0.851104i \(-0.324066\pi\)
\(180\) 0 0
\(181\) 93.4345 225.571i 0.516213 1.24625i −0.424000 0.905662i \(-0.639374\pi\)
0.940213 0.340586i \(-0.110626\pi\)
\(182\) −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 \(-0.983190\pi\)
0.998606 0.0527851i \(-0.0168098\pi\)
\(192\) 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 0.785010 0.619483i \(-0.212658\pi\)
0.117045 + 0.993127i \(0.462658\pi\)
\(198\) 0 0
\(199\) −22.1763 + 22.1763i −0.111439 + 0.111439i −0.760627 0.649189i \(-0.775109\pi\)
0.649189 + 0.760627i \(0.275109\pi\)
\(200\) 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 −0.914300 0.405038i \(-0.867258\pi\)
0.360103 0.932913i \(-0.382742\pi\)
\(212\) 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 \(-0.991334\pi\)
0.999629 0.0272217i \(-0.00866601\pi\)
\(224\) −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 −0.802350 0.596854i \(-0.796417\pi\)
−0.145307 + 0.989387i \(0.546417\pi\)
\(228\) 0 0
\(229\) 85.4872 + 35.4100i 0.373307 + 0.154629i 0.561445 0.827514i \(-0.310245\pi\)
−0.188139 + 0.982142i \(0.560245\pi\)
\(230\) −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 −0.774591 0.632462i \(-0.782044\pi\)
0.632462 + 0.774591i \(0.282044\pi\)
\(234\) 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 \(0.150032\pi\)
−0.890961 + 0.454080i \(0.849968\pi\)
\(242\) 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 0.624687 + 0.780875i \(0.285227\pi\)
−0.993883 + 0.110442i \(0.964773\pi\)
\(252\) 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 −0.859605 0.510959i \(-0.829290\pi\)
0.510959 + 0.859605i \(0.329290\pi\)
\(264\) 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 −0.690507 0.723325i \(-0.742613\pi\)
0.0232059 + 0.999731i \(0.492613\pi\)
\(270\) 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 −0.944889 0.327391i \(-0.893830\pi\)
0.899638 + 0.436637i \(0.143830\pi\)
\(278\) 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 −0.992731 0.120353i \(-0.961597\pi\)
−0.120353 0.992731i \(-0.538403\pi\)
\(282\) 0 0
\(283\) −74.2838 + 179.337i −0.262487 + 0.633700i −0.999091 0.0426244i \(-0.986428\pi\)
0.736604 + 0.676324i \(0.236428\pi\)
\(284\) −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 0.632979 0.774169i \(-0.281832\pi\)
−0.0998364 + 0.995004i \(0.531832\pi\)
\(294\) 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 0.994835 + 0.101504i \(0.0323654\pi\)
−0.631681 + 0.775229i \(0.717635\pi\)
\(308\) 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 0.816065 0.577960i \(-0.196151\pi\)
−0.577960 + 0.816065i \(0.696151\pi\)
\(312\) 0 0
\(313\) −119.709 119.709i −0.382458 0.382458i 0.489529 0.871987i \(-0.337169\pi\)
−0.871987 + 0.489529i \(0.837169\pi\)
\(314\) 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 −0.955942 0.293554i \(-0.905162\pi\)
0.468379 0.883528i \(-0.344838\pi\)
\(318\) 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 −0.266190 0.963921i \(-0.585765\pi\)
−0.869820 + 0.493370i \(0.835765\pi\)
\(332\) 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 \(-0.666115\pi\)
0.498499 0.866890i \(-0.333885\pi\)
\(338\) 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 −0.900754 0.434330i \(-0.856985\pi\)
0.944047 + 0.329812i \(0.106985\pi\)
\(348\) 0 0
\(349\) 82.9090 + 200.160i 0.237562 + 0.573525i 0.997030 0.0770202i \(-0.0245406\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(350\) −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 −0.954483 0.298264i \(-0.903592\pi\)
0.298264 + 0.954483i \(0.403592\pi\)
\(360\) 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 −0.637232 0.770672i \(-0.719921\pi\)
0.995539 0.0943560i \(-0.0300792\pi\)
\(374\) 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 −0.922204 0.386704i \(-0.873614\pi\)
0.925538 + 0.378656i \(0.123614\pi\)
\(380\) −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 \(-0.867111\pi\)
0.914112 0.405462i \(-0.132889\pi\)
\(384\) 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 0.998695 + 0.0510705i \(0.0162633\pi\)
0.742296 + 0.670072i \(0.233737\pi\)
\(390\) 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 −0.883840 0.467789i \(-0.845051\pi\)
−0.294192 + 0.955746i \(0.595051\pi\)
\(398\) 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 \(-0.811441\pi\)
0.829617 0.558333i \(-0.188559\pi\)
\(402\) 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 0.953458 0.301527i \(-0.0974962\pi\)
−0.301527 + 0.953458i \(0.597496\pi\)
\(410\) 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 0.413481 0.910513i \(-0.364313\pi\)
0.936205 + 0.351455i \(0.114313\pi\)
\(420\) 0 0
\(421\) −184.538 76.4382i −0.438333 0.181564i 0.152593 0.988289i \(-0.451238\pi\)
−0.590926 + 0.806726i \(0.701238\pi\)
\(422\) −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 \(0.154261\pi\)
−0.884850 + 0.465877i \(0.845739\pi\)
\(434\) 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 0.999882 0.0153402i \(-0.00488314\pi\)
−0.0153402 + 0.999882i \(0.504883\pi\)
\(440\) 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 0.687799 + 0.725901i \(0.258577\pi\)
−0.999637 + 0.0269419i \(0.991423\pi\)
\(444\) 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 −0.850569 0.525864i \(-0.823742\pi\)
0.525864 + 0.850569i \(0.323742\pi\)
\(458\) −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 −0.125899 0.992043i \(-0.540182\pi\)
0.612456 + 0.790505i \(0.290182\pi\)
\(462\) 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 −0.985448 0.169977i \(-0.945631\pi\)
0.576625 0.817009i \(-0.304369\pi\)
\(468\) 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 \(0.300379\pi\)
−0.586821 + 0.809717i \(0.699621\pi\)
\(480\) 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 −0.992110 0.125372i \(-0.959988\pi\)
0.125372 + 0.992110i \(0.459988\pi\)
\(488\) 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 0.646987 0.762501i \(-0.276029\pi\)
−0.0816809 + 0.996659i \(0.526029\pi\)
\(492\) 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 −0.800410 0.599452i \(-0.795385\pi\)
0.142099 0.989852i \(-0.454615\pi\)
\(500\) −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 0.812501 0.582960i \(-0.198106\pi\)
−0.582960 + 0.812501i \(0.698106\pi\)
\(504\) 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 0.990331 0.138727i \(-0.0443009\pi\)
−0.798364 + 0.602175i \(0.794301\pi\)
\(510\) 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 −0.892437 0.451173i \(-0.851006\pi\)
0.451173 + 0.892437i \(0.351006\pi\)
\(522\) 0 0
\(523\) −900.921 373.174i −1.72260 0.713525i −0.999746 0.0225265i \(-0.992829\pi\)
−0.722856 0.690999i \(-0.757171\pi\)
\(524\) 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 0.983385 0.181533i \(-0.0581058\pi\)
−0.823721 + 0.566995i \(0.808106\pi\)
\(542\) 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 0.121628 0.992576i \(-0.461188\pi\)
0.787861 + 0.615853i \(0.211188\pi\)
\(548\) −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 0.145385 0.989375i \(-0.453558\pi\)
0.802397 + 0.596791i \(0.203558\pi\)
\(558\) 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 0.924871 + 0.380281i \(0.124173\pi\)
−0.385084 + 0.922882i \(0.625827\pi\)
\(564\) 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 0.821965 0.569538i \(-0.192878\pi\)
−0.569538 + 0.821965i \(0.692878\pi\)
\(570\) 0 0
\(571\) −371.018 + 895.717i −0.649769 + 1.56868i 0.163339 + 0.986570i \(0.447773\pi\)
−0.813109 + 0.582112i \(0.802227\pi\)
\(572\) 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 0.118312 0.992976i \(-0.462252\pi\)
−0.618481 + 0.785800i \(0.712252\pi\)
\(588\) 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 \(-0.807398\pi\)
0.822458 0.568825i \(-0.192602\pi\)
\(594\) 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 0.315120 0.949052i \(-0.397955\pi\)
−0.949052 + 0.315120i \(0.897955\pi\)
\(600\) 0 0
\(601\) −548.542 548.542i −0.912715 0.912715i 0.0837700 0.996485i \(-0.473304\pi\)
−0.996485 + 0.0837700i \(0.973304\pi\)
\(602\) −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 \(0.000275484\pi\)
−1.00000 0.000865460i \(0.999725\pi\)
\(608\) 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 0.829428 0.558613i \(-0.188666\pi\)
0.191495 + 0.981494i \(0.438666\pi\)
\(614\) 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 −0.838177 0.545398i \(-0.816378\pi\)
0.545398 + 0.838177i \(0.316378\pi\)
\(618\) 0 0
\(619\) 555.651 + 230.158i 0.897658 + 0.371822i 0.783319 0.621620i \(-0.213525\pi\)
0.114339 + 0.993442i \(0.463525\pi\)
\(620\) 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 0.462537 0.886600i \(-0.346939\pi\)
−0.886600 + 0.462537i \(0.846939\pi\)
\(632\) −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 0.579592 0.814907i \(-0.303212\pi\)
0.986060 + 0.166393i \(0.0532119\pi\)
\(644\) −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 0.415099 0.909776i \(-0.363747\pi\)
0.909776 0.415099i \(-0.136253\pi\)
\(648\) 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 −0.300636 0.953739i \(-0.597199\pi\)
0.461813 + 0.886977i \(0.347199\pi\)
\(654\) 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 0.997889 + 0.0649499i \(0.0206888\pi\)
−0.659687 + 0.751540i \(0.729311\pi\)
\(660\) 0 0
\(661\) −396.971 + 958.372i −0.600561 + 1.44988i 0.272445 + 0.962171i \(0.412168\pi\)
−0.873005 + 0.487711i \(0.837832\pi\)
\(662\) 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 −0.467134 0.884186i \(-0.654713\pi\)
−0.955528 + 0.294900i \(0.904713\pi\)
\(678\) 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 0.192906 0.981217i \(-0.438209\pi\)
−0.557420 + 0.830230i \(0.688209\pi\)
\(684\) 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 −0.999116 0.0420488i \(-0.986612\pi\)
0.676748 0.736214i \(-0.263388\pi\)
\(692\) 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 0.997986 + 0.0634324i \(0.0202047\pi\)
−0.660829 + 0.750536i \(0.729795\pi\)
\(702\) 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 −0.0826257 0.996581i \(-0.526331\pi\)
−0.763114 + 0.646264i \(0.776331\pi\)
\(710\) 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 0.0252626 0.999681i \(-0.491958\pi\)
−0.999681 + 0.0252626i \(0.991958\pi\)
\(728\) −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 0.788458 0.615088i \(-0.210880\pi\)
−0.992457 + 0.122591i \(0.960880\pi\)
\(734\) −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 −0.926205 0.377021i \(-0.876948\pi\)
−0.388331 + 0.921520i \(0.626948\pi\)
\(740\) 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 −0.781553 0.623839i \(-0.785572\pi\)
0.623839 + 0.781553i \(0.285572\pi\)
\(744\) 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 0.258152 + 0.966104i \(0.416887\pi\)
−0.865680 + 0.500598i \(0.833113\pi\)
\(758\) −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 0.561230 0.827660i \(-0.310328\pi\)
−0.827660 + 0.561230i \(0.810328\pi\)
\(762\) 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 0.219090 0.975705i \(-0.429691\pi\)
−0.535007 + 0.844847i \(0.679691\pi\)
\(774\) 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 0.910776 0.412902i \(-0.135485\pi\)
−0.935981 + 0.352050i \(0.885485\pi\)