Properties

Label 288.3.u.a.91.6
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 91.6
Character \(\chi\) \(=\) 288.91
Dual form 288.3.u.a.19.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.62478 + 1.16623i) q^{2} +(1.27980 + 3.78974i) q^{4} +(4.51028 + 1.86822i) q^{5} +(-3.85317 + 3.85317i) q^{7} +(-2.34032 + 7.65003i) q^{8} +O(q^{10})\) \(q+(1.62478 + 1.16623i) q^{2} +(1.27980 + 3.78974i) q^{4} +(4.51028 + 1.86822i) q^{5} +(-3.85317 + 3.85317i) q^{7} +(-2.34032 + 7.65003i) q^{8} +(5.14942 + 8.29547i) q^{10} +(4.56441 + 1.89064i) q^{11} +(-5.58307 + 2.31258i) q^{13} +(-10.7542 + 1.76685i) q^{14} +(-12.7242 + 9.70024i) q^{16} -25.0539i q^{17} +(6.43433 + 15.5338i) q^{19} +(-1.30778 + 19.4837i) q^{20} +(5.21122 + 8.39503i) q^{22} +(26.9024 + 26.9024i) q^{23} +(-0.825315 - 0.825315i) q^{25} +(-11.7682 - 2.75372i) q^{26} +(-19.5338 - 9.67119i) q^{28} +(0.210028 + 0.507052i) q^{29} -15.8372i q^{31} +(-31.9867 + 0.921357i) q^{32} +(29.2186 - 40.7070i) q^{34} +(-24.5774 + 10.1803i) q^{35} +(-2.18606 - 0.905498i) q^{37} +(-7.66172 + 32.7430i) q^{38} +(-24.8474 + 30.1315i) q^{40} +(31.1517 - 31.1517i) q^{41} +(12.9078 + 5.34659i) q^{43} +(-1.32348 + 19.7175i) q^{44} +(12.3360 + 75.0848i) q^{46} -15.0033 q^{47} +19.3062i q^{49} +(-0.378444 - 2.30346i) q^{50} +(-15.9093 - 18.1987i) q^{52} +(15.4409 - 37.2776i) q^{53} +(17.0546 + 17.0546i) q^{55} +(-20.4592 - 38.4945i) q^{56} +(-0.250092 + 1.06879i) q^{58} +(14.7242 - 35.5473i) q^{59} +(-15.4603 - 37.3243i) q^{61} +(18.4698 - 25.7319i) q^{62} +(-53.0458 - 35.8070i) q^{64} -29.5016 q^{65} +(61.3598 - 25.4161i) q^{67} +(94.9476 - 32.0641i) q^{68} +(-51.8054 - 12.1223i) q^{70} +(51.7789 - 51.7789i) q^{71} +(64.9440 - 64.9440i) q^{73} +(-2.49585 - 4.02069i) q^{74} +(-50.6345 + 44.2647i) q^{76} +(-24.8724 + 10.3025i) q^{77} -38.1202 q^{79} +(-75.5118 + 19.9792i) q^{80} +(86.9447 - 14.2845i) q^{82} +(-15.9782 - 38.5748i) q^{83} +(46.8061 - 113.000i) q^{85} +(14.7370 + 23.7405i) q^{86} +(-25.1456 + 30.4932i) q^{88} +(-23.7666 - 23.7666i) q^{89} +(12.6017 - 30.4233i) q^{91} +(-67.5231 + 136.383i) q^{92} +(-24.3771 - 17.4974i) q^{94} +82.0827i q^{95} -118.710 q^{97} +(-22.5155 + 31.3682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.62478 + 1.16623i 0.812389 + 0.583116i
\(3\) 0 0
\(4\) 1.27980 + 3.78974i 0.319951 + 0.947434i
\(5\) 4.51028 + 1.86822i 0.902055 + 0.373644i 0.785010 0.619483i \(-0.212658\pi\)
0.117045 + 0.993127i \(0.462658\pi\)
\(6\) 0 0
\(7\) −3.85317 + 3.85317i −0.550453 + 0.550453i −0.926571 0.376119i \(-0.877258\pi\)
0.376119 + 0.926571i \(0.377258\pi\)
\(8\) −2.34032 + 7.65003i −0.292539 + 0.956253i
\(9\) 0 0
\(10\) 5.14942 + 8.29547i 0.514942 + 0.829547i
\(11\) 4.56441 + 1.89064i 0.414946 + 0.171876i 0.580382 0.814344i \(-0.302903\pi\)
−0.165436 + 0.986221i \(0.552903\pi\)
\(12\) 0 0
\(13\) −5.58307 + 2.31258i −0.429467 + 0.177891i −0.586937 0.809633i \(-0.699666\pi\)
0.157470 + 0.987524i \(0.449666\pi\)
\(14\) −10.7542 + 1.76685i −0.768159 + 0.126204i
\(15\) 0 0
\(16\) −12.7242 + 9.70024i −0.795263 + 0.606265i
\(17\) 25.0539i 1.47376i −0.676025 0.736879i \(-0.736299\pi\)
0.676025 0.736879i \(-0.263701\pi\)
\(18\) 0 0
\(19\) 6.43433 + 15.5338i 0.338649 + 0.817571i 0.997846 + 0.0656005i \(0.0208963\pi\)
−0.659197 + 0.751970i \(0.729104\pi\)
\(20\) −1.30778 + 19.4837i −0.0653891 + 0.974186i
\(21\) 0 0
\(22\) 5.21122 + 8.39503i 0.236874 + 0.381592i
\(23\) 26.9024 + 26.9024i 1.16967 + 1.16967i 0.982287 + 0.187381i \(0.0600000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(24\) 0 0
\(25\) −0.825315 0.825315i −0.0330126 0.0330126i
\(26\) −11.7682 2.75372i −0.452625 0.105912i
\(27\) 0 0
\(28\) −19.5338 9.67119i −0.697636 0.345400i
\(29\) 0.210028 + 0.507052i 0.00724234 + 0.0174846i 0.927459 0.373924i \(-0.121988\pi\)
−0.920217 + 0.391409i \(0.871988\pi\)
\(30\) 0 0
\(31\) 15.8372i 0.510877i −0.966825 0.255438i \(-0.917780\pi\)
0.966825 0.255438i \(-0.0822198\pi\)
\(32\) −31.9867 + 0.921357i −0.999585 + 0.0287924i
\(33\) 0 0
\(34\) 29.2186 40.7070i 0.859372 1.19726i
\(35\) −24.5774 + 10.1803i −0.702212 + 0.290866i
\(36\) 0 0
\(37\) −2.18606 0.905498i −0.0590828 0.0244729i 0.352946 0.935644i \(-0.385180\pi\)
−0.412029 + 0.911171i \(0.635180\pi\)
\(38\) −7.66172 + 32.7430i −0.201624 + 0.861657i
\(39\) 0 0
\(40\) −24.8474 + 30.1315i −0.621185 + 0.753288i
\(41\) 31.1517 31.1517i 0.759798 0.759798i −0.216488 0.976285i \(-0.569460\pi\)
0.976285 + 0.216488i \(0.0694601\pi\)
\(42\) 0 0
\(43\) 12.9078 + 5.34659i 0.300182 + 0.124339i 0.527691 0.849437i \(-0.323058\pi\)
−0.227509 + 0.973776i \(0.573058\pi\)
\(44\) −1.32348 + 19.7175i −0.0300790 + 0.448126i
\(45\) 0 0
\(46\) 12.3360 + 75.0848i 0.268173 + 1.63228i
\(47\) −15.0033 −0.319220 −0.159610 0.987180i \(-0.551024\pi\)
−0.159610 + 0.987180i \(0.551024\pi\)
\(48\) 0 0
\(49\) 19.3062i 0.394004i
\(50\) −0.378444 2.30346i −0.00756888 0.0460692i
\(51\) 0 0
\(52\) −15.9093 18.1987i −0.305948 0.349975i
\(53\) 15.4409 37.2776i 0.291338 0.703352i −0.708660 0.705550i \(-0.750700\pi\)
0.999998 + 0.00219873i \(0.000699877\pi\)
\(54\) 0 0
\(55\) 17.0546 + 17.0546i 0.310084 + 0.310084i
\(56\) −20.4592 38.4945i −0.365343 0.687401i
\(57\) 0 0
\(58\) −0.250092 + 1.06879i −0.00431193 + 0.0184274i
\(59\) 14.7242 35.5473i 0.249562 0.602496i −0.748605 0.663016i \(-0.769276\pi\)
0.998167 + 0.0605202i \(0.0192760\pi\)
\(60\) 0 0
\(61\) −15.4603 37.3243i −0.253447 0.611875i 0.745031 0.667030i \(-0.232435\pi\)
−0.998478 + 0.0551552i \(0.982435\pi\)
\(62\) 18.4698 25.7319i 0.297900 0.415030i
\(63\) 0 0
\(64\) −53.0458 35.8070i −0.828841 0.559484i
\(65\) −29.5016 −0.453870
\(66\) 0 0
\(67\) 61.3598 25.4161i 0.915818 0.379344i 0.125537 0.992089i \(-0.459935\pi\)
0.790281 + 0.612745i \(0.209935\pi\)
\(68\) 94.9476 32.0641i 1.39629 0.471530i
\(69\) 0 0
\(70\) −51.8054 12.1223i −0.740077 0.173175i
\(71\) 51.7789 51.7789i 0.729281 0.729281i −0.241196 0.970477i \(-0.577540\pi\)
0.970477 + 0.241196i \(0.0775395\pi\)
\(72\) 0 0
\(73\) 64.9440 64.9440i 0.889643 0.889643i −0.104845 0.994489i \(-0.533435\pi\)
0.994489 + 0.104845i \(0.0334347\pi\)
\(74\) −2.49585 4.02069i −0.0337277 0.0543337i
\(75\) 0 0
\(76\) −50.6345 + 44.2647i −0.666243 + 0.582430i
\(77\) −24.8724 + 10.3025i −0.323018 + 0.133798i
\(78\) 0 0
\(79\) −38.1202 −0.482535 −0.241267 0.970459i \(-0.577563\pi\)
−0.241267 + 0.970459i \(0.577563\pi\)
\(80\) −75.5118 + 19.9792i −0.943898 + 0.249740i
\(81\) 0 0
\(82\) 86.9447 14.2845i 1.06030 0.174201i
\(83\) −15.9782 38.5748i −0.192509 0.464757i 0.797923 0.602759i \(-0.205932\pi\)
−0.990432 + 0.138002i \(0.955932\pi\)
\(84\) 0 0
\(85\) 46.8061 113.000i 0.550660 1.32941i
\(86\) 14.7370 + 23.7405i 0.171360 + 0.276053i
\(87\) 0 0
\(88\) −25.1456 + 30.4932i −0.285745 + 0.346513i
\(89\) −23.7666 23.7666i −0.267040 0.267040i 0.560866 0.827906i \(-0.310468\pi\)
−0.827906 + 0.560866i \(0.810468\pi\)
\(90\) 0 0
\(91\) 12.6017 30.4233i 0.138481 0.334322i
\(92\) −67.5231 + 136.383i −0.733947 + 1.48242i
\(93\) 0 0
\(94\) −24.3771 17.4974i −0.259331 0.186142i
\(95\) 82.0827i 0.864028i
\(96\) 0 0
\(97\) −118.710 −1.22382 −0.611908 0.790929i \(-0.709598\pi\)
−0.611908 + 0.790929i \(0.709598\pi\)
\(98\) −22.5155 + 31.3682i −0.229750 + 0.320084i
\(99\) 0 0
\(100\) 2.07148 4.18397i 0.0207148 0.0418397i
\(101\) 182.236 + 75.4846i 1.80432 + 0.747372i 0.984652 + 0.174529i \(0.0558402\pi\)
0.819665 + 0.572844i \(0.194160\pi\)
\(102\) 0 0
\(103\) −80.3171 + 80.3171i −0.779777 + 0.779777i −0.979793 0.200016i \(-0.935901\pi\)
0.200016 + 0.979793i \(0.435901\pi\)
\(104\) −4.62518 48.1228i −0.0444728 0.462719i
\(105\) 0 0
\(106\) 68.5624 42.5602i 0.646815 0.401511i
\(107\) −22.6854 9.39659i −0.212013 0.0878186i 0.274150 0.961687i \(-0.411604\pi\)
−0.486162 + 0.873868i \(0.661604\pi\)
\(108\) 0 0
\(109\) 181.428 75.1501i 1.66448 0.689450i 0.666074 0.745886i \(-0.267974\pi\)
0.998406 + 0.0564360i \(0.0179737\pi\)
\(110\) 7.82031 + 47.5996i 0.0710937 + 0.432724i
\(111\) 0 0
\(112\) 11.6518 86.4052i 0.104034 0.771475i
\(113\) 32.7876i 0.290156i −0.989420 0.145078i \(-0.953657\pi\)
0.989420 0.145078i \(-0.0463433\pi\)
\(114\) 0 0
\(115\) 71.0777 + 171.597i 0.618067 + 1.49214i
\(116\) −1.65280 + 1.44488i −0.0142483 + 0.0124558i
\(117\) 0 0
\(118\) 65.3799 40.5846i 0.554067 0.343937i
\(119\) 96.5368 + 96.5368i 0.811234 + 0.811234i
\(120\) 0 0
\(121\) −68.3006 68.3006i −0.564468 0.564468i
\(122\) 18.4094 78.6740i 0.150897 0.644869i
\(123\) 0 0
\(124\) 60.0187 20.2685i 0.484022 0.163456i
\(125\) −48.8860 118.021i −0.391088 0.944169i
\(126\) 0 0
\(127\) 130.165i 1.02492i 0.858710 + 0.512462i \(0.171266\pi\)
−0.858710 + 0.512462i \(0.828734\pi\)
\(128\) −44.4285 120.042i −0.347097 0.937829i
\(129\) 0 0
\(130\) −47.9335 34.4057i −0.368719 0.264659i
\(131\) −24.3356 + 10.0801i −0.185768 + 0.0769476i −0.473628 0.880725i \(-0.657056\pi\)
0.287861 + 0.957672i \(0.407056\pi\)
\(132\) 0 0
\(133\) −84.6471 35.0620i −0.636444 0.263624i
\(134\) 129.337 + 30.2643i 0.965202 + 0.225853i
\(135\) 0 0
\(136\) 191.663 + 58.6340i 1.40929 + 0.431132i
\(137\) −147.886 + 147.886i −1.07946 + 1.07946i −0.0829047 + 0.996557i \(0.526420\pi\)
−0.996557 + 0.0829047i \(0.973580\pi\)
\(138\) 0 0
\(139\) −206.929 85.7129i −1.48870 0.616639i −0.517666 0.855583i \(-0.673199\pi\)
−0.971033 + 0.238944i \(0.923199\pi\)
\(140\) −70.0349 80.1131i −0.500249 0.572237i
\(141\) 0 0
\(142\) 144.516 23.7430i 1.01772 0.167204i
\(143\) −29.8556 −0.208781
\(144\) 0 0
\(145\) 2.67932i 0.0184781i
\(146\) 181.259 29.7797i 1.24150 0.203971i
\(147\) 0 0
\(148\) 0.633863 9.44347i 0.00428286 0.0638072i
\(149\) 20.4247 49.3095i 0.137078 0.330936i −0.840402 0.541964i \(-0.817681\pi\)
0.977480 + 0.211028i \(0.0676810\pi\)
\(150\) 0 0
\(151\) 180.137 + 180.137i 1.19296 + 1.19296i 0.976232 + 0.216726i \(0.0695379\pi\)
0.216726 + 0.976232i \(0.430462\pi\)
\(152\) −133.893 + 12.8687i −0.880873 + 0.0846624i
\(153\) 0 0
\(154\) −52.4272 12.2677i −0.340436 0.0796607i
\(155\) 29.5873 71.4300i 0.190886 0.460839i
\(156\) 0 0
\(157\) −60.3999 145.818i −0.384713 0.928779i −0.991040 0.133564i \(-0.957358\pi\)
0.606327 0.795215i \(-0.292642\pi\)
\(158\) −61.9369 44.4571i −0.392006 0.281374i
\(159\) 0 0
\(160\) −145.990 55.6026i −0.912439 0.347516i
\(161\) −207.319 −1.28769
\(162\) 0 0
\(163\) −152.162 + 63.0277i −0.933512 + 0.386673i −0.797010 0.603966i \(-0.793586\pi\)
−0.136502 + 0.990640i \(0.543586\pi\)
\(164\) 157.925 + 78.1887i 0.962956 + 0.476760i
\(165\) 0 0
\(166\) 19.0262 81.3099i 0.114615 0.489818i
\(167\) −94.8188 + 94.8188i −0.567777 + 0.567777i −0.931505 0.363728i \(-0.881504\pi\)
0.363728 + 0.931505i \(0.381504\pi\)
\(168\) 0 0
\(169\) −93.6785 + 93.6785i −0.554310 + 0.554310i
\(170\) 207.834 129.013i 1.22255 0.758900i
\(171\) 0 0
\(172\) −3.74270 + 55.7598i −0.0217599 + 0.324185i
\(173\) 107.416 44.4930i 0.620900 0.257185i −0.0499813 0.998750i \(-0.515916\pi\)
0.670881 + 0.741565i \(0.265916\pi\)
\(174\) 0 0
\(175\) 6.36016 0.0363437
\(176\) −76.4181 + 20.2190i −0.434194 + 0.114881i
\(177\) 0 0
\(178\) −10.8981 66.3328i −0.0612250 0.372656i
\(179\) −54.7154 132.095i −0.305673 0.737959i −0.999835 0.0181410i \(-0.994225\pi\)
0.694163 0.719818i \(-0.255775\pi\)
\(180\) 0 0
\(181\) −128.496 + 310.218i −0.709925 + 1.71391i −0.00973575 + 0.999953i \(0.503099\pi\)
−0.700189 + 0.713957i \(0.746901\pi\)
\(182\) 55.9556 34.7345i 0.307448 0.190849i
\(183\) 0 0
\(184\) −268.764 + 142.844i −1.46067 + 0.776325i
\(185\) −8.16809 8.16809i −0.0441518 0.0441518i
\(186\) 0 0
\(187\) 47.3678 114.356i 0.253304 0.611530i
\(188\) −19.2013 56.8587i −0.102135 0.302440i
\(189\) 0 0
\(190\) −95.7274 + 133.366i −0.503829 + 0.701927i
\(191\) 312.806i 1.63773i 0.573986 + 0.818865i \(0.305396\pi\)
−0.573986 + 0.818865i \(0.694604\pi\)
\(192\) 0 0
\(193\) −70.6708 −0.366170 −0.183085 0.983097i \(-0.558608\pi\)
−0.183085 + 0.983097i \(0.558608\pi\)
\(194\) −192.878 138.444i −0.994215 0.713627i
\(195\) 0 0
\(196\) −73.1653 + 24.7081i −0.373292 + 0.126062i
\(197\) −81.5762 33.7900i −0.414092 0.171523i 0.165904 0.986142i \(-0.446946\pi\)
−0.579996 + 0.814619i \(0.696946\pi\)
\(198\) 0 0
\(199\) 102.666 102.666i 0.515910 0.515910i −0.400421 0.916331i \(-0.631136\pi\)
0.916331 + 0.400421i \(0.131136\pi\)
\(200\) 8.24518 4.38218i 0.0412259 0.0219109i
\(201\) 0 0
\(202\) 208.060 + 335.175i 1.03000 + 1.65928i
\(203\) −2.76303 1.14449i −0.0136110 0.00563786i
\(204\) 0 0
\(205\) 198.701 82.3046i 0.969273 0.401486i
\(206\) −224.166 + 36.8290i −1.08818 + 0.178782i
\(207\) 0 0
\(208\) 48.6075 83.5828i 0.233690 0.401841i
\(209\) 83.0678i 0.397454i
\(210\) 0 0
\(211\) 8.35160 + 20.1625i 0.0395810 + 0.0955571i 0.942434 0.334393i \(-0.108531\pi\)
−0.902853 + 0.429950i \(0.858531\pi\)
\(212\) 161.034 + 10.8089i 0.759593 + 0.0509852i
\(213\) 0 0
\(214\) −25.9001 41.7238i −0.121028 0.194971i
\(215\) 48.2292 + 48.2292i 0.224322 + 0.224322i
\(216\) 0 0
\(217\) 61.0233 + 61.0233i 0.281213 + 0.281213i
\(218\) 382.423 + 89.4854i 1.75423 + 0.410484i
\(219\) 0 0
\(220\) −42.8059 + 86.4591i −0.194572 + 0.392996i
\(221\) 57.9391 + 139.877i 0.262168 + 0.632930i
\(222\) 0 0
\(223\) 131.685i 0.590516i 0.955418 + 0.295258i \(0.0954056\pi\)
−0.955418 + 0.295258i \(0.904594\pi\)
\(224\) 119.700 126.800i 0.534376 0.566073i
\(225\) 0 0
\(226\) 38.2380 53.2726i 0.169194 0.235719i
\(227\) −60.7552 + 25.1656i −0.267644 + 0.110862i −0.512470 0.858705i \(-0.671269\pi\)
0.244825 + 0.969567i \(0.421269\pi\)
\(228\) 0 0
\(229\) 123.210 + 51.0352i 0.538035 + 0.222861i 0.635118 0.772415i \(-0.280951\pi\)
−0.0970835 + 0.995276i \(0.530951\pi\)
\(230\) −84.6362 + 361.699i −0.367983 + 1.57261i
\(231\) 0 0
\(232\) −4.37050 + 0.420057i −0.0188383 + 0.00181059i
\(233\) −110.005 + 110.005i −0.472124 + 0.472124i −0.902601 0.430477i \(-0.858345\pi\)
0.430477 + 0.902601i \(0.358345\pi\)
\(234\) 0 0
\(235\) −67.6692 28.0295i −0.287954 0.119274i
\(236\) 153.559 + 10.3071i 0.650673 + 0.0436743i
\(237\) 0 0
\(238\) 44.2665 + 269.435i 0.185994 + 1.13208i
\(239\) −277.831 −1.16247 −0.581236 0.813735i \(-0.697431\pi\)
−0.581236 + 0.813735i \(0.697431\pi\)
\(240\) 0 0
\(241\) 52.0006i 0.215770i −0.994163 0.107885i \(-0.965592\pi\)
0.994163 0.107885i \(-0.0344079\pi\)
\(242\) −31.3189 190.628i −0.129417 0.787718i
\(243\) 0 0
\(244\) 121.663 106.358i 0.498620 0.435894i
\(245\) −36.0681 + 87.0762i −0.147217 + 0.355413i
\(246\) 0 0
\(247\) −71.8466 71.8466i −0.290877 0.290877i
\(248\) 121.155 + 37.0640i 0.488528 + 0.149452i
\(249\) 0 0
\(250\) 58.2113 248.771i 0.232845 0.995082i
\(251\) −28.7912 + 69.5080i −0.114706 + 0.276924i −0.970798 0.239899i \(-0.922886\pi\)
0.856092 + 0.516823i \(0.172886\pi\)
\(252\) 0 0
\(253\) 71.9307 + 173.656i 0.284311 + 0.686388i
\(254\) −151.803 + 211.490i −0.597650 + 0.832637i
\(255\) 0 0
\(256\) 67.8107 246.856i 0.264885 0.964280i
\(257\) −241.501 −0.939692 −0.469846 0.882748i \(-0.655691\pi\)
−0.469846 + 0.882748i \(0.655691\pi\)
\(258\) 0 0
\(259\) 11.9123 4.93424i 0.0459935 0.0190511i
\(260\) −37.7562 111.803i −0.145216 0.430012i
\(261\) 0 0
\(262\) −51.2957 12.0030i −0.195785 0.0458129i
\(263\) 118.637 118.637i 0.451090 0.451090i −0.444626 0.895716i \(-0.646664\pi\)
0.895716 + 0.444626i \(0.146664\pi\)
\(264\) 0 0
\(265\) 139.285 139.285i 0.525606 0.525606i
\(266\) −96.6423 155.686i −0.363317 0.585286i
\(267\) 0 0
\(268\) 174.849 + 200.010i 0.652420 + 0.746305i
\(269\) 231.194 95.7638i 0.859459 0.355999i 0.0909629 0.995854i \(-0.471006\pi\)
0.768496 + 0.639855i \(0.221006\pi\)
\(270\) 0 0
\(271\) −2.13724 −0.00788650 −0.00394325 0.999992i \(-0.501255\pi\)
−0.00394325 + 0.999992i \(0.501255\pi\)
\(272\) 243.029 + 318.791i 0.893488 + 1.17202i
\(273\) 0 0
\(274\) −412.752 + 67.8126i −1.50639 + 0.247491i
\(275\) −2.20670 5.32745i −0.00802437 0.0193725i
\(276\) 0 0
\(277\) −177.679 + 428.955i −0.641441 + 1.54857i 0.183296 + 0.983058i \(0.441323\pi\)
−0.824737 + 0.565517i \(0.808677\pi\)
\(278\) −236.253 380.592i −0.849830 1.36904i
\(279\) 0 0
\(280\) −20.3606 211.843i −0.0727166 0.756582i
\(281\) 261.664 + 261.664i 0.931188 + 0.931188i 0.997780 0.0665922i \(-0.0212126\pi\)
−0.0665922 + 0.997780i \(0.521213\pi\)
\(282\) 0 0
\(283\) 160.904 388.456i 0.568564 1.37264i −0.334201 0.942502i \(-0.608466\pi\)
0.902765 0.430134i \(-0.141534\pi\)
\(284\) 262.495 + 129.962i 0.924280 + 0.457611i
\(285\) 0 0
\(286\) −48.5088 34.8186i −0.169611 0.121743i
\(287\) 240.066i 0.836465i
\(288\) 0 0
\(289\) −338.697 −1.17196
\(290\) −3.12471 + 4.35331i −0.0107749 + 0.0150114i
\(291\) 0 0
\(292\) 329.236 + 163.005i 1.12752 + 0.558236i
\(293\) 141.895 + 58.7749i 0.484284 + 0.200597i 0.611448 0.791285i \(-0.290587\pi\)
−0.127164 + 0.991882i \(0.540587\pi\)
\(294\) 0 0
\(295\) 132.820 132.820i 0.450238 0.450238i
\(296\) 12.0432 14.6043i 0.0406864 0.0493389i
\(297\) 0 0
\(298\) 90.6919 56.2971i 0.304335 0.188916i
\(299\) −212.412 87.9838i −0.710407 0.294260i
\(300\) 0 0
\(301\) −70.3373 + 29.1347i −0.233679 + 0.0967929i
\(302\) 82.6009 + 502.764i 0.273513 + 1.66478i
\(303\) 0 0
\(304\) −232.554 135.241i −0.764979 0.444872i
\(305\) 197.226i 0.646643i
\(306\) 0 0
\(307\) −36.1806 87.3476i −0.117852 0.284520i 0.853935 0.520379i \(-0.174209\pi\)
−0.971787 + 0.235860i \(0.924209\pi\)
\(308\) −70.8755 81.0746i −0.230115 0.263229i
\(309\) 0 0
\(310\) 131.377 81.5523i 0.423796 0.263072i
\(311\) −221.462 221.462i −0.712098 0.712098i 0.254876 0.966974i \(-0.417965\pi\)
−0.966974 + 0.254876i \(0.917965\pi\)
\(312\) 0 0
\(313\) 280.384 + 280.384i 0.895795 + 0.895795i 0.995061 0.0992662i \(-0.0316495\pi\)
−0.0992662 + 0.995061i \(0.531650\pi\)
\(314\) 71.9216 307.363i 0.229050 0.978862i
\(315\) 0 0
\(316\) −48.7864 144.466i −0.154387 0.457170i
\(317\) −155.972 376.549i −0.492024 1.18785i −0.953688 0.300796i \(-0.902748\pi\)
0.461665 0.887055i \(-0.347252\pi\)
\(318\) 0 0
\(319\) 2.71148i 0.00849994i
\(320\) −172.356 260.600i −0.538613 0.814376i
\(321\) 0 0
\(322\) −336.847 241.782i −1.04611 0.750875i
\(323\) 389.183 161.205i 1.20490 0.499086i
\(324\) 0 0
\(325\) 6.51640 + 2.69918i 0.0200505 + 0.00830517i
\(326\) −320.735 75.0507i −0.983850 0.230217i
\(327\) 0 0
\(328\) 165.407 + 311.216i 0.504288 + 0.948830i
\(329\) 57.8104 57.8104i 0.175715 0.175715i
\(330\) 0 0
\(331\) −418.148 173.202i −1.26329 0.523270i −0.352370 0.935861i \(-0.614624\pi\)
−0.910917 + 0.412591i \(0.864624\pi\)
\(332\) 125.739 109.921i 0.378733 0.331089i
\(333\) 0 0
\(334\) −264.640 + 43.4787i −0.792336 + 0.130176i
\(335\) 324.232 0.967857
\(336\) 0 0
\(337\) 38.1203i 0.113116i 0.998399 + 0.0565582i \(0.0180127\pi\)
−0.998399 + 0.0565582i \(0.981987\pi\)
\(338\) −261.457 + 42.9558i −0.773543 + 0.127088i
\(339\) 0 0
\(340\) 488.142 + 32.7650i 1.43571 + 0.0963676i
\(341\) 29.9424 72.2873i 0.0878076 0.211986i
\(342\) 0 0
\(343\) −263.195 263.195i −0.767333 0.767333i
\(344\) −71.1100 + 86.2324i −0.206715 + 0.250676i
\(345\) 0 0
\(346\) 226.416 + 52.9803i 0.654381 + 0.153122i
\(347\) 201.452 486.348i 0.580553 1.40158i −0.311760 0.950161i \(-0.600918\pi\)
0.892313 0.451418i \(-0.149082\pi\)
\(348\) 0 0
\(349\) −53.2160 128.475i −0.152481 0.368122i 0.829118 0.559073i \(-0.188843\pi\)
−0.981600 + 0.190951i \(0.938843\pi\)
\(350\) 10.3338 + 7.41742i 0.0295253 + 0.0211926i
\(351\) 0 0
\(352\) −147.742 56.2699i −0.419723 0.159858i
\(353\) 223.875 0.634208 0.317104 0.948391i \(-0.397290\pi\)
0.317104 + 0.948391i \(0.397290\pi\)
\(354\) 0 0
\(355\) 330.272 136.803i 0.930343 0.385361i
\(356\) 59.6525 120.486i 0.167563 0.338443i
\(357\) 0 0
\(358\) 65.1527 278.435i 0.181991 0.777752i
\(359\) 44.5652 44.5652i 0.124137 0.124137i −0.642309 0.766446i \(-0.722023\pi\)
0.766446 + 0.642309i \(0.222023\pi\)
\(360\) 0 0
\(361\) 55.3658 55.3658i 0.153368 0.153368i
\(362\) −570.564 + 354.178i −1.57614 + 0.978393i
\(363\) 0 0
\(364\) 131.424 + 8.82141i 0.361055 + 0.0242346i
\(365\) 414.245 171.586i 1.13492 0.470098i
\(366\) 0 0
\(367\) −294.972 −0.803739 −0.401869 0.915697i \(-0.631639\pi\)
−0.401869 + 0.915697i \(0.631639\pi\)
\(368\) −603.271 81.3518i −1.63932 0.221065i
\(369\) 0 0
\(370\) −3.74544 22.7972i −0.0101228 0.0616141i
\(371\) 84.1406 + 203.133i 0.226794 + 0.547529i
\(372\) 0 0
\(373\) 96.5187 233.017i 0.258763 0.624710i −0.740094 0.672504i \(-0.765219\pi\)
0.998857 + 0.0477936i \(0.0152190\pi\)
\(374\) 210.328 130.561i 0.562374 0.349094i
\(375\) 0 0
\(376\) 35.1125 114.776i 0.0933844 0.305255i
\(377\) −2.34520 2.34520i −0.00622069 0.00622069i
\(378\) 0 0
\(379\) −70.2002 + 169.478i −0.185225 + 0.447172i −0.989029 0.147722i \(-0.952806\pi\)
0.803804 + 0.594894i \(0.202806\pi\)
\(380\) −311.072 + 105.050i −0.818609 + 0.276447i
\(381\) 0 0
\(382\) −364.805 + 508.241i −0.954987 + 1.33047i
\(383\) 519.043i 1.35520i −0.735429 0.677602i \(-0.763019\pi\)
0.735429 0.677602i \(-0.236981\pi\)
\(384\) 0 0
\(385\) −131.429 −0.341373
\(386\) −114.824 82.4186i −0.297473 0.213520i
\(387\) 0 0
\(388\) −151.926 449.880i −0.391561 1.15949i
\(389\) −52.0121 21.5441i −0.133707 0.0553834i 0.314827 0.949149i \(-0.398054\pi\)
−0.448534 + 0.893766i \(0.648054\pi\)
\(390\) 0 0
\(391\) 674.009 674.009i 1.72381 1.72381i
\(392\) −147.693 45.1826i −0.376767 0.115262i
\(393\) 0 0
\(394\) −93.1362 150.038i −0.236386 0.380807i
\(395\) −171.933 71.2169i −0.435273 0.180296i
\(396\) 0 0
\(397\) 138.533 57.3823i 0.348950 0.144540i −0.201322 0.979525i \(-0.564524\pi\)
0.550272 + 0.834985i \(0.314524\pi\)
\(398\) 286.542 47.0770i 0.719955 0.118284i
\(399\) 0 0
\(400\) 18.5072 + 2.49572i 0.0462681 + 0.00623930i
\(401\) 11.3014i 0.0281830i −0.999901 0.0140915i \(-0.995514\pi\)
0.999901 0.0140915i \(-0.00448560\pi\)
\(402\) 0 0
\(403\) 36.6248 + 88.4200i 0.0908803 + 0.219404i
\(404\) −52.8404 + 787.232i −0.130793 + 1.94859i
\(405\) 0 0
\(406\) −3.15458 5.08187i −0.00776989 0.0125169i
\(407\) −8.26612 8.26612i −0.0203099 0.0203099i
\(408\) 0 0
\(409\) 188.958 + 188.958i 0.462001 + 0.462001i 0.899311 0.437310i \(-0.144069\pi\)
−0.437310 + 0.899311i \(0.644069\pi\)
\(410\) 418.831 + 98.0048i 1.02154 + 0.239036i
\(411\) 0 0
\(412\) −407.171 201.590i −0.988278 0.489297i
\(413\) 80.2350 + 193.704i 0.194274 + 0.469018i
\(414\) 0 0
\(415\) 203.834i 0.491166i
\(416\) 176.453 79.1159i 0.424167 0.190183i
\(417\) 0 0
\(418\) −96.8763 + 134.967i −0.231762 + 0.322887i
\(419\) 238.026 98.5936i 0.568081 0.235307i −0.0801080 0.996786i \(-0.525527\pi\)
0.648189 + 0.761479i \(0.275527\pi\)
\(420\) 0 0
\(421\) 324.923 + 134.588i 0.771790 + 0.319686i 0.733597 0.679585i \(-0.237840\pi\)
0.0381925 + 0.999270i \(0.487840\pi\)
\(422\) −9.94472 + 42.4995i −0.0235657 + 0.100710i
\(423\) 0 0
\(424\) 249.038 + 205.365i 0.587355 + 0.484351i
\(425\) −20.6773 + 20.6773i −0.0486526 + 0.0486526i
\(426\) 0 0
\(427\) 203.388 + 84.2461i 0.476318 + 0.197298i
\(428\) 6.57776 97.9973i 0.0153686 0.228966i
\(429\) 0 0
\(430\) 22.1153 + 134.608i 0.0514309 + 0.313042i
\(431\) 16.1400 0.0374479 0.0187239 0.999825i \(-0.494040\pi\)
0.0187239 + 0.999825i \(0.494040\pi\)
\(432\) 0 0
\(433\) 732.781i 1.69233i −0.532918 0.846167i \(-0.678905\pi\)
0.532918 0.846167i \(-0.321095\pi\)
\(434\) 27.9819 + 170.317i 0.0644745 + 0.392435i
\(435\) 0 0
\(436\) 516.992 + 591.388i 1.18576 + 1.35639i
\(437\) −244.799 + 590.996i −0.560180 + 1.35239i
\(438\) 0 0
\(439\) 460.630 + 460.630i 1.04927 + 1.04927i 0.998722 + 0.0505487i \(0.0160970\pi\)
0.0505487 + 0.998722i \(0.483903\pi\)
\(440\) −170.381 + 90.5551i −0.387231 + 0.205807i
\(441\) 0 0
\(442\) −68.9914 + 294.840i −0.156089 + 0.667059i
\(443\) 55.5453 134.098i 0.125384 0.302705i −0.848705 0.528866i \(-0.822618\pi\)
0.974090 + 0.226161i \(0.0726175\pi\)
\(444\) 0 0
\(445\) −62.7927 151.595i −0.141107 0.340663i
\(446\) −153.575 + 213.959i −0.344339 + 0.479728i
\(447\) 0 0
\(448\) 342.365 66.4243i 0.764207 0.148269i
\(449\) −731.262 −1.62865 −0.814323 0.580412i \(-0.802892\pi\)
−0.814323 + 0.580412i \(0.802892\pi\)
\(450\) 0 0
\(451\) 201.086 83.2924i 0.445866 0.184684i
\(452\) 124.256 41.9617i 0.274903 0.0928356i
\(453\) 0 0
\(454\) −128.063 29.9662i −0.282077 0.0660047i
\(455\) 113.675 113.675i 0.249834 0.249834i
\(456\) 0 0
\(457\) −332.873 + 332.873i −0.728388 + 0.728388i −0.970298 0.241911i \(-0.922226\pi\)
0.241911 + 0.970298i \(0.422226\pi\)
\(458\) 140.670 + 226.612i 0.307139 + 0.494787i
\(459\) 0 0
\(460\) −559.341 + 488.976i −1.21596 + 1.06299i
\(461\) 132.650 54.9455i 0.287744 0.119188i −0.234143 0.972202i \(-0.575228\pi\)
0.521887 + 0.853015i \(0.325228\pi\)
\(462\) 0 0
\(463\) −873.591 −1.88680 −0.943402 0.331650i \(-0.892395\pi\)
−0.943402 + 0.331650i \(0.892395\pi\)
\(464\) −7.59097 4.41452i −0.0163598 0.00951404i
\(465\) 0 0
\(466\) −307.025 + 50.4422i −0.658852 + 0.108245i
\(467\) 135.550 + 327.247i 0.290258 + 0.700744i 0.999993 0.00372448i \(-0.00118554\pi\)
−0.709735 + 0.704468i \(0.751186\pi\)
\(468\) 0 0
\(469\) −138.497 + 334.362i −0.295303 + 0.712925i
\(470\) −77.2585 124.460i −0.164380 0.264808i
\(471\) 0 0
\(472\) 237.478 + 195.832i 0.503132 + 0.414899i
\(473\) 48.8081 + 48.8081i 0.103188 + 0.103188i
\(474\) 0 0
\(475\) 7.50997 18.1307i 0.0158105 0.0381698i
\(476\) −242.301 + 489.397i −0.509035 + 1.02815i
\(477\) 0 0
\(478\) −451.413 324.015i −0.944379 0.677856i
\(479\) 296.032i 0.618021i −0.951059 0.309011i \(-0.900002\pi\)
0.951059 0.309011i \(-0.0999979\pi\)
\(480\) 0 0
\(481\) 14.2990 0.0297276
\(482\) 60.6448 84.4895i 0.125819 0.175289i
\(483\) 0 0
\(484\) 171.430 346.253i 0.354194 0.715398i
\(485\) −535.416 221.777i −1.10395 0.457271i
\(486\) 0 0
\(487\) −232.632 + 232.632i −0.477683 + 0.477683i −0.904390 0.426707i \(-0.859674\pi\)
0.426707 + 0.904390i \(0.359674\pi\)
\(488\) 321.714 30.9206i 0.659250 0.0633618i
\(489\) 0 0
\(490\) −160.154 + 99.4156i −0.326844 + 0.202889i
\(491\) −217.435 90.0644i −0.442840 0.183430i 0.150110 0.988669i \(-0.452037\pi\)
−0.592951 + 0.805239i \(0.702037\pi\)
\(492\) 0 0
\(493\) 12.7036 5.26201i 0.0257680 0.0106735i
\(494\) −32.9449 200.524i −0.0666901 0.405920i
\(495\) 0 0
\(496\) 153.624 + 201.515i 0.309727 + 0.406281i
\(497\) 399.026i 0.802869i
\(498\) 0 0
\(499\) 64.7699 + 156.368i 0.129799 + 0.313364i 0.975396 0.220458i \(-0.0707553\pi\)
−0.845597 + 0.533822i \(0.820755\pi\)
\(500\) 384.705 336.309i 0.769409 0.672618i
\(501\) 0 0
\(502\) −127.842 + 79.3579i −0.254665 + 0.158083i
\(503\) 612.203 + 612.203i 1.21710 + 1.21710i 0.968642 + 0.248460i \(0.0799246\pi\)
0.248460 + 0.968642i \(0.420075\pi\)
\(504\) 0 0
\(505\) 680.913 + 680.913i 1.34834 + 1.34834i
\(506\) −85.6520 + 366.041i −0.169273 + 0.723400i
\(507\) 0 0
\(508\) −493.292 + 166.586i −0.971048 + 0.327925i
\(509\) 273.870 + 661.182i 0.538056 + 1.29898i 0.926078 + 0.377332i \(0.123158\pi\)
−0.388022 + 0.921650i \(0.626842\pi\)
\(510\) 0 0
\(511\) 500.480i 0.979413i
\(512\) 398.068 322.003i 0.777477 0.628911i
\(513\) 0 0
\(514\) −392.385 281.646i −0.763395 0.547950i
\(515\) −512.302 + 212.202i −0.994761 + 0.412043i
\(516\) 0 0
\(517\) −68.4813 28.3659i −0.132459 0.0548663i
\(518\) 25.1093 + 5.87548i 0.0484736 + 0.0113426i
\(519\) 0 0
\(520\) 69.0430 225.688i 0.132775 0.434015i
\(521\) 527.816 527.816i 1.01308 1.01308i 0.0131690 0.999913i \(-0.495808\pi\)
0.999913 0.0131690i \(-0.00419195\pi\)
\(522\) 0 0
\(523\) 5.01268 + 2.07632i 0.00958447 + 0.00397002i 0.387471 0.921882i \(-0.373349\pi\)
−0.377886 + 0.925852i \(0.623349\pi\)
\(524\) −69.3458 79.3249i −0.132339 0.151383i
\(525\) 0 0
\(526\) 331.116 54.4002i 0.629498 0.103423i
\(527\) −396.783 −0.752908
\(528\) 0 0
\(529\) 918.476i 1.73625i
\(530\) 388.747 63.8687i 0.733485 0.120507i
\(531\) 0 0
\(532\) 24.5439 365.663i 0.0461352 0.687336i
\(533\) −101.881 + 245.963i −0.191147 + 0.461469i
\(534\) 0 0
\(535\) −84.7624 84.7624i −0.158434 0.158434i
\(536\) 50.8322 + 528.886i 0.0948363 + 0.986727i
\(537\) 0 0
\(538\) 487.322 + 114.031i 0.905804 + 0.211954i
\(539\) −36.5010 + 88.1213i −0.0677199 + 0.163490i
\(540\) 0 0
\(541\) −229.279 553.528i −0.423806 1.02316i −0.981215 0.192919i \(-0.938204\pi\)
0.557409 0.830238i \(-0.311796\pi\)
\(542\) −3.47254 2.49252i −0.00640691 0.00459875i
\(543\) 0 0
\(544\) 23.0836 + 801.392i 0.0424330 + 1.47315i
\(545\) 958.688 1.75906
\(546\) 0 0
\(547\) −391.381 + 162.115i −0.715504 + 0.296371i −0.710580 0.703617i \(-0.751567\pi\)
−0.00492387 + 0.999988i \(0.501567\pi\)
\(548\) −749.716 371.185i −1.36809 0.677344i
\(549\) 0 0
\(550\) 2.62764 11.2294i 0.00477753 0.0204172i
\(551\) −6.52508 + 6.52508i −0.0118423 + 0.0118423i
\(552\) 0 0
\(553\) 146.884 146.884i 0.265613 0.265613i
\(554\) −788.950 + 489.742i −1.42410 + 0.884010i
\(555\) 0 0
\(556\) 60.0003 893.903i 0.107914 1.60774i
\(557\) −364.486 + 150.975i −0.654374 + 0.271050i −0.685069 0.728478i \(-0.740228\pi\)
0.0306953 + 0.999529i \(0.490228\pi\)
\(558\) 0 0
\(559\) −84.4296 −0.151037
\(560\) 213.977 367.943i 0.382101 0.657041i
\(561\) 0 0
\(562\) 119.985 + 730.306i 0.213496 + 1.29948i
\(563\) −114.762 277.059i −0.203840 0.492113i 0.788591 0.614918i \(-0.210811\pi\)
−0.992431 + 0.122805i \(0.960811\pi\)
\(564\) 0 0
\(565\) 61.2544 147.881i 0.108415 0.261736i
\(566\) 714.463 443.503i 1.26230 0.783575i
\(567\) 0 0
\(568\) 274.931 + 517.289i 0.484034 + 0.910721i
\(569\) −172.424 172.424i −0.303029 0.303029i 0.539169 0.842198i \(-0.318739\pi\)
−0.842198 + 0.539169i \(0.818739\pi\)
\(570\) 0 0
\(571\) 295.206 712.690i 0.516998 1.24814i −0.422740 0.906251i \(-0.638932\pi\)
0.939739 0.341894i \(-0.111068\pi\)
\(572\) −38.2094 113.145i −0.0667996 0.197806i
\(573\) 0 0
\(574\) −279.972 + 390.053i −0.487757 + 0.679535i
\(575\) 44.4059i 0.0772276i
\(576\) 0 0
\(577\) −756.330 −1.31080 −0.655398 0.755283i \(-0.727499\pi\)
−0.655398 + 0.755283i \(0.727499\pi\)
\(578\) −550.307 394.999i −0.952088 0.683389i
\(579\) 0 0
\(580\) −10.1539 + 3.42901i −0.0175068 + 0.00591209i
\(581\) 210.202 + 87.0686i 0.361794 + 0.149860i
\(582\) 0 0
\(583\) 140.957 140.957i 0.241779 0.241779i
\(584\) 344.834 + 648.813i 0.590469 + 1.11098i
\(585\) 0 0
\(586\) 162.003 + 260.979i 0.276455 + 0.445356i
\(587\) −736.720 305.159i −1.25506 0.519863i −0.346670 0.937987i \(-0.612688\pi\)
−0.908390 + 0.418125i \(0.862688\pi\)
\(588\) 0 0
\(589\) 246.012 101.902i 0.417678 0.173008i
\(590\) 370.702 60.9040i 0.628309 0.103227i
\(591\) 0 0
\(592\) 36.5995 9.68362i 0.0618234 0.0163575i
\(593\) 76.7003i 0.129343i 0.997907 + 0.0646714i \(0.0205999\pi\)
−0.997907 + 0.0646714i \(0.979400\pi\)
\(594\) 0 0
\(595\) 255.056 + 615.759i 0.428665 + 1.03489i
\(596\) 213.010 + 14.2976i 0.357399 + 0.0239892i
\(597\) 0 0
\(598\) −242.512 390.676i −0.405539 0.653304i
\(599\) −34.1251 34.1251i −0.0569702 0.0569702i 0.678048 0.735018i \(-0.262826\pi\)
−0.735018 + 0.678048i \(0.762826\pi\)
\(600\) 0 0
\(601\) 212.552 + 212.552i 0.353664 + 0.353664i 0.861471 0.507807i \(-0.169544\pi\)
−0.507807 + 0.861471i \(0.669544\pi\)
\(602\) −148.260 34.6923i −0.246280 0.0576284i
\(603\) 0 0
\(604\) −452.131 + 913.211i −0.748561 + 1.51194i
\(605\) −180.454 435.655i −0.298271 0.720091i
\(606\) 0 0
\(607\) 56.8377i 0.0936371i −0.998903 0.0468186i \(-0.985092\pi\)
0.998903 0.0468186i \(-0.0149083\pi\)
\(608\) −220.125 490.949i −0.362048 0.807481i
\(609\) 0 0
\(610\) 230.012 320.449i 0.377068 0.525326i
\(611\) 83.7646 34.6964i 0.137094 0.0567863i
\(612\) 0 0
\(613\) −7.45320 3.08722i −0.0121586 0.00503624i 0.376596 0.926378i \(-0.377095\pi\)
−0.388754 + 0.921341i \(0.627095\pi\)
\(614\) 43.0822 184.115i 0.0701665 0.299862i
\(615\) 0 0
\(616\) −20.6050 214.386i −0.0334497 0.348028i
\(617\) 325.733 325.733i 0.527931 0.527931i −0.392024 0.919955i \(-0.628225\pi\)
0.919955 + 0.392024i \(0.128225\pi\)
\(618\) 0 0
\(619\) 76.1643 + 31.5483i 0.123044 + 0.0509665i 0.443356 0.896346i \(-0.353788\pi\)
−0.320312 + 0.947312i \(0.603788\pi\)
\(620\) 308.567 + 20.7116i 0.497689 + 0.0334058i
\(621\) 0 0
\(622\) −101.551 618.104i −0.163265 0.993736i
\(623\) 183.153 0.293986
\(624\) 0 0
\(625\) 594.458i 0.951133i
\(626\) 128.569 + 782.554i 0.205381 + 1.25009i
\(627\) 0 0
\(628\) 475.313 415.519i 0.756868 0.661654i
\(629\) −22.6862 + 54.7694i −0.0360671 + 0.0870738i
\(630\) 0 0
\(631\) 70.1301 + 70.1301i 0.111141 + 0.111141i 0.760490 0.649349i \(-0.224959\pi\)
−0.649349 + 0.760490i \(0.724959\pi\)
\(632\) 89.2134 291.621i 0.141160 0.461425i
\(633\) 0 0
\(634\) 185.724 793.707i 0.292940 1.25190i
\(635\) −243.177 + 587.082i −0.382956 + 0.924538i
\(636\) 0 0
\(637\) −44.6471 107.788i −0.0700897 0.169211i
\(638\) −3.16222 + 4.40555i −0.00495645 + 0.00690526i
\(639\) 0 0
\(640\) 23.8802 624.425i 0.0373128 0.975664i
\(641\) −458.396 −0.715126 −0.357563 0.933889i \(-0.616392\pi\)
−0.357563 + 0.933889i \(0.616392\pi\)
\(642\) 0 0
\(643\) −882.443 + 365.520i −1.37238 + 0.568460i −0.942434 0.334393i \(-0.891469\pi\)
−0.429950 + 0.902853i \(0.641469\pi\)
\(644\) −265.327 785.684i −0.411999 1.22001i
\(645\) 0 0
\(646\) 820.338 + 191.956i 1.26987 + 0.297145i
\(647\) 130.433 130.433i 0.201597 0.201597i −0.599087 0.800684i \(-0.704470\pi\)
0.800684 + 0.599087i \(0.204470\pi\)
\(648\) 0 0
\(649\) 134.414 134.414i 0.207110 0.207110i
\(650\) 7.43982 + 11.9852i 0.0114459 + 0.0184388i
\(651\) 0 0
\(652\) −433.597 495.992i −0.665026 0.760724i
\(653\) −989.811 + 409.993i −1.51579 + 0.627861i −0.976743 0.214415i \(-0.931216\pi\)
−0.539047 + 0.842275i \(0.681216\pi\)
\(654\) 0 0
\(655\) −128.592 −0.196324
\(656\) −94.2016 + 698.560i −0.143600 + 1.06488i
\(657\) 0 0
\(658\) 161.349 26.5087i 0.245212 0.0402867i
\(659\) 457.745 + 1105.09i 0.694605 + 1.67693i 0.735289 + 0.677753i \(0.237046\pi\)
−0.0406841 + 0.999172i \(0.512954\pi\)
\(660\) 0 0
\(661\) −96.2729 + 232.423i −0.145647 + 0.351624i −0.979821 0.199879i \(-0.935945\pi\)
0.834173 + 0.551502i \(0.185945\pi\)
\(662\) −477.403 769.073i −0.721152 1.16174i
\(663\) 0 0
\(664\) 332.493 31.9565i 0.500742 0.0481273i
\(665\) −316.278 316.278i −0.475607 0.475607i
\(666\) 0 0
\(667\) −7.99066 + 19.2912i −0.0119800 + 0.0289223i
\(668\) −480.688 237.989i −0.719592 0.356271i
\(669\) 0 0
\(670\) 526.805 + 378.130i 0.786277 + 0.564373i
\(671\) 199.593i 0.297456i
\(672\) 0 0
\(673\) −135.640 −0.201545 −0.100772 0.994910i \(-0.532131\pi\)
−0.100772 + 0.994910i \(0.532131\pi\)
\(674\) −44.4571 + 61.9369i −0.0659601 + 0.0918946i
\(675\) 0 0
\(676\) −474.907 235.127i −0.702525 0.347820i
\(677\) 348.196 + 144.228i 0.514322 + 0.213039i 0.624721 0.780848i \(-0.285213\pi\)
−0.110399 + 0.993887i \(0.535213\pi\)
\(678\) 0 0
\(679\) 457.411 457.411i 0.673653 0.673653i
\(680\) 754.911 + 622.523i 1.11016 + 0.915476i
\(681\) 0 0
\(682\) 132.954 82.5310i 0.194947 0.121013i
\(683\) 812.940 + 336.731i 1.19025 + 0.493017i 0.887836 0.460159i \(-0.152208\pi\)
0.302413 + 0.953177i \(0.402208\pi\)
\(684\) 0 0
\(685\) −943.292 + 390.724i −1.37707 + 0.570400i
\(686\) −120.687 734.581i −0.175928 1.07082i
\(687\) 0 0
\(688\) −216.105 + 57.1778i −0.314106 + 0.0831073i
\(689\) 243.832i 0.353892i
\(690\) 0 0
\(691\) −78.3893 189.249i −0.113443 0.273876i 0.856953 0.515395i \(-0.172355\pi\)
−0.970396 + 0.241518i \(0.922355\pi\)
\(692\) 306.088 + 350.135i 0.442323 + 0.505975i
\(693\) 0 0
\(694\) 894.509 555.267i 1.28892 0.800097i
\(695\) −773.177 773.177i −1.11249 1.11249i
\(696\) 0 0
\(697\) −780.471 780.471i −1.11976 1.11976i
\(698\) 63.3672 270.805i 0.0907840 0.387973i
\(699\) 0 0
\(700\) 8.13975 + 24.1033i 0.0116282 + 0.0344333i
\(701\) −432.140 1043.28i −0.616463 1.48827i −0.855785 0.517332i \(-0.826925\pi\)
0.239322 0.970940i \(-0.423075\pi\)
\(702\) 0 0
\(703\) 39.7843i 0.0565921i
\(704\) −174.425 263.728i −0.247762 0.374614i
\(705\) 0 0
\(706\) 363.748 + 261.091i 0.515223 + 0.369817i
\(707\) −993.041 + 411.331i −1.40458 + 0.581798i
\(708\) 0 0
\(709\) 367.507 + 152.226i 0.518345 + 0.214706i 0.626490 0.779430i \(-0.284491\pi\)
−0.108145 + 0.994135i \(0.534491\pi\)
\(710\) 696.162 + 162.899i 0.980510 + 0.229435i
\(711\) 0 0
\(712\) 237.436 126.194i 0.333478 0.177238i
\(713\) 426.058 426.058i 0.597556 0.597556i
\(714\) 0 0
\(715\) −134.657 55.7768i −0.188332 0.0780096i
\(716\) 430.579 376.412i 0.601367 0.525715i
\(717\) 0 0
\(718\) 124.382 20.4352i 0.173234 0.0284612i
\(719\) 100.566 0.139869 0.0699344 0.997552i \(-0.477721\pi\)
0.0699344 + 0.997552i \(0.477721\pi\)
\(720\) 0 0
\(721\) 618.950i 0.858461i
\(722\) 154.527 25.3877i 0.214026 0.0351631i
\(723\) 0 0
\(724\) −1340.09 89.9495i −1.85096 0.124240i
\(725\) 0.245139 0.591817i 0.000338122 0.000816300i
\(726\) 0 0
\(727\) −332.402 332.402i −0.457224 0.457224i 0.440519 0.897743i \(-0.354794\pi\)
−0.897743 + 0.440519i \(0.854794\pi\)
\(728\) 203.247 + 167.604i 0.279185 + 0.230225i
\(729\) 0 0
\(730\) 873.164 + 204.317i 1.19612 + 0.279886i
\(731\) 133.953 323.391i 0.183246 0.442395i
\(732\) 0 0
\(733\) −166.189 401.215i −0.226724 0.547360i 0.769051 0.639187i \(-0.220729\pi\)
−0.995775 + 0.0918276i \(0.970729\pi\)
\(734\) −479.264 344.006i −0.652948 0.468673i
\(735\) 0 0
\(736\) −885.306 835.733i −1.20286 1.13551i
\(737\) 328.124 0.445215
\(738\) 0 0
\(739\) 1011.25 418.874i 1.36840 0.566812i 0.427049 0.904229i \(-0.359553\pi\)
0.941355 + 0.337417i \(0.109553\pi\)
\(740\) 20.5014 41.4085i 0.0277045 0.0559574i
\(741\) 0 0
\(742\) −100.191 + 428.174i −0.135028 + 0.577054i
\(743\) −458.897 + 458.897i −0.617627 + 0.617627i −0.944922 0.327295i \(-0.893863\pi\)
0.327295 + 0.944922i \(0.393863\pi\)
\(744\) 0 0
\(745\) 184.242 184.242i 0.247304 0.247304i
\(746\) 428.573 266.037i 0.574495 0.356618i
\(747\) 0 0
\(748\) 494.001 + 33.1582i 0.660429 + 0.0443292i
\(749\) 123.617 51.2039i 0.165043 0.0683630i
\(750\) 0 0
\(751\) −636.920 −0.848096 −0.424048 0.905640i \(-0.639391\pi\)
−0.424048 + 0.905640i \(0.639391\pi\)
\(752\) 190.905 145.536i 0.253864 0.193532i
\(753\) 0 0
\(754\) −1.07538 6.54548i −0.00142623 0.00868100i
\(755\) 475.932 + 1149.00i 0.630373 + 1.52186i
\(756\) 0 0
\(757\) −414.804 + 1001.43i −0.547958 + 1.32289i 0.371038 + 0.928618i \(0.379002\pi\)
−0.918995 + 0.394269i \(0.870998\pi\)
\(758\) −311.711 + 193.495i −0.411228 + 0.255270i
\(759\) 0 0
\(760\) −627.935 192.099i −0.826230 0.252762i
\(761\) 520.779 + 520.779i 0.684334 + 0.684334i 0.960974 0.276639i \(-0.0892207\pi\)
−0.276639 + 0.960974i \(0.589221\pi\)
\(762\) 0 0
\(763\) −409.508 + 988.640i −0.536708 + 1.29573i
\(764\) −1185.45 + 400.331i −1.55164 + 0.523993i
\(765\) 0 0
\(766\) 605.325 843.330i 0.790241 1.10095i
\(767\) 232.514i 0.303147i
\(768\) 0 0
\(769\) 973.035 1.26533 0.632663 0.774427i \(-0.281962\pi\)
0.632663 + 0.774427i \(0.281962\pi\)
\(770\) −213.542 153.276i −0.277328 0.199060i
\(771\) 0 0
\(772\) −90.4448 267.824i −0.117157 0.346922i
\(773\) −959.578 397.470i −1.24137 0.514192i −0.337227 0.941423i \(-0.609489\pi\)
−0.904142 + 0.427232i \(0.859489\pi\)
\(774\) 0 0
\(775\) −13.0707 + 13.0707i −0.0168654 + 0.0168654i
\(776\) 277.819 908.136i 0.358015 1.17028i
\(777\) 0 0
\(778\) −59.3827 95.6626i −0.0763273 0.122960i
\(779\) 684.346 + 283.465i 0.878493 + 0.363884i
\(780\) 0 0
\(781\) 334.236 138.445i 0.427958 0.177266i
\(782\) 1881.17 309.064i 2.40558 0.395222i
\(783\) 0 0
\(784\) −187.275 245.656i −0.238871 0.313336i
\(785\) 770.521i 0.981556i
\(786\) 0 0
\(787\) 412.612 + 996.133i 0.524284 + 1.26573i 0.935219 + 0.354070i \(0.115202\pi\)