Properties

Label 2646.2.m.c.1763.19
Level $2646$
Weight $2$
Character 2646.1763
Analytic conductor $21.128$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1763.19
Character \(\chi\) \(=\) 2646.1763
Dual form 2646.2.m.c.881.19

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.712984 - 1.23492i) q^{5} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.712984 - 1.23492i) q^{5} +1.00000i q^{8} -1.42597i q^{10} +(2.12170 + 1.22496i) q^{11} +(-1.61819 + 0.934264i) q^{13} +(-0.500000 + 0.866025i) q^{16} -1.98625 q^{17} +5.90920i q^{19} +(0.712984 - 1.23492i) q^{20} +(1.22496 + 2.12170i) q^{22} +(5.65337 - 3.26397i) q^{23} +(1.48331 - 2.56917i) q^{25} -1.86853 q^{26} +(5.51198 + 3.18234i) q^{29} +(-4.15157 + 2.39691i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.72014 - 0.993125i) q^{34} -1.83032 q^{37} +(-2.95460 + 5.11752i) q^{38} +(1.23492 - 0.712984i) q^{40} +(2.32289 + 4.02337i) q^{41} +(-5.07994 + 8.79872i) q^{43} +2.44993i q^{44} +6.52794 q^{46} +(6.47952 - 11.2229i) q^{47} +(2.56917 - 1.48331i) q^{50} +(-1.61819 - 0.934264i) q^{52} +11.8930i q^{53} -3.49352i q^{55} +(3.18234 + 5.51198i) q^{58} +(-2.88911 - 5.00408i) q^{59} +(8.38524 + 4.84122i) q^{61} -4.79382 q^{62} -1.00000 q^{64} +(2.30749 + 1.33223i) q^{65} +(7.60449 + 13.1714i) q^{67} +(-0.993125 - 1.72014i) q^{68} +0.594087i q^{71} +13.5874i q^{73} +(-1.58511 - 0.915162i) q^{74} +(-5.11752 + 2.95460i) q^{76} +(4.87348 - 8.44111i) q^{79} +1.42597 q^{80} +4.64578i q^{82} +(1.60586 - 2.78143i) q^{83} +(1.41616 + 2.45287i) q^{85} +(-8.79872 + 5.07994i) q^{86} +(-1.22496 + 2.12170i) q^{88} +0.144657 q^{89} +(5.65337 + 3.26397i) q^{92} +(11.2229 - 6.47952i) q^{94} +(7.29742 - 4.21317i) q^{95} +(-2.32972 - 1.34506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{4} + O(q^{10}) \) \( 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.712984 1.23492i −0.318856 0.552275i 0.661394 0.750039i \(-0.269965\pi\)
−0.980250 + 0.197764i \(0.936632\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.42597i 0.450931i
\(11\) 2.12170 + 1.22496i 0.639717 + 0.369341i 0.784505 0.620122i \(-0.212917\pi\)
−0.144789 + 0.989463i \(0.546250\pi\)
\(12\) 0 0
\(13\) −1.61819 + 0.934264i −0.448806 + 0.259118i −0.707326 0.706888i \(-0.750099\pi\)
0.258520 + 0.966006i \(0.416765\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.98625 −0.481737 −0.240868 0.970558i \(-0.577432\pi\)
−0.240868 + 0.970558i \(0.577432\pi\)
\(18\) 0 0
\(19\) 5.90920i 1.35566i 0.735217 + 0.677832i \(0.237080\pi\)
−0.735217 + 0.677832i \(0.762920\pi\)
\(20\) 0.712984 1.23492i 0.159428 0.276137i
\(21\) 0 0
\(22\) 1.22496 + 2.12170i 0.261163 + 0.452348i
\(23\) 5.65337 3.26397i 1.17881 0.680585i 0.223070 0.974802i \(-0.428392\pi\)
0.955739 + 0.294217i \(0.0950589\pi\)
\(24\) 0 0
\(25\) 1.48331 2.56917i 0.296662 0.513833i
\(26\) −1.86853 −0.366448
\(27\) 0 0
\(28\) 0 0
\(29\) 5.51198 + 3.18234i 1.02355 + 0.590946i 0.915130 0.403159i \(-0.132088\pi\)
0.108419 + 0.994105i \(0.465421\pi\)
\(30\) 0 0
\(31\) −4.15157 + 2.39691i −0.745644 + 0.430498i −0.824118 0.566419i \(-0.808329\pi\)
0.0784741 + 0.996916i \(0.474995\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −1.72014 0.993125i −0.295002 0.170320i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.83032 −0.300903 −0.150452 0.988617i \(-0.548073\pi\)
−0.150452 + 0.988617i \(0.548073\pi\)
\(38\) −2.95460 + 5.11752i −0.479300 + 0.830171i
\(39\) 0 0
\(40\) 1.23492 0.712984i 0.195259 0.112733i
\(41\) 2.32289 + 4.02337i 0.362775 + 0.628344i 0.988416 0.151766i \(-0.0484961\pi\)
−0.625642 + 0.780111i \(0.715163\pi\)
\(42\) 0 0
\(43\) −5.07994 + 8.79872i −0.774684 + 1.34179i 0.160288 + 0.987070i \(0.448758\pi\)
−0.934972 + 0.354722i \(0.884575\pi\)
\(44\) 2.44993i 0.369341i
\(45\) 0 0
\(46\) 6.52794 0.962493
\(47\) 6.47952 11.2229i 0.945135 1.63702i 0.189654 0.981851i \(-0.439263\pi\)
0.755481 0.655170i \(-0.227403\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.56917 1.48331i 0.363335 0.209771i
\(51\) 0 0
\(52\) −1.61819 0.934264i −0.224403 0.129559i
\(53\) 11.8930i 1.63363i 0.576897 + 0.816817i \(0.304264\pi\)
−0.576897 + 0.816817i \(0.695736\pi\)
\(54\) 0 0
\(55\) 3.49352i 0.471066i
\(56\) 0 0
\(57\) 0 0
\(58\) 3.18234 + 5.51198i 0.417862 + 0.723759i
\(59\) −2.88911 5.00408i −0.376130 0.651475i 0.614366 0.789021i \(-0.289412\pi\)
−0.990495 + 0.137546i \(0.956079\pi\)
\(60\) 0 0
\(61\) 8.38524 + 4.84122i 1.07362 + 0.619855i 0.929168 0.369657i \(-0.120525\pi\)
0.144452 + 0.989512i \(0.453858\pi\)
\(62\) −4.79382 −0.608815
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 2.30749 + 1.33223i 0.286209 + 0.165243i
\(66\) 0 0
\(67\) 7.60449 + 13.1714i 0.929036 + 1.60914i 0.784938 + 0.619574i \(0.212695\pi\)
0.144098 + 0.989563i \(0.453972\pi\)
\(68\) −0.993125 1.72014i −0.120434 0.208598i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.594087i 0.0705051i 0.999378 + 0.0352526i \(0.0112236\pi\)
−0.999378 + 0.0352526i \(0.988776\pi\)
\(72\) 0 0
\(73\) 13.5874i 1.59029i 0.606422 + 0.795143i \(0.292604\pi\)
−0.606422 + 0.795143i \(0.707396\pi\)
\(74\) −1.58511 0.915162i −0.184265 0.106385i
\(75\) 0 0
\(76\) −5.11752 + 2.95460i −0.587020 + 0.338916i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.87348 8.44111i 0.548309 0.949699i −0.450081 0.892988i \(-0.648605\pi\)
0.998391 0.0567119i \(-0.0180616\pi\)
\(80\) 1.42597 0.159428
\(81\) 0 0
\(82\) 4.64578i 0.513041i
\(83\) 1.60586 2.78143i 0.176266 0.305302i −0.764333 0.644822i \(-0.776931\pi\)
0.940599 + 0.339520i \(0.110265\pi\)
\(84\) 0 0
\(85\) 1.41616 + 2.45287i 0.153605 + 0.266051i
\(86\) −8.79872 + 5.07994i −0.948791 + 0.547784i
\(87\) 0 0
\(88\) −1.22496 + 2.12170i −0.130582 + 0.226174i
\(89\) 0.144657 0.0153336 0.00766680 0.999971i \(-0.497560\pi\)
0.00766680 + 0.999971i \(0.497560\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.65337 + 3.26397i 0.589404 + 0.340293i
\(93\) 0 0
\(94\) 11.2229 6.47952i 1.15755 0.668311i
\(95\) 7.29742 4.21317i 0.748699 0.432262i
\(96\) 0 0
\(97\) −2.32972 1.34506i −0.236547 0.136571i 0.377042 0.926196i \(-0.376941\pi\)
−0.613589 + 0.789626i \(0.710275\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.96662 0.296662
\(101\) −1.84869 + 3.20202i −0.183951 + 0.318613i −0.943223 0.332161i \(-0.892222\pi\)
0.759271 + 0.650774i \(0.225556\pi\)
\(102\) 0 0
\(103\) 13.9648 8.06260i 1.37600 0.794431i 0.384321 0.923200i \(-0.374436\pi\)
0.991675 + 0.128768i \(0.0411024\pi\)
\(104\) −0.934264 1.61819i −0.0916121 0.158677i
\(105\) 0 0
\(106\) −5.94652 + 10.2997i −0.577577 + 1.00039i
\(107\) 0.545248i 0.0527111i −0.999653 0.0263556i \(-0.991610\pi\)
0.999653 0.0263556i \(-0.00839020\pi\)
\(108\) 0 0
\(109\) −6.33018 −0.606321 −0.303161 0.952939i \(-0.598042\pi\)
−0.303161 + 0.952939i \(0.598042\pi\)
\(110\) 1.74676 3.02547i 0.166547 0.288468i
\(111\) 0 0
\(112\) 0 0
\(113\) 9.21222 5.31868i 0.866612 0.500339i 0.000391395 1.00000i \(-0.499875\pi\)
0.866221 + 0.499661i \(0.166542\pi\)
\(114\) 0 0
\(115\) −8.06152 4.65432i −0.751740 0.434017i
\(116\) 6.36469i 0.590946i
\(117\) 0 0
\(118\) 5.77821i 0.531927i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.49893 4.32827i −0.227175 0.393479i
\(122\) 4.84122 + 8.38524i 0.438304 + 0.759164i
\(123\) 0 0
\(124\) −4.15157 2.39691i −0.372822 0.215249i
\(125\) −11.3601 −1.01608
\(126\) 0 0
\(127\) 5.92432 0.525698 0.262849 0.964837i \(-0.415338\pi\)
0.262849 + 0.964837i \(0.415338\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 1.33223 + 2.30749i 0.116844 + 0.202380i
\(131\) 6.81751 + 11.8083i 0.595649 + 1.03169i 0.993455 + 0.114224i \(0.0364383\pi\)
−0.397806 + 0.917469i \(0.630228\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 15.2090i 1.31386i
\(135\) 0 0
\(136\) 1.98625i 0.170320i
\(137\) 15.5598 + 8.98348i 1.32937 + 0.767510i 0.985202 0.171399i \(-0.0548288\pi\)
0.344165 + 0.938909i \(0.388162\pi\)
\(138\) 0 0
\(139\) −8.22479 + 4.74858i −0.697617 + 0.402769i −0.806459 0.591290i \(-0.798619\pi\)
0.108842 + 0.994059i \(0.465286\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.297043 + 0.514494i −0.0249273 + 0.0431754i
\(143\) −4.57776 −0.382811
\(144\) 0 0
\(145\) 9.07584i 0.753707i
\(146\) −6.79371 + 11.7670i −0.562251 + 0.973847i
\(147\) 0 0
\(148\) −0.915162 1.58511i −0.0752258 0.130295i
\(149\) −4.61041 + 2.66182i −0.377699 + 0.218065i −0.676817 0.736151i \(-0.736641\pi\)
0.299117 + 0.954216i \(0.403308\pi\)
\(150\) 0 0
\(151\) −6.97282 + 12.0773i −0.567440 + 0.982834i 0.429378 + 0.903125i \(0.358733\pi\)
−0.996818 + 0.0797096i \(0.974601\pi\)
\(152\) −5.90920 −0.479300
\(153\) 0 0
\(154\) 0 0
\(155\) 5.92000 + 3.41791i 0.475506 + 0.274533i
\(156\) 0 0
\(157\) −4.55518 + 2.62993i −0.363543 + 0.209891i −0.670634 0.741789i \(-0.733978\pi\)
0.307091 + 0.951680i \(0.400644\pi\)
\(158\) 8.44111 4.87348i 0.671539 0.387713i
\(159\) 0 0
\(160\) 1.23492 + 0.712984i 0.0976293 + 0.0563663i
\(161\) 0 0
\(162\) 0 0
\(163\) −9.87851 −0.773745 −0.386872 0.922133i \(-0.626445\pi\)
−0.386872 + 0.922133i \(0.626445\pi\)
\(164\) −2.32289 + 4.02337i −0.181387 + 0.314172i
\(165\) 0 0
\(166\) 2.78143 1.60586i 0.215881 0.124639i
\(167\) 8.86749 + 15.3589i 0.686187 + 1.18851i 0.973062 + 0.230542i \(0.0740500\pi\)
−0.286876 + 0.957968i \(0.592617\pi\)
\(168\) 0 0
\(169\) −4.75430 + 8.23469i −0.365716 + 0.633438i
\(170\) 2.83233i 0.217230i
\(171\) 0 0
\(172\) −10.1599 −0.774684
\(173\) 4.20045 7.27539i 0.319354 0.553137i −0.660999 0.750386i \(-0.729867\pi\)
0.980353 + 0.197249i \(0.0632007\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.12170 + 1.22496i −0.159929 + 0.0923351i
\(177\) 0 0
\(178\) 0.125277 + 0.0723285i 0.00938988 + 0.00542125i
\(179\) 3.02300i 0.225950i −0.993598 0.112975i \(-0.963962\pi\)
0.993598 0.112975i \(-0.0360380\pi\)
\(180\) 0 0
\(181\) 4.94729i 0.367729i −0.982952 0.183865i \(-0.941139\pi\)
0.982952 0.183865i \(-0.0588608\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.26397 + 5.65337i 0.240623 + 0.416772i
\(185\) 1.30499 + 2.26031i 0.0959449 + 0.166181i
\(186\) 0 0
\(187\) −4.21423 2.43309i −0.308175 0.177925i
\(188\) 12.9590 0.945135
\(189\) 0 0
\(190\) 8.42633 0.611310
\(191\) −4.42179 2.55292i −0.319949 0.184723i 0.331421 0.943483i \(-0.392472\pi\)
−0.651370 + 0.758760i \(0.725805\pi\)
\(192\) 0 0
\(193\) −0.527061 0.912897i −0.0379387 0.0657118i 0.846433 0.532496i \(-0.178746\pi\)
−0.884371 + 0.466784i \(0.845413\pi\)
\(194\) −1.34506 2.32972i −0.0965700 0.167264i
\(195\) 0 0
\(196\) 0 0
\(197\) 4.97775i 0.354650i −0.984152 0.177325i \(-0.943256\pi\)
0.984152 0.177325i \(-0.0567444\pi\)
\(198\) 0 0
\(199\) 1.15120i 0.0816064i 0.999167 + 0.0408032i \(0.0129917\pi\)
−0.999167 + 0.0408032i \(0.987008\pi\)
\(200\) 2.56917 + 1.48331i 0.181667 + 0.104886i
\(201\) 0 0
\(202\) −3.20202 + 1.84869i −0.225294 + 0.130073i
\(203\) 0 0
\(204\) 0 0
\(205\) 3.31237 5.73719i 0.231346 0.400703i
\(206\) 16.1252 1.12350
\(207\) 0 0
\(208\) 1.86853i 0.129559i
\(209\) −7.23856 + 12.5376i −0.500702 + 0.867241i
\(210\) 0 0
\(211\) −7.03245 12.1806i −0.484134 0.838545i 0.515700 0.856769i \(-0.327532\pi\)
−0.999834 + 0.0182244i \(0.994199\pi\)
\(212\) −10.2997 + 5.94652i −0.707384 + 0.408409i
\(213\) 0 0
\(214\) 0.272624 0.472199i 0.0186362 0.0322788i
\(215\) 14.4877 0.988051
\(216\) 0 0
\(217\) 0 0
\(218\) −5.48210 3.16509i −0.371294 0.214367i
\(219\) 0 0
\(220\) 3.02547 1.74676i 0.203977 0.117766i
\(221\) 3.21414 1.85568i 0.216206 0.124827i
\(222\) 0 0
\(223\) −17.3777 10.0330i −1.16370 0.671860i −0.211509 0.977376i \(-0.567838\pi\)
−0.952187 + 0.305516i \(0.901171\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 10.6374 0.707586
\(227\) 3.01495 5.22205i 0.200109 0.346600i −0.748454 0.663187i \(-0.769204\pi\)
0.948563 + 0.316587i \(0.102537\pi\)
\(228\) 0 0
\(229\) 19.8379 11.4534i 1.31092 0.756862i 0.328674 0.944443i \(-0.393398\pi\)
0.982249 + 0.187581i \(0.0600648\pi\)
\(230\) −4.65432 8.06152i −0.306897 0.531561i
\(231\) 0 0
\(232\) −3.18234 + 5.51198i −0.208931 + 0.361879i
\(233\) 29.7780i 1.95082i −0.220395 0.975411i \(-0.570735\pi\)
0.220395 0.975411i \(-0.429265\pi\)
\(234\) 0 0
\(235\) −18.4792 −1.20545
\(236\) 2.88911 5.00408i 0.188065 0.325738i
\(237\) 0 0
\(238\) 0 0
\(239\) −10.5976 + 6.11850i −0.685499 + 0.395773i −0.801924 0.597427i \(-0.796190\pi\)
0.116425 + 0.993200i \(0.462857\pi\)
\(240\) 0 0
\(241\) −21.0423 12.1488i −1.35545 0.782571i −0.366445 0.930440i \(-0.619425\pi\)
−0.989007 + 0.147869i \(0.952759\pi\)
\(242\) 4.99785i 0.321274i
\(243\) 0 0
\(244\) 9.68245i 0.619855i
\(245\) 0 0
\(246\) 0 0
\(247\) −5.52075 9.56223i −0.351277 0.608430i
\(248\) −2.39691 4.15157i −0.152204 0.263625i
\(249\) 0 0
\(250\) −9.83817 5.68007i −0.622220 0.359239i
\(251\) −13.0834 −0.825815 −0.412908 0.910773i \(-0.635487\pi\)
−0.412908 + 0.910773i \(0.635487\pi\)
\(252\) 0 0
\(253\) 15.9930 1.00547
\(254\) 5.13061 + 2.96216i 0.321923 + 0.185862i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.24569 + 5.62170i 0.202461 + 0.350672i 0.949321 0.314309i \(-0.101773\pi\)
−0.746860 + 0.664981i \(0.768439\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.66446i 0.165243i
\(261\) 0 0
\(262\) 13.6350i 0.842375i
\(263\) −23.2937 13.4486i −1.43635 0.829276i −0.438755 0.898607i \(-0.644580\pi\)
−0.997594 + 0.0693309i \(0.977914\pi\)
\(264\) 0 0
\(265\) 14.6870 8.47954i 0.902215 0.520894i
\(266\) 0 0
\(267\) 0 0
\(268\) −7.60449 + 13.1714i −0.464518 + 0.804569i
\(269\) −15.3040 −0.933099 −0.466550 0.884495i \(-0.654503\pi\)
−0.466550 + 0.884495i \(0.654503\pi\)
\(270\) 0 0
\(271\) 9.36077i 0.568626i 0.958731 + 0.284313i \(0.0917656\pi\)
−0.958731 + 0.284313i \(0.908234\pi\)
\(272\) 0.993125 1.72014i 0.0602171 0.104299i
\(273\) 0 0
\(274\) 8.98348 + 15.5598i 0.542712 + 0.940004i
\(275\) 6.29427 3.63400i 0.379559 0.219138i
\(276\) 0 0
\(277\) 13.5195 23.4164i 0.812307 1.40696i −0.0989390 0.995093i \(-0.531545\pi\)
0.911246 0.411863i \(-0.135122\pi\)
\(278\) −9.49716 −0.569602
\(279\) 0 0
\(280\) 0 0
\(281\) 16.4502 + 9.49754i 0.981338 + 0.566576i 0.902674 0.430325i \(-0.141601\pi\)
0.0786642 + 0.996901i \(0.474935\pi\)
\(282\) 0 0
\(283\) 15.6354 9.02710i 0.929428 0.536606i 0.0427975 0.999084i \(-0.486373\pi\)
0.886631 + 0.462478i \(0.153040\pi\)
\(284\) −0.514494 + 0.297043i −0.0305296 + 0.0176263i
\(285\) 0 0
\(286\) −3.96445 2.28888i −0.234423 0.135344i
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0548 −0.767930
\(290\) 4.53792 7.85991i 0.266476 0.461550i
\(291\) 0 0
\(292\) −11.7670 + 6.79371i −0.688614 + 0.397572i
\(293\) 9.99970 + 17.3200i 0.584189 + 1.01184i 0.994976 + 0.100113i \(0.0319205\pi\)
−0.410788 + 0.911731i \(0.634746\pi\)
\(294\) 0 0
\(295\) −4.11977 + 7.13565i −0.239862 + 0.415454i
\(296\) 1.83032i 0.106385i
\(297\) 0 0
\(298\) −5.32364 −0.308390
\(299\) −6.09882 + 10.5635i −0.352704 + 0.610901i
\(300\) 0 0
\(301\) 0 0
\(302\) −12.0773 + 6.97282i −0.694969 + 0.401240i
\(303\) 0 0
\(304\) −5.11752 2.95460i −0.293510 0.169458i
\(305\) 13.8069i 0.790578i
\(306\) 0 0
\(307\) 2.13374i 0.121779i 0.998145 + 0.0608896i \(0.0193937\pi\)
−0.998145 + 0.0608896i \(0.980606\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3.41791 + 5.92000i 0.194124 + 0.336233i
\(311\) −4.56419 7.90541i −0.258812 0.448275i 0.707112 0.707101i \(-0.249998\pi\)
−0.965924 + 0.258827i \(0.916664\pi\)
\(312\) 0 0
\(313\) −12.9579 7.48122i −0.732421 0.422864i 0.0868859 0.996218i \(-0.472308\pi\)
−0.819307 + 0.573355i \(0.805642\pi\)
\(314\) −5.25986 −0.296831
\(315\) 0 0
\(316\) 9.74696 0.548309
\(317\) −1.83555 1.05976i −0.103095 0.0595219i 0.447566 0.894251i \(-0.352291\pi\)
−0.550661 + 0.834729i \(0.685624\pi\)
\(318\) 0 0
\(319\) 7.79651 + 13.5040i 0.436521 + 0.756076i
\(320\) 0.712984 + 1.23492i 0.0398570 + 0.0690344i
\(321\) 0 0
\(322\) 0 0
\(323\) 11.7372i 0.653073i
\(324\) 0 0
\(325\) 5.54321i 0.307482i
\(326\) −8.55504 4.93926i −0.473820 0.273560i
\(327\) 0 0
\(328\) −4.02337 + 2.32289i −0.222153 + 0.128260i
\(329\) 0 0
\(330\) 0 0
\(331\) 6.21840 10.7706i 0.341794 0.592005i −0.642972 0.765890i \(-0.722299\pi\)
0.984766 + 0.173885i \(0.0556322\pi\)
\(332\) 3.21172 0.176266
\(333\) 0 0
\(334\) 17.7350i 0.970414i
\(335\) 10.8438 18.7819i 0.592457 1.02617i
\(336\) 0 0
\(337\) −9.57144 16.5782i −0.521389 0.903073i −0.999691 0.0248771i \(-0.992081\pi\)
0.478301 0.878196i \(-0.341253\pi\)
\(338\) −8.23469 + 4.75430i −0.447908 + 0.258600i
\(339\) 0 0
\(340\) −1.41616 + 2.45287i −0.0768023 + 0.133025i
\(341\) −11.7445 −0.636001
\(342\) 0 0
\(343\) 0 0
\(344\) −8.79872 5.07994i −0.474395 0.273892i
\(345\) 0 0
\(346\) 7.27539 4.20045i 0.391127 0.225817i
\(347\) −3.85149 + 2.22366i −0.206759 + 0.119372i −0.599804 0.800147i \(-0.704755\pi\)
0.393045 + 0.919519i \(0.371422\pi\)
\(348\) 0 0
\(349\) 25.0865 + 14.4837i 1.34285 + 0.775294i 0.987225 0.159335i \(-0.0509349\pi\)
0.355624 + 0.934629i \(0.384268\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.44993 −0.130582
\(353\) 10.7060 18.5433i 0.569822 0.986961i −0.426761 0.904365i \(-0.640345\pi\)
0.996583 0.0825966i \(-0.0263213\pi\)
\(354\) 0 0
\(355\) 0.733652 0.423574i 0.0389382 0.0224810i
\(356\) 0.0723285 + 0.125277i 0.00383340 + 0.00663965i
\(357\) 0 0
\(358\) 1.51150 2.61800i 0.0798853 0.138365i
\(359\) 11.4103i 0.602214i 0.953590 + 0.301107i \(0.0973561\pi\)
−0.953590 + 0.301107i \(0.902644\pi\)
\(360\) 0 0
\(361\) −15.9187 −0.837825
\(362\) 2.47364 4.28448i 0.130012 0.225187i
\(363\) 0 0
\(364\) 0 0
\(365\) 16.7794 9.68760i 0.878275 0.507072i
\(366\) 0 0
\(367\) −13.4460 7.76303i −0.701873 0.405227i 0.106171 0.994348i \(-0.466141\pi\)
−0.808045 + 0.589121i \(0.799474\pi\)
\(368\) 6.52794i 0.340293i
\(369\) 0 0
\(370\) 2.60998i 0.135687i
\(371\) 0 0
\(372\) 0 0
\(373\) 9.04807 + 15.6717i 0.468491 + 0.811451i 0.999351 0.0360087i \(-0.0114644\pi\)
−0.530860 + 0.847459i \(0.678131\pi\)
\(374\) −2.43309 4.21423i −0.125812 0.217913i
\(375\) 0 0
\(376\) 11.2229 + 6.47952i 0.578774 + 0.334156i
\(377\) −11.8926 −0.612500
\(378\) 0 0
\(379\) −24.2482 −1.24555 −0.622774 0.782402i \(-0.713994\pi\)
−0.622774 + 0.782402i \(0.713994\pi\)
\(380\) 7.29742 + 4.21317i 0.374350 + 0.216131i
\(381\) 0 0
\(382\) −2.55292 4.42179i −0.130619 0.226238i
\(383\) 3.05053 + 5.28368i 0.155875 + 0.269983i 0.933377 0.358897i \(-0.116847\pi\)
−0.777502 + 0.628880i \(0.783514\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.05412i 0.0536534i
\(387\) 0 0
\(388\) 2.69013i 0.136571i
\(389\) −8.39221 4.84524i −0.425502 0.245664i 0.271927 0.962318i \(-0.412339\pi\)
−0.697429 + 0.716654i \(0.745673\pi\)
\(390\) 0 0
\(391\) −11.2290 + 6.48307i −0.567875 + 0.327863i
\(392\) 0 0
\(393\) 0 0
\(394\) 2.48888 4.31086i 0.125388 0.217178i
\(395\) −13.8988 −0.699327
\(396\) 0 0
\(397\) 14.4928i 0.727373i 0.931521 + 0.363687i \(0.118482\pi\)
−0.931521 + 0.363687i \(0.881518\pi\)
\(398\) −0.575600 + 0.996968i −0.0288522 + 0.0499735i
\(399\) 0 0
\(400\) 1.48331 + 2.56917i 0.0741654 + 0.128458i
\(401\) 21.6413 12.4946i 1.08072 0.623952i 0.149627 0.988742i \(-0.452193\pi\)
0.931090 + 0.364790i \(0.118859\pi\)
\(402\) 0 0
\(403\) 4.47869 7.75732i 0.223099 0.386420i
\(404\) −3.69738 −0.183951
\(405\) 0 0
\(406\) 0 0
\(407\) −3.88340 2.24208i −0.192493 0.111136i
\(408\) 0 0
\(409\) 32.2174 18.6007i 1.59305 0.919746i 0.600266 0.799801i \(-0.295061\pi\)
0.992781 0.119945i \(-0.0382718\pi\)
\(410\) 5.73719 3.31237i 0.283340 0.163586i
\(411\) 0 0
\(412\) 13.9648 + 8.06260i 0.687998 + 0.397216i
\(413\) 0 0
\(414\) 0 0
\(415\) −4.57981 −0.224814
\(416\) 0.934264 1.61819i 0.0458061 0.0793384i
\(417\) 0 0
\(418\) −12.5376 + 7.23856i −0.613232 + 0.354050i
\(419\) −17.7624 30.7654i −0.867750 1.50299i −0.864290 0.502993i \(-0.832232\pi\)
−0.00345977 0.999994i \(-0.501101\pi\)
\(420\) 0 0
\(421\) 16.8698 29.2193i 0.822181 1.42406i −0.0818731 0.996643i \(-0.526090\pi\)
0.904055 0.427417i \(-0.140576\pi\)
\(422\) 14.0649i 0.684669i
\(423\) 0 0
\(424\) −11.8930 −0.577577
\(425\) −2.94622 + 5.10301i −0.142913 + 0.247532i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.472199 0.272624i 0.0228246 0.0131778i
\(429\) 0 0
\(430\) 12.5467 + 7.24384i 0.605055 + 0.349329i
\(431\) 3.13857i 0.151180i 0.997139 + 0.0755899i \(0.0240840\pi\)
−0.997139 + 0.0755899i \(0.975916\pi\)
\(432\) 0 0
\(433\) 36.1258i 1.73609i 0.496482 + 0.868047i \(0.334625\pi\)
−0.496482 + 0.868047i \(0.665375\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3.16509 5.48210i −0.151580 0.262545i
\(437\) 19.2875 + 33.4069i 0.922645 + 1.59807i
\(438\) 0 0
\(439\) −12.5331 7.23602i −0.598175 0.345356i 0.170149 0.985418i \(-0.445575\pi\)
−0.768323 + 0.640062i \(0.778909\pi\)
\(440\) 3.49352 0.166547
\(441\) 0 0
\(442\) 3.71136 0.176532
\(443\) 9.50209 + 5.48604i 0.451458 + 0.260649i 0.708446 0.705765i \(-0.249397\pi\)
−0.256988 + 0.966415i \(0.582730\pi\)
\(444\) 0 0
\(445\) −0.103138 0.178640i −0.00488921 0.00846837i
\(446\) −10.0330 17.3777i −0.475077 0.822857i
\(447\) 0 0
\(448\) 0 0
\(449\) 29.7298i 1.40304i −0.712652 0.701518i \(-0.752506\pi\)
0.712652 0.701518i \(-0.247494\pi\)
\(450\) 0 0
\(451\) 11.3818i 0.535949i
\(452\) 9.21222 + 5.31868i 0.433306 + 0.250169i
\(453\) 0 0
\(454\) 5.22205 3.01495i 0.245083 0.141499i
\(455\) 0 0
\(456\) 0 0
\(457\) −5.07662 + 8.79296i −0.237474 + 0.411317i −0.959989 0.280038i \(-0.909653\pi\)
0.722515 + 0.691356i \(0.242986\pi\)
\(458\) 22.9068 1.07036
\(459\) 0 0
\(460\) 9.30864i 0.434017i
\(461\) 13.9677 24.1927i 0.650539 1.12677i −0.332454 0.943120i \(-0.607876\pi\)
0.982992 0.183647i \(-0.0587902\pi\)
\(462\) 0 0
\(463\) −11.4477 19.8280i −0.532019 0.921485i −0.999301 0.0373763i \(-0.988100\pi\)
0.467282 0.884108i \(-0.345233\pi\)
\(464\) −5.51198 + 3.18234i −0.255887 + 0.147737i
\(465\) 0 0
\(466\) 14.8890 25.7885i 0.689719 1.19463i
\(467\) 14.8691 0.688059 0.344029 0.938959i \(-0.388208\pi\)
0.344029 + 0.938959i \(0.388208\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −16.0034 9.23958i −0.738183 0.426190i
\(471\) 0 0
\(472\) 5.00408 2.88911i 0.230331 0.132982i
\(473\) −21.5562 + 12.4455i −0.991157 + 0.572245i
\(474\) 0 0
\(475\) 15.1817 + 8.76517i 0.696585 + 0.402174i
\(476\) 0 0
\(477\) 0 0
\(478\) −12.2370 −0.559707
\(479\) −3.82550 + 6.62595i −0.174791 + 0.302748i −0.940089 0.340929i \(-0.889258\pi\)
0.765298 + 0.643677i \(0.222592\pi\)
\(480\) 0 0
\(481\) 2.96182 1.71001i 0.135047 0.0779695i
\(482\) −12.1488 21.0423i −0.553361 0.958449i
\(483\) 0 0
\(484\) 2.49893 4.32827i 0.113588 0.196739i
\(485\) 3.83604i 0.174186i
\(486\) 0 0
\(487\) 22.0497 0.999168 0.499584 0.866265i \(-0.333486\pi\)
0.499584 + 0.866265i \(0.333486\pi\)
\(488\) −4.84122 + 8.38524i −0.219152 + 0.379582i
\(489\) 0 0
\(490\) 0 0
\(491\) −26.3385 + 15.2065i −1.18864 + 0.686261i −0.957997 0.286778i \(-0.907416\pi\)
−0.230641 + 0.973039i \(0.574082\pi\)
\(492\) 0 0
\(493\) −10.9482 6.32093i −0.493081 0.284681i
\(494\) 11.0415i 0.496781i
\(495\) 0 0
\(496\) 4.79382i 0.215249i
\(497\) 0 0
\(498\) 0 0
\(499\) −12.6832 21.9680i −0.567778 0.983421i −0.996785 0.0801195i \(-0.974470\pi\)
0.429007 0.903301i \(-0.358864\pi\)
\(500\) −5.68007 9.83817i −0.254020 0.439976i
\(501\) 0 0
\(502\) −11.3305 6.54169i −0.505706 0.291970i
\(503\) 29.1075 1.29784 0.648919 0.760858i \(-0.275222\pi\)
0.648919 + 0.760858i \(0.275222\pi\)
\(504\) 0 0
\(505\) 5.27234 0.234616
\(506\) 13.8503 + 7.99650i 0.615723 + 0.355488i
\(507\) 0 0
\(508\) 2.96216 + 5.13061i 0.131425 + 0.227634i
\(509\) −5.80749 10.0589i −0.257412 0.445851i 0.708136 0.706076i \(-0.249537\pi\)
−0.965548 + 0.260225i \(0.916203\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 6.49138i 0.286323i
\(515\) −19.9134 11.4970i −0.877489 0.506618i
\(516\) 0 0
\(517\) 27.4952 15.8744i 1.20924 0.698153i
\(518\) 0 0
\(519\) 0 0
\(520\) −1.33223 + 2.30749i −0.0584221 + 0.101190i
\(521\) −1.41619 −0.0620443 −0.0310221 0.999519i \(-0.509876\pi\)
−0.0310221 + 0.999519i \(0.509876\pi\)
\(522\) 0 0
\(523\) 8.91703i 0.389915i 0.980812 + 0.194957i \(0.0624568\pi\)
−0.980812 + 0.194957i \(0.937543\pi\)
\(524\) −6.81751 + 11.8083i −0.297824 + 0.515847i
\(525\) 0 0
\(526\) −13.4486 23.2937i −0.586387 1.01565i
\(527\) 8.24605 4.76086i 0.359204 0.207386i
\(528\) 0 0
\(529\) 9.80703 16.9863i 0.426393 0.738534i
\(530\) 16.9591 0.736656
\(531\) 0 0
\(532\) 0 0
\(533\) −7.51777 4.34039i −0.325631 0.188003i
\(534\) 0 0
\(535\) −0.673340 + 0.388753i −0.0291110 + 0.0168073i
\(536\) −13.1714 + 7.60449i −0.568916 + 0.328464i
\(537\) 0 0
\(538\) −13.2536 7.65198i −0.571404 0.329900i
\(539\) 0 0
\(540\) 0 0
\(541\) 8.74127 0.375817 0.187908 0.982187i \(-0.439829\pi\)
0.187908 + 0.982187i \(0.439829\pi\)
\(542\) −4.68039 + 8.10667i −0.201040 + 0.348211i
\(543\) 0 0
\(544\) 1.72014 0.993125i 0.0737505 0.0425799i
\(545\) 4.51332 + 7.81729i 0.193329 + 0.334856i
\(546\) 0 0
\(547\) −12.4767 + 21.6103i −0.533466 + 0.923990i 0.465770 + 0.884906i \(0.345777\pi\)
−0.999236 + 0.0390840i \(0.987556\pi\)
\(548\) 17.9670i 0.767510i
\(549\) 0 0
\(550\) 7.26800 0.309908
\(551\) −18.8051 + 32.5714i −0.801125 + 1.38759i
\(552\) 0 0
\(553\) 0 0
\(554\) 23.4164 13.5195i 0.994869 0.574388i
\(555\) 0 0
\(556\) −8.22479 4.74858i −0.348809 0.201385i
\(557\) 0.0493284i 0.00209011i 0.999999 + 0.00104506i \(0.000332652\pi\)
−0.999999 + 0.00104506i \(0.999667\pi\)
\(558\) 0 0
\(559\) 18.9840i 0.802939i
\(560\) 0 0
\(561\) 0 0
\(562\) 9.49754 + 16.4502i 0.400630 + 0.693911i
\(563\) −3.24507 5.62062i −0.136763 0.236881i 0.789506 0.613742i \(-0.210337\pi\)
−0.926270 + 0.376861i \(0.877003\pi\)
\(564\) 0 0
\(565\) −13.1363 7.58426i −0.552649 0.319072i
\(566\) 18.0542 0.758875
\(567\) 0 0
\(568\) −0.594087 −0.0249273
\(569\) −33.5802 19.3876i −1.40776 0.812768i −0.412585 0.910919i \(-0.635374\pi\)
−0.995172 + 0.0981509i \(0.968707\pi\)
\(570\) 0 0
\(571\) −0.128832 0.223143i −0.00539143 0.00933824i 0.863317 0.504662i \(-0.168383\pi\)
−0.868709 + 0.495324i \(0.835049\pi\)
\(572\) −2.28888 3.96445i −0.0957028 0.165762i
\(573\) 0 0
\(574\) 0 0
\(575\) 19.3659i 0.807614i
\(576\) 0 0
\(577\) 33.5074i 1.39493i 0.716618 + 0.697465i \(0.245689\pi\)
−0.716618 + 0.697465i \(0.754311\pi\)
\(578\) −11.3058 6.52740i −0.470259 0.271504i
\(579\) 0 0
\(580\) 7.85991 4.53792i 0.326365 0.188427i
\(581\) 0 0
\(582\) 0 0
\(583\) −14.5685 + 25.2335i −0.603367 + 1.04506i
\(584\) −13.5874 −0.562251
\(585\) 0 0
\(586\) 19.9994i 0.826167i
\(587\) 22.4541 38.8916i 0.926779 1.60523i 0.138104 0.990418i \(-0.455899\pi\)
0.788675 0.614811i \(-0.210768\pi\)
\(588\) 0 0
\(589\) −14.1638 24.5325i −0.583610 1.01084i
\(590\) −7.13565 + 4.11977i −0.293770 + 0.169608i
\(591\) 0 0
\(592\) 0.915162 1.58511i 0.0376129 0.0651475i
\(593\) −21.2653 −0.873260 −0.436630 0.899641i \(-0.643828\pi\)
−0.436630 + 0.899641i \(0.643828\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.61041 2.66182i −0.188850 0.109032i
\(597\) 0 0
\(598\) −10.5635 + 6.09882i −0.431972 + 0.249399i
\(599\) −22.1002 + 12.7596i −0.902990 + 0.521341i −0.878169 0.478351i \(-0.841235\pi\)
−0.0248208 + 0.999692i \(0.507902\pi\)
\(600\) 0 0
\(601\) 14.4139 + 8.32184i 0.587953 + 0.339455i 0.764288 0.644875i \(-0.223091\pi\)
−0.176335 + 0.984330i \(0.556424\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −13.9456 −0.567440
\(605\) −3.56339 + 6.17197i −0.144872 + 0.250926i
\(606\) 0 0
\(607\) −4.89357 + 2.82531i −0.198624 + 0.114676i −0.596014 0.802974i \(-0.703250\pi\)
0.397389 + 0.917650i \(0.369916\pi\)
\(608\) −2.95460 5.11752i −0.119825 0.207543i
\(609\) 0 0
\(610\) 6.90343 11.9571i 0.279512 0.484128i
\(611\) 24.2143i 0.979606i
\(612\) 0 0
\(613\) 39.8457 1.60935 0.804676 0.593714i \(-0.202339\pi\)
0.804676 + 0.593714i \(0.202339\pi\)
\(614\) −1.06687 + 1.84788i −0.0430554 + 0.0745742i
\(615\) 0 0
\(616\) 0 0
\(617\) −13.6398 + 7.87493i −0.549117 + 0.317033i −0.748766 0.662835i \(-0.769353\pi\)
0.199649 + 0.979868i \(0.436020\pi\)
\(618\) 0 0
\(619\) 23.3655 + 13.4901i 0.939140 + 0.542213i 0.889691 0.456564i \(-0.150920\pi\)
0.0494494 + 0.998777i \(0.484253\pi\)
\(620\) 6.83583i 0.274533i
\(621\) 0 0
\(622\) 9.12838i 0.366015i
\(623\) 0 0
\(624\) 0 0
\(625\) 0.683051 + 1.18308i 0.0273220 + 0.0473232i
\(626\) −7.48122 12.9579i −0.299010 0.517900i
\(627\) 0 0
\(628\) −4.55518 2.62993i −0.181771 0.104946i
\(629\) 3.63548 0.144956
\(630\) 0 0
\(631\) 22.1618 0.882246 0.441123 0.897447i \(-0.354580\pi\)
0.441123 + 0.897447i \(0.354580\pi\)
\(632\) 8.44111 + 4.87348i 0.335769 + 0.193857i
\(633\) 0 0
\(634\) −1.05976 1.83555i −0.0420883 0.0728992i
\(635\) −4.22394 7.31609i −0.167622 0.290330i
\(636\) 0 0
\(637\) 0 0
\(638\) 15.5930i 0.617334i
\(639\) 0 0
\(640\) 1.42597i 0.0563663i
\(641\) 21.1748 + 12.2253i 0.836356 + 0.482870i 0.856024 0.516936i \(-0.172928\pi\)
−0.0196680 + 0.999807i \(0.506261\pi\)
\(642\) 0 0
\(643\) 5.38012 3.10621i 0.212171 0.122497i −0.390149 0.920752i \(-0.627576\pi\)
0.602320 + 0.798255i \(0.294243\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 5.86858 10.1647i 0.230896 0.399924i
\(647\) 34.2800 1.34769 0.673844 0.738874i \(-0.264642\pi\)
0.673844 + 0.738874i \(0.264642\pi\)
\(648\) 0 0
\(649\) 14.1562i 0.555679i
\(650\) −2.77160 + 4.80056i −0.108711 + 0.188293i
\(651\) 0 0
\(652\) −4.93926 8.55504i −0.193436 0.335041i
\(653\) 7.85846 4.53709i 0.307525 0.177550i −0.338293 0.941041i \(-0.609850\pi\)
0.645819 + 0.763491i \(0.276516\pi\)
\(654\) 0 0
\(655\) 9.72155 16.8382i 0.379852 0.657924i
\(656\) −4.64578 −0.181387
\(657\) 0 0
\(658\) 0 0
\(659\) −42.1898 24.3583i −1.64348 0.948865i −0.979582 0.201043i \(-0.935567\pi\)
−0.663900 0.747821i \(-0.731100\pi\)
\(660\) 0 0
\(661\) 9.43876 5.44947i 0.367125 0.211960i −0.305077 0.952328i \(-0.598682\pi\)
0.672202 + 0.740368i \(0.265349\pi\)
\(662\) 10.7706 6.21840i 0.418610 0.241685i
\(663\) 0 0
\(664\) 2.78143 + 1.60586i 0.107941 + 0.0623195i
\(665\) 0 0
\(666\) 0 0
\(667\) 41.5483 1.60876
\(668\) −8.86749 + 15.3589i −0.343093 + 0.594255i
\(669\) 0 0
\(670\) 18.7819 10.8438i 0.725609 0.418931i
\(671\) 11.8606 + 20.5432i 0.457875 + 0.793063i
\(672\) 0 0
\(673\) 23.6565 40.9743i 0.911893 1.57944i 0.100505 0.994937i \(-0.467954\pi\)
0.811388 0.584508i \(-0.198712\pi\)
\(674\) 19.1429i 0.737356i
\(675\) 0 0
\(676\) −9.50860 −0.365716
\(677\) 2.46212 4.26452i 0.0946270 0.163899i −0.814826 0.579706i \(-0.803167\pi\)
0.909453 + 0.415807i \(0.136501\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.45287 + 1.41616i −0.0940632 + 0.0543074i
\(681\) 0 0
\(682\) −10.1710 5.87225i −0.389469 0.224860i
\(683\) 11.2280i 0.429629i −0.976655 0.214814i \(-0.931085\pi\)
0.976655 0.214814i \(-0.0689147\pi\)
\(684\) 0 0
\(685\) 25.6203i 0.978901i
\(686\) 0 0
\(687\) 0 0
\(688\) −5.07994 8.79872i −0.193671 0.335448i
\(689\) −11.1112 19.2452i −0.423304 0.733185i
\(690\) 0 0
\(691\) 12.0725 + 6.97005i 0.459259 + 0.265153i 0.711732 0.702451i \(-0.247911\pi\)
−0.252474 + 0.967604i \(0.581244\pi\)
\(692\) 8.40089 0.319354
\(693\) 0 0
\(694\) −4.44732 −0.168818
\(695\) 11.7283 + 6.77132i 0.444879 + 0.256851i
\(696\) 0 0
\(697\) −4.61384 7.99141i −0.174762 0.302696i
\(698\) 14.4837 + 25.0865i 0.548216 + 0.949538i
\(699\) 0 0
\(700\) 0 0
\(701\) 33.1186i 1.25087i 0.780276 + 0.625435i \(0.215079\pi\)
−0.780276 + 0.625435i \(0.784921\pi\)
\(702\) 0 0
\(703\) 10.8158i 0.407924i
\(704\) −2.12170 1.22496i −0.0799646 0.0461676i
\(705\) 0 0
\(706\) 18.5433 10.7060i 0.697887 0.402925i
\(707\) 0 0
\(708\) 0 0
\(709\) 9.06989 15.7095i 0.340627 0.589983i −0.643922 0.765091i \(-0.722694\pi\)
0.984549 + 0.175108i \(0.0560274\pi\)
\(710\) 0.847148 0.0317929
\(711\) 0 0
\(712\) 0.144657i 0.00542125i
\(713\) −15.6469 + 27.1012i −0.585981 + 1.01495i
\(714\) 0 0
\(715\) 3.26387 + 5.65318i 0.122062 + 0.211417i
\(716\) 2.61800 1.51150i 0.0978391 0.0564874i
\(717\) 0 0
\(718\) −5.70516 + 9.88163i −0.212915 + 0.368779i
\(719\) −25.0164 −0.932953 −0.466476 0.884534i \(-0.654477\pi\)
−0.466476 + 0.884534i \(0.654477\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −13.7860 7.95934i −0.513061 0.296216i
\(723\) 0 0
\(724\) 4.28448 2.47364i 0.159231 0.0919323i
\(725\) 16.3519 9.44080i 0.607296 0.350622i
\(726\) 0 0
\(727\) −32.3382 18.6705i −1.19936 0.692450i −0.238946 0.971033i \(-0.576802\pi\)
−0.960412 + 0.278583i \(0.910135\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 19.3752 0.717109
\(731\) 10.0900 17.4765i 0.373194 0.646390i
\(732\) 0 0
\(733\) −34.3841 + 19.8516i −1.27000 + 0.733237i −0.974989 0.222255i \(-0.928658\pi\)
−0.295016 + 0.955492i \(0.595325\pi\)
\(734\) −7.76303 13.4460i −0.286539 0.496299i
\(735\) 0 0
\(736\) −3.26397 + 5.65337i −0.120312 + 0.208386i
\(737\) 37.2609i 1.37252i
\(738\) 0 0
\(739\) −39.8006 −1.46409 −0.732044 0.681257i \(-0.761433\pi\)
−0.732044 + 0.681257i \(0.761433\pi\)
\(740\) −1.30499 + 2.26031i −0.0479724 + 0.0830907i
\(741\) 0 0
\(742\) 0 0
\(743\) −34.6622 + 20.0123i −1.27163 + 0.734178i −0.975295 0.220905i \(-0.929099\pi\)
−0.296339 + 0.955083i \(0.595766\pi\)
\(744\) 0 0
\(745\) 6.57429 + 3.79567i 0.240863 + 0.139063i
\(746\) 18.0961i 0.662547i
\(747\) 0 0
\(748\) 4.86617i 0.177925i
\(749\) 0 0
\(750\) 0 0
\(751\) 5.98284 + 10.3626i 0.218317 + 0.378136i 0.954294 0.298871i \(-0.0966100\pi\)
−0.735977 + 0.677007i \(0.763277\pi\)
\(752\) 6.47952 + 11.2229i 0.236284 + 0.409255i
\(753\) 0 0
\(754\) −10.2993 5.94630i −0.375078 0.216551i
\(755\) 19.8860 0.723726
\(756\) 0 0
\(757\) −0.372779 −0.0135489 −0.00677443 0.999977i \(-0.502156\pi\)
−0.00677443 + 0.999977i \(0.502156\pi\)
\(758\) −20.9996 12.1241i −0.762739 0.440368i
\(759\) 0 0
\(760\) 4.21317 + 7.29742i 0.152828 + 0.264705i
\(761\) 3.82232 + 6.62046i 0.138559 + 0.239991i 0.926951 0.375181i \(-0.122420\pi\)
−0.788392 + 0.615173i \(0.789086\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 5.10584i 0.184723i
\(765\) 0 0
\(766\) 6.10106i 0.220440i
\(767\) 9.35026 + 5.39837i 0.337618 + 0.194924i
\(768\) 0 0
\(769\) −7.18496 + 4.14824i −0.259096 + 0.149589i −0.623922 0.781486i \(-0.714462\pi\)
0.364826 + 0.931076i \(0.381128\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.527061 0.912897i 0.0189694 0.0328559i
\(773\) −16.8724 −0.606856 −0.303428 0.952854i \(-0.598131\pi\)
−0.303428 + 0.952854i \(0.598131\pi\)
\(774\) 0 0
\(775\) 14.2214i 0.510848i
\(776\) 1.34506 2.32972i 0.0482850 0.0836321i
\(777\) 0 0
\(778\) −4.84524 8.39221i −0.173710 0.300875i
\(779\) −23.7749 + 13.7264i −0.851823 + 0.491801i
\(780\) 0 0
\(781\) −0.727735 + 1.26047i −0.0260404 + 0.0451033i
\(782\) −12.9661 −0.463668
\(783\) 0 0
\(784\) 0 0
\(785\) 6.49553 + 3.75020i 0.231835 + 0.133850i
\(786\) 0 0
\(787\) −28.6503 + 16.5413i −1.02127 + 0.589633i −0.914473 0.404647i \(-0.867394\pi\)
−0.106802 + 0.994280i \(0.534061\pi\)
\(788\) 4.31086 2.48888i 0.153568 0.0886625i
\(789\) 0 0
\(790\) −12.0368 6.94942i −0.428248 0.247249i
\(791\) 0 0
\(792\) 0 0
\(793\) −18.0919 −0.642463
\(794\) −7.24641 + 12.5511i −0.257165 + 0.445423i
\(795\) 0 0