Properties

Label 324.5.d.f.163.4
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.4
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.f.163.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.49753 + 1.94095i) q^{2} +(8.46540 - 13.5771i) q^{4} -33.2277 q^{5} -46.1602i q^{7} +(-3.25547 + 63.9171i) q^{8} +O(q^{10})\) \(q+(-3.49753 + 1.94095i) q^{2} +(8.46540 - 13.5771i) q^{4} -33.2277 q^{5} -46.1602i q^{7} +(-3.25547 + 63.9171i) q^{8} +(116.215 - 64.4935i) q^{10} +73.4515i q^{11} -303.039 q^{13} +(89.5949 + 161.447i) q^{14} +(-112.674 - 229.871i) q^{16} -182.019 q^{17} -314.215i q^{19} +(-281.286 + 451.135i) q^{20} +(-142.566 - 256.899i) q^{22} -335.924i q^{23} +479.081 q^{25} +(1059.89 - 588.185i) q^{26} +(-626.721 - 390.765i) q^{28} -714.740 q^{29} +1137.60i q^{31} +(840.249 + 585.284i) q^{32} +(636.616 - 353.290i) q^{34} +1533.80i q^{35} +1008.45 q^{37} +(609.877 + 1098.98i) q^{38} +(108.172 - 2123.82i) q^{40} +1115.11 q^{41} -2519.63i q^{43} +(997.257 + 621.796i) q^{44} +(652.014 + 1174.90i) q^{46} -1132.16i q^{47} +270.233 q^{49} +(-1675.60 + 929.873i) q^{50} +(-2565.35 + 4114.39i) q^{52} -1057.77 q^{53} -2440.63i q^{55} +(2950.43 + 150.273i) q^{56} +(2499.82 - 1387.28i) q^{58} +1014.38i q^{59} +860.608 q^{61} +(-2208.02 - 3978.77i) q^{62} +(-4074.80 - 416.161i) q^{64} +10069.3 q^{65} +645.525i q^{67} +(-1540.86 + 2471.29i) q^{68} +(-2977.03 - 5364.50i) q^{70} +9567.89i q^{71} +1899.10 q^{73} +(-3527.08 + 1957.35i) q^{74} +(-4266.13 - 2659.96i) q^{76} +3390.54 q^{77} +7815.14i q^{79} +(3743.90 + 7638.08i) q^{80} +(-3900.11 + 2164.37i) q^{82} +8143.59i q^{83} +6048.07 q^{85} +(4890.49 + 8812.48i) q^{86} +(-4694.81 - 239.119i) q^{88} +7653.39 q^{89} +13988.4i q^{91} +(-4560.87 - 2843.73i) q^{92} +(2197.46 + 3959.75i) q^{94} +10440.7i q^{95} +12733.5 q^{97} +(-945.149 + 524.510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + O(q^{10}) \) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + 14q^{10} + 2q^{13} - 252q^{14} + q^{16} - 28q^{17} + 140q^{20} + 33q^{22} + 1752q^{25} + 548q^{26} - 258q^{28} - 526q^{29} + 121q^{32} - 385q^{34} - 4q^{37} - 1395q^{38} + 2276q^{40} + 2762q^{41} + 3357q^{44} + 1788q^{46} - 3428q^{49} - 6375q^{50} - 1438q^{52} - 5044q^{53} + 7506q^{56} + 4064q^{58} + 2q^{61} - 9162q^{62} + 4513q^{64} + 2014q^{65} + 11405q^{68} - 3666q^{70} - 1708q^{73} - 14620q^{74} - 1581q^{76} + 3942q^{77} + 22760q^{80} - 4243q^{82} + 1252q^{85} - 22113q^{86} - 1995q^{88} + 6524q^{89} + 30294q^{92} - 7524q^{94} - 5638q^{97} - 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.49753 + 1.94095i −0.874382 + 0.485238i
\(3\) 0 0
\(4\) 8.46540 13.5771i 0.529087 0.848567i
\(5\) −33.2277 −1.32911 −0.664554 0.747240i \(-0.731379\pi\)
−0.664554 + 0.747240i \(0.731379\pi\)
\(6\) 0 0
\(7\) 46.1602i 0.942045i −0.882121 0.471023i \(-0.843885\pi\)
0.882121 0.471023i \(-0.156115\pi\)
\(8\) −3.25547 + 63.9171i −0.0508667 + 0.998705i
\(9\) 0 0
\(10\) 116.215 64.4935i 1.16215 0.644935i
\(11\) 73.4515i 0.607037i 0.952825 + 0.303519i \(0.0981615\pi\)
−0.952825 + 0.303519i \(0.901839\pi\)
\(12\) 0 0
\(13\) −303.039 −1.79313 −0.896566 0.442911i \(-0.853946\pi\)
−0.896566 + 0.442911i \(0.853946\pi\)
\(14\) 89.5949 + 161.447i 0.457117 + 0.823707i
\(15\) 0 0
\(16\) −112.674 229.871i −0.440133 0.897932i
\(17\) −182.019 −0.629823 −0.314912 0.949121i \(-0.601975\pi\)
−0.314912 + 0.949121i \(0.601975\pi\)
\(18\) 0 0
\(19\) 314.215i 0.870402i −0.900333 0.435201i \(-0.856677\pi\)
0.900333 0.435201i \(-0.143323\pi\)
\(20\) −281.286 + 451.135i −0.703214 + 1.12784i
\(21\) 0 0
\(22\) −142.566 256.899i −0.294558 0.530782i
\(23\) 335.924i 0.635018i −0.948255 0.317509i \(-0.897154\pi\)
0.948255 0.317509i \(-0.102846\pi\)
\(24\) 0 0
\(25\) 479.081 0.766529
\(26\) 1059.89 588.185i 1.56788 0.870096i
\(27\) 0 0
\(28\) −626.721 390.765i −0.799389 0.498424i
\(29\) −714.740 −0.849869 −0.424935 0.905224i \(-0.639703\pi\)
−0.424935 + 0.905224i \(0.639703\pi\)
\(30\) 0 0
\(31\) 1137.60i 1.18376i 0.806025 + 0.591881i \(0.201614\pi\)
−0.806025 + 0.591881i \(0.798386\pi\)
\(32\) 840.249 + 585.284i 0.820556 + 0.571566i
\(33\) 0 0
\(34\) 636.616 353.290i 0.550706 0.305614i
\(35\) 1533.80i 1.25208i
\(36\) 0 0
\(37\) 1008.45 0.736632 0.368316 0.929701i \(-0.379934\pi\)
0.368316 + 0.929701i \(0.379934\pi\)
\(38\) 609.877 + 1098.98i 0.422353 + 0.761064i
\(39\) 0 0
\(40\) 108.172 2123.82i 0.0676074 1.32739i
\(41\) 1115.11 0.663358 0.331679 0.943392i \(-0.392385\pi\)
0.331679 + 0.943392i \(0.392385\pi\)
\(42\) 0 0
\(43\) 2519.63i 1.36270i −0.731958 0.681349i \(-0.761393\pi\)
0.731958 0.681349i \(-0.238607\pi\)
\(44\) 997.257 + 621.796i 0.515112 + 0.321176i
\(45\) 0 0
\(46\) 652.014 + 1174.90i 0.308135 + 0.555248i
\(47\) 1132.16i 0.512520i −0.966608 0.256260i \(-0.917510\pi\)
0.966608 0.256260i \(-0.0824903\pi\)
\(48\) 0 0
\(49\) 270.233 0.112550
\(50\) −1675.60 + 929.873i −0.670239 + 0.371949i
\(51\) 0 0
\(52\) −2565.35 + 4114.39i −0.948723 + 1.52159i
\(53\) −1057.77 −0.376566 −0.188283 0.982115i \(-0.560292\pi\)
−0.188283 + 0.982115i \(0.560292\pi\)
\(54\) 0 0
\(55\) 2440.63i 0.806818i
\(56\) 2950.43 + 150.273i 0.940826 + 0.0479188i
\(57\) 0 0
\(58\) 2499.82 1387.28i 0.743110 0.412389i
\(59\) 1014.38i 0.291404i 0.989329 + 0.145702i \(0.0465440\pi\)
−0.989329 + 0.145702i \(0.953456\pi\)
\(60\) 0 0
\(61\) 860.608 0.231284 0.115642 0.993291i \(-0.463107\pi\)
0.115642 + 0.993291i \(0.463107\pi\)
\(62\) −2208.02 3978.77i −0.574407 1.03506i
\(63\) 0 0
\(64\) −4074.80 416.161i −0.994825 0.101602i
\(65\) 10069.3 2.38327
\(66\) 0 0
\(67\) 645.525i 0.143802i 0.997412 + 0.0719008i \(0.0229065\pi\)
−0.997412 + 0.0719008i \(0.977094\pi\)
\(68\) −1540.86 + 2471.29i −0.333231 + 0.534448i
\(69\) 0 0
\(70\) −2977.03 5364.50i −0.607558 1.09480i
\(71\) 9567.89i 1.89801i 0.315254 + 0.949007i \(0.397910\pi\)
−0.315254 + 0.949007i \(0.602090\pi\)
\(72\) 0 0
\(73\) 1899.10 0.356372 0.178186 0.983997i \(-0.442977\pi\)
0.178186 + 0.983997i \(0.442977\pi\)
\(74\) −3527.08 + 1957.35i −0.644098 + 0.357442i
\(75\) 0 0
\(76\) −4266.13 2659.96i −0.738595 0.460519i
\(77\) 3390.54 0.571857
\(78\) 0 0
\(79\) 7815.14i 1.25223i 0.779733 + 0.626113i \(0.215355\pi\)
−0.779733 + 0.626113i \(0.784645\pi\)
\(80\) 3743.90 + 7638.08i 0.584985 + 1.19345i
\(81\) 0 0
\(82\) −3900.11 + 2164.37i −0.580028 + 0.321887i
\(83\) 8143.59i 1.18212i 0.806629 + 0.591058i \(0.201289\pi\)
−0.806629 + 0.591058i \(0.798711\pi\)
\(84\) 0 0
\(85\) 6048.07 0.837103
\(86\) 4890.49 + 8812.48i 0.661234 + 1.19152i
\(87\) 0 0
\(88\) −4694.81 239.119i −0.606251 0.0308780i
\(89\) 7653.39 0.966215 0.483107 0.875561i \(-0.339508\pi\)
0.483107 + 0.875561i \(0.339508\pi\)
\(90\) 0 0
\(91\) 13988.4i 1.68921i
\(92\) −4560.87 2843.73i −0.538855 0.335980i
\(93\) 0 0
\(94\) 2197.46 + 3959.75i 0.248694 + 0.448138i
\(95\) 10440.7i 1.15686i
\(96\) 0 0
\(97\) 12733.5 1.35333 0.676666 0.736290i \(-0.263424\pi\)
0.676666 + 0.736290i \(0.263424\pi\)
\(98\) −945.149 + 524.510i −0.0984120 + 0.0546137i
\(99\) 0 0
\(100\) 4055.61 6504.52i 0.405561 0.650452i
\(101\) −13746.4 −1.34755 −0.673777 0.738935i \(-0.735329\pi\)
−0.673777 + 0.738935i \(0.735329\pi\)
\(102\) 0 0
\(103\) 12992.1i 1.22463i 0.790615 + 0.612313i \(0.209761\pi\)
−0.790615 + 0.612313i \(0.790239\pi\)
\(104\) 986.536 19369.4i 0.0912108 1.79081i
\(105\) 0 0
\(106\) 3699.59 2053.09i 0.329262 0.182724i
\(107\) 14891.8i 1.30071i −0.759631 0.650354i \(-0.774621\pi\)
0.759631 0.650354i \(-0.225379\pi\)
\(108\) 0 0
\(109\) 7539.02 0.634544 0.317272 0.948335i \(-0.397233\pi\)
0.317272 + 0.948335i \(0.397233\pi\)
\(110\) 4737.14 + 8536.16i 0.391499 + 0.705467i
\(111\) 0 0
\(112\) −10610.9 + 5201.06i −0.845893 + 0.414626i
\(113\) −992.279 −0.0777100 −0.0388550 0.999245i \(-0.512371\pi\)
−0.0388550 + 0.999245i \(0.512371\pi\)
\(114\) 0 0
\(115\) 11162.0i 0.844007i
\(116\) −6050.56 + 9704.08i −0.449655 + 0.721171i
\(117\) 0 0
\(118\) −1968.86 3547.81i −0.141400 0.254798i
\(119\) 8402.04i 0.593322i
\(120\) 0 0
\(121\) 9245.87 0.631506
\(122\) −3010.00 + 1670.40i −0.202231 + 0.112228i
\(123\) 0 0
\(124\) 15445.2 + 9630.20i 1.00450 + 0.626313i
\(125\) 4848.57 0.310308
\(126\) 0 0
\(127\) 7123.52i 0.441659i 0.975312 + 0.220829i \(0.0708764\pi\)
−0.975312 + 0.220829i \(0.929124\pi\)
\(128\) 15059.5 6453.47i 0.919158 0.393889i
\(129\) 0 0
\(130\) −35217.7 + 19544.0i −2.08388 + 1.15645i
\(131\) 6959.56i 0.405545i −0.979226 0.202773i \(-0.935005\pi\)
0.979226 0.202773i \(-0.0649952\pi\)
\(132\) 0 0
\(133\) −14504.2 −0.819959
\(134\) −1252.93 2257.74i −0.0697780 0.125737i
\(135\) 0 0
\(136\) 592.557 11634.1i 0.0320371 0.629008i
\(137\) −8488.85 −0.452280 −0.226140 0.974095i \(-0.572611\pi\)
−0.226140 + 0.974095i \(0.572611\pi\)
\(138\) 0 0
\(139\) 21343.3i 1.10467i −0.833622 0.552335i \(-0.813737\pi\)
0.833622 0.552335i \(-0.186263\pi\)
\(140\) 20824.5 + 12984.2i 1.06247 + 0.662460i
\(141\) 0 0
\(142\) −18570.8 33464.0i −0.920990 1.65959i
\(143\) 22258.7i 1.08850i
\(144\) 0 0
\(145\) 23749.2 1.12957
\(146\) −6642.17 + 3686.07i −0.311605 + 0.172925i
\(147\) 0 0
\(148\) 8536.92 13691.8i 0.389743 0.625082i
\(149\) −12733.6 −0.573558 −0.286779 0.957997i \(-0.592585\pi\)
−0.286779 + 0.957997i \(0.592585\pi\)
\(150\) 0 0
\(151\) 3535.51i 0.155059i 0.996990 + 0.0775296i \(0.0247032\pi\)
−0.996990 + 0.0775296i \(0.975297\pi\)
\(152\) 20083.7 + 1022.92i 0.869276 + 0.0442745i
\(153\) 0 0
\(154\) −11858.5 + 6580.88i −0.500021 + 0.277487i
\(155\) 37799.7i 1.57335i
\(156\) 0 0
\(157\) 29741.1 1.20658 0.603292 0.797520i \(-0.293855\pi\)
0.603292 + 0.797520i \(0.293855\pi\)
\(158\) −15168.8 27333.7i −0.607628 1.09492i
\(159\) 0 0
\(160\) −27919.6 19447.6i −1.09061 0.759673i
\(161\) −15506.3 −0.598216
\(162\) 0 0
\(163\) 5903.96i 0.222213i −0.993809 0.111106i \(-0.964561\pi\)
0.993809 0.111106i \(-0.0354394\pi\)
\(164\) 9439.81 15139.9i 0.350974 0.562904i
\(165\) 0 0
\(166\) −15806.3 28482.4i −0.573608 1.03362i
\(167\) 20566.0i 0.737425i −0.929544 0.368712i \(-0.879799\pi\)
0.929544 0.368712i \(-0.120201\pi\)
\(168\) 0 0
\(169\) 63271.8 2.21532
\(170\) −21153.3 + 11739.0i −0.731948 + 0.406195i
\(171\) 0 0
\(172\) −34209.2 21329.7i −1.15634 0.720987i
\(173\) 6109.97 0.204149 0.102074 0.994777i \(-0.467452\pi\)
0.102074 + 0.994777i \(0.467452\pi\)
\(174\) 0 0
\(175\) 22114.5i 0.722105i
\(176\) 16884.4 8276.09i 0.545079 0.267177i
\(177\) 0 0
\(178\) −26767.9 + 14854.9i −0.844840 + 0.468844i
\(179\) 11534.8i 0.360001i −0.983667 0.180001i \(-0.942390\pi\)
0.983667 0.180001i \(-0.0576099\pi\)
\(180\) 0 0
\(181\) −25544.2 −0.779713 −0.389857 0.920876i \(-0.627475\pi\)
−0.389857 + 0.920876i \(0.627475\pi\)
\(182\) −27150.8 48924.7i −0.819670 1.47702i
\(183\) 0 0
\(184\) 21471.3 + 1093.59i 0.634196 + 0.0323013i
\(185\) −33508.5 −0.979064
\(186\) 0 0
\(187\) 13369.6i 0.382326i
\(188\) −15371.4 9584.15i −0.434908 0.271168i
\(189\) 0 0
\(190\) −20264.8 36516.5i −0.561353 1.01154i
\(191\) 39067.8i 1.07091i 0.844564 + 0.535454i \(0.179859\pi\)
−0.844564 + 0.535454i \(0.820141\pi\)
\(192\) 0 0
\(193\) 27830.3 0.747143 0.373572 0.927601i \(-0.378133\pi\)
0.373572 + 0.927601i \(0.378133\pi\)
\(194\) −44535.8 + 24715.1i −1.18333 + 0.656689i
\(195\) 0 0
\(196\) 2287.63 3668.98i 0.0595489 0.0955065i
\(197\) −21103.0 −0.543765 −0.271883 0.962330i \(-0.587646\pi\)
−0.271883 + 0.962330i \(0.587646\pi\)
\(198\) 0 0
\(199\) 5447.97i 0.137572i −0.997631 0.0687858i \(-0.978087\pi\)
0.997631 0.0687858i \(-0.0219125\pi\)
\(200\) −1559.63 + 30621.5i −0.0389908 + 0.765537i
\(201\) 0 0
\(202\) 48078.4 26681.1i 1.17828 0.653885i
\(203\) 32992.6i 0.800615i
\(204\) 0 0
\(205\) −37052.4 −0.881675
\(206\) −25217.0 45440.1i −0.594236 1.07079i
\(207\) 0 0
\(208\) 34144.7 + 69659.8i 0.789217 + 1.61011i
\(209\) 23079.6 0.528367
\(210\) 0 0
\(211\) 69207.1i 1.55448i 0.629203 + 0.777241i \(0.283381\pi\)
−0.629203 + 0.777241i \(0.716619\pi\)
\(212\) −8954.47 + 14361.5i −0.199236 + 0.319542i
\(213\) 0 0
\(214\) 28904.3 + 52084.5i 0.631154 + 1.13732i
\(215\) 83721.5i 1.81117i
\(216\) 0 0
\(217\) 52511.7 1.11516
\(218\) −26367.9 + 14632.9i −0.554834 + 0.307905i
\(219\) 0 0
\(220\) −33136.6 20660.9i −0.684640 0.426877i
\(221\) 55158.9 1.12936
\(222\) 0 0
\(223\) 25327.7i 0.509315i 0.967031 + 0.254658i \(0.0819628\pi\)
−0.967031 + 0.254658i \(0.918037\pi\)
\(224\) 27016.8 38786.1i 0.538441 0.773001i
\(225\) 0 0
\(226\) 3470.52 1925.97i 0.0679482 0.0377079i
\(227\) 97207.4i 1.88646i −0.332139 0.943230i \(-0.607770\pi\)
0.332139 0.943230i \(-0.392230\pi\)
\(228\) 0 0
\(229\) −85892.8 −1.63789 −0.818947 0.573869i \(-0.805442\pi\)
−0.818947 + 0.573869i \(0.805442\pi\)
\(230\) −21664.9 39039.4i −0.409545 0.737985i
\(231\) 0 0
\(232\) 2326.82 45684.1i 0.0432301 0.848769i
\(233\) −12774.0 −0.235297 −0.117649 0.993055i \(-0.537536\pi\)
−0.117649 + 0.993055i \(0.537536\pi\)
\(234\) 0 0
\(235\) 37619.0i 0.681194i
\(236\) 13772.3 + 8587.10i 0.247276 + 0.154178i
\(237\) 0 0
\(238\) −16308.0 29386.3i −0.287903 0.518790i
\(239\) 105942.i 1.85469i −0.374202 0.927347i \(-0.622083\pi\)
0.374202 0.927347i \(-0.377917\pi\)
\(240\) 0 0
\(241\) −10179.5 −0.175263 −0.0876316 0.996153i \(-0.527930\pi\)
−0.0876316 + 0.996153i \(0.527930\pi\)
\(242\) −32337.7 + 17945.8i −0.552177 + 0.306431i
\(243\) 0 0
\(244\) 7285.38 11684.5i 0.122369 0.196260i
\(245\) −8979.23 −0.149592
\(246\) 0 0
\(247\) 95219.6i 1.56075i
\(248\) −72711.9 3703.41i −1.18223 0.0602141i
\(249\) 0 0
\(250\) −16958.0 + 9410.84i −0.271328 + 0.150573i
\(251\) 21848.1i 0.346790i −0.984852 0.173395i \(-0.944526\pi\)
0.984852 0.173395i \(-0.0554738\pi\)
\(252\) 0 0
\(253\) 24674.2 0.385479
\(254\) −13826.4 24914.7i −0.214310 0.386178i
\(255\) 0 0
\(256\) −40145.1 + 51801.0i −0.612565 + 0.790420i
\(257\) 55561.4 0.841216 0.420608 0.907243i \(-0.361817\pi\)
0.420608 + 0.907243i \(0.361817\pi\)
\(258\) 0 0
\(259\) 46550.3i 0.693941i
\(260\) 85240.6 136712.i 1.26096 2.02236i
\(261\) 0 0
\(262\) 13508.2 + 24341.3i 0.196786 + 0.354601i
\(263\) 25163.3i 0.363794i 0.983318 + 0.181897i \(0.0582238\pi\)
−0.983318 + 0.181897i \(0.941776\pi\)
\(264\) 0 0
\(265\) 35147.4 0.500497
\(266\) 50729.0 28152.1i 0.716957 0.397875i
\(267\) 0 0
\(268\) 8764.34 + 5464.62i 0.122025 + 0.0760835i
\(269\) 54154.0 0.748386 0.374193 0.927351i \(-0.377920\pi\)
0.374193 + 0.927351i \(0.377920\pi\)
\(270\) 0 0
\(271\) 94942.5i 1.29277i −0.763011 0.646386i \(-0.776280\pi\)
0.763011 0.646386i \(-0.223720\pi\)
\(272\) 20508.8 + 41840.8i 0.277206 + 0.565539i
\(273\) 0 0
\(274\) 29690.0 16476.5i 0.395466 0.219464i
\(275\) 35189.2i 0.465312i
\(276\) 0 0
\(277\) 108039. 1.40807 0.704033 0.710167i \(-0.251381\pi\)
0.704033 + 0.710167i \(0.251381\pi\)
\(278\) 41426.4 + 74648.9i 0.536029 + 0.965904i
\(279\) 0 0
\(280\) −98036.0 4993.24i −1.25046 0.0636893i
\(281\) −68926.1 −0.872913 −0.436456 0.899725i \(-0.643767\pi\)
−0.436456 + 0.899725i \(0.643767\pi\)
\(282\) 0 0
\(283\) 45211.4i 0.564514i −0.959339 0.282257i \(-0.908917\pi\)
0.959339 0.282257i \(-0.0910831\pi\)
\(284\) 129904. + 80996.0i 1.61059 + 1.00422i
\(285\) 0 0
\(286\) 43203.1 + 77850.4i 0.528181 + 0.951763i
\(287\) 51473.5i 0.624914i
\(288\) 0 0
\(289\) −50390.1 −0.603323
\(290\) −83063.4 + 46096.0i −0.987674 + 0.548110i
\(291\) 0 0
\(292\) 16076.7 25784.3i 0.188552 0.302405i
\(293\) −71707.2 −0.835271 −0.417636 0.908615i \(-0.637141\pi\)
−0.417636 + 0.908615i \(0.637141\pi\)
\(294\) 0 0
\(295\) 33705.4i 0.387307i
\(296\) −3282.98 + 64457.2i −0.0374701 + 0.735679i
\(297\) 0 0
\(298\) 44536.0 24715.3i 0.501509 0.278313i
\(299\) 101798.i 1.13867i
\(300\) 0 0
\(301\) −116307. −1.28372
\(302\) −6862.25 12365.5i −0.0752407 0.135581i
\(303\) 0 0
\(304\) −72228.9 + 35403.9i −0.781563 + 0.383093i
\(305\) −28596.0 −0.307401
\(306\) 0 0
\(307\) 95866.9i 1.01717i 0.861013 + 0.508583i \(0.169830\pi\)
−0.861013 + 0.508583i \(0.830170\pi\)
\(308\) 28702.3 46033.6i 0.302562 0.485259i
\(309\) 0 0
\(310\) 73367.4 + 132205.i 0.763449 + 1.37571i
\(311\) 24068.5i 0.248845i 0.992229 + 0.124423i \(0.0397078\pi\)
−0.992229 + 0.124423i \(0.960292\pi\)
\(312\) 0 0
\(313\) −99309.0 −1.01368 −0.506839 0.862041i \(-0.669186\pi\)
−0.506839 + 0.862041i \(0.669186\pi\)
\(314\) −104020. + 57726.1i −1.05502 + 0.585481i
\(315\) 0 0
\(316\) 106107. + 66158.2i 1.06260 + 0.662536i
\(317\) 59441.0 0.591517 0.295759 0.955263i \(-0.404428\pi\)
0.295759 + 0.955263i \(0.404428\pi\)
\(318\) 0 0
\(319\) 52498.7i 0.515902i
\(320\) 135396. + 13828.1i 1.32223 + 0.135040i
\(321\) 0 0
\(322\) 54233.9 30097.1i 0.523069 0.290277i
\(323\) 57193.1i 0.548200i
\(324\) 0 0
\(325\) −145180. −1.37449
\(326\) 11459.3 + 20649.3i 0.107826 + 0.194299i
\(327\) 0 0
\(328\) −3630.19 + 71274.3i −0.0337429 + 0.662499i
\(329\) −52260.6 −0.482817
\(330\) 0 0
\(331\) 92205.2i 0.841588i 0.907156 + 0.420794i \(0.138248\pi\)
−0.907156 + 0.420794i \(0.861752\pi\)
\(332\) 110566. + 68938.8i 1.00310 + 0.625442i
\(333\) 0 0
\(334\) 39917.7 + 71930.3i 0.357827 + 0.644791i
\(335\) 21449.3i 0.191128i
\(336\) 0 0
\(337\) 45908.3 0.404233 0.202117 0.979361i \(-0.435218\pi\)
0.202117 + 0.979361i \(0.435218\pi\)
\(338\) −221295. + 122808.i −1.93704 + 1.07496i
\(339\) 0 0
\(340\) 51199.3 82115.2i 0.442901 0.710339i
\(341\) −83558.1 −0.718588
\(342\) 0 0
\(343\) 123305.i 1.04807i
\(344\) 161048. + 8202.58i 1.36093 + 0.0693161i
\(345\) 0 0
\(346\) −21369.8 + 11859.2i −0.178504 + 0.0990609i
\(347\) 151976.i 1.26216i 0.775717 + 0.631081i \(0.217389\pi\)
−0.775717 + 0.631081i \(0.782611\pi\)
\(348\) 0 0
\(349\) −187291. −1.53768 −0.768841 0.639440i \(-0.779166\pi\)
−0.768841 + 0.639440i \(0.779166\pi\)
\(350\) 42923.2 + 77346.0i 0.350393 + 0.631396i
\(351\) 0 0
\(352\) −42990.0 + 61717.6i −0.346962 + 0.498108i
\(353\) 45415.6 0.364465 0.182232 0.983255i \(-0.441668\pi\)
0.182232 + 0.983255i \(0.441668\pi\)
\(354\) 0 0
\(355\) 317919.i 2.52267i
\(356\) 64788.9 103911.i 0.511212 0.819898i
\(357\) 0 0
\(358\) 22388.5 + 40343.3i 0.174686 + 0.314778i
\(359\) 71504.2i 0.554808i 0.960753 + 0.277404i \(0.0894740\pi\)
−0.960753 + 0.277404i \(0.910526\pi\)
\(360\) 0 0
\(361\) 31589.8 0.242400
\(362\) 89341.5 49580.1i 0.681767 0.378347i
\(363\) 0 0
\(364\) 189921. + 118417.i 1.43341 + 0.893740i
\(365\) −63102.9 −0.473656
\(366\) 0 0
\(367\) 66286.7i 0.492146i 0.969251 + 0.246073i \(0.0791404\pi\)
−0.969251 + 0.246073i \(0.920860\pi\)
\(368\) −77219.2 + 37850.0i −0.570203 + 0.279492i
\(369\) 0 0
\(370\) 117197. 65038.4i 0.856076 0.475080i
\(371\) 48827.1i 0.354742i
\(372\) 0 0
\(373\) 143569. 1.03191 0.515955 0.856616i \(-0.327437\pi\)
0.515955 + 0.856616i \(0.327437\pi\)
\(374\) 25949.7 + 46760.4i 0.185519 + 0.334299i
\(375\) 0 0
\(376\) 72364.2 + 3685.70i 0.511856 + 0.0260702i
\(377\) 216594. 1.52393
\(378\) 0 0
\(379\) 183178.i 1.27525i 0.770348 + 0.637624i \(0.220083\pi\)
−0.770348 + 0.637624i \(0.779917\pi\)
\(380\) 141754. + 88384.3i 0.981673 + 0.612079i
\(381\) 0 0
\(382\) −75828.8 136641.i −0.519646 0.936382i
\(383\) 17523.6i 0.119461i 0.998215 + 0.0597303i \(0.0190241\pi\)
−0.998215 + 0.0597303i \(0.980976\pi\)
\(384\) 0 0
\(385\) −112660. −0.760060
\(386\) −97337.4 + 54017.4i −0.653288 + 0.362543i
\(387\) 0 0
\(388\) 107794. 172884.i 0.716031 1.14839i
\(389\) 76861.5 0.507937 0.253968 0.967212i \(-0.418264\pi\)
0.253968 + 0.967212i \(0.418264\pi\)
\(390\) 0 0
\(391\) 61144.6i 0.399949i
\(392\) −879.737 + 17272.5i −0.00572507 + 0.112405i
\(393\) 0 0
\(394\) 73808.3 40959.9i 0.475459 0.263856i
\(395\) 259679.i 1.66434i
\(396\) 0 0
\(397\) −73295.7 −0.465047 −0.232524 0.972591i \(-0.574698\pi\)
−0.232524 + 0.972591i \(0.574698\pi\)
\(398\) 10574.3 + 19054.4i 0.0667550 + 0.120290i
\(399\) 0 0
\(400\) −53980.0 110127.i −0.337375 0.688291i
\(401\) 284548. 1.76957 0.884784 0.466002i \(-0.154306\pi\)
0.884784 + 0.466002i \(0.154306\pi\)
\(402\) 0 0
\(403\) 344736.i 2.12264i
\(404\) −116369. + 186636.i −0.712973 + 1.14349i
\(405\) 0 0
\(406\) −64037.0 115392.i −0.388489 0.700044i
\(407\) 74072.1i 0.447163i
\(408\) 0 0
\(409\) −113154. −0.676430 −0.338215 0.941069i \(-0.609823\pi\)
−0.338215 + 0.941069i \(0.609823\pi\)
\(410\) 129592. 71917.0i 0.770921 0.427823i
\(411\) 0 0
\(412\) 176394. + 109983.i 1.03918 + 0.647934i
\(413\) 46823.9 0.274516
\(414\) 0 0
\(415\) 270593.i 1.57116i
\(416\) −254628. 177364.i −1.47136 1.02489i
\(417\) 0 0
\(418\) −80721.5 + 44796.4i −0.461994 + 0.256384i
\(419\) 274026.i 1.56086i 0.625242 + 0.780431i \(0.285000\pi\)
−0.625242 + 0.780431i \(0.715000\pi\)
\(420\) 0 0
\(421\) 12483.8 0.0704339 0.0352170 0.999380i \(-0.488788\pi\)
0.0352170 + 0.999380i \(0.488788\pi\)
\(422\) −134328. 242054.i −0.754294 1.35921i
\(423\) 0 0
\(424\) 3443.55 67609.9i 0.0191547 0.376078i
\(425\) −87201.7 −0.482778
\(426\) 0 0
\(427\) 39725.8i 0.217880i
\(428\) −202187. 126065.i −1.10374 0.688188i
\(429\) 0 0
\(430\) −162500. 292818.i −0.878852 1.58366i
\(431\) 119855.i 0.645211i 0.946533 + 0.322606i \(0.104559\pi\)
−0.946533 + 0.322606i \(0.895441\pi\)
\(432\) 0 0
\(433\) −282465. −1.50657 −0.753284 0.657696i \(-0.771531\pi\)
−0.753284 + 0.657696i \(0.771531\pi\)
\(434\) −183661. + 101923.i −0.975074 + 0.541117i
\(435\) 0 0
\(436\) 63820.8 102358.i 0.335729 0.538454i
\(437\) −105553. −0.552721
\(438\) 0 0
\(439\) 171426.i 0.889501i 0.895654 + 0.444751i \(0.146708\pi\)
−0.895654 + 0.444751i \(0.853292\pi\)
\(440\) 155998. + 7945.39i 0.805774 + 0.0410402i
\(441\) 0 0
\(442\) −192920. + 107061.i −0.987488 + 0.548007i
\(443\) 83009.3i 0.422980i 0.977380 + 0.211490i \(0.0678315\pi\)
−0.977380 + 0.211490i \(0.932168\pi\)
\(444\) 0 0
\(445\) −254304. −1.28420
\(446\) −49160.0 88584.5i −0.247139 0.445336i
\(447\) 0 0
\(448\) −19210.1 + 188094.i −0.0957135 + 0.937171i
\(449\) 252767. 1.25380 0.626898 0.779101i \(-0.284324\pi\)
0.626898 + 0.779101i \(0.284324\pi\)
\(450\) 0 0
\(451\) 81906.2i 0.402683i
\(452\) −8400.04 + 13472.3i −0.0411154 + 0.0659422i
\(453\) 0 0
\(454\) 188675. + 339986.i 0.915383 + 1.64949i
\(455\) 464801.i 2.24515i
\(456\) 0 0
\(457\) −18979.6 −0.0908771 −0.0454386 0.998967i \(-0.514469\pi\)
−0.0454386 + 0.998967i \(0.514469\pi\)
\(458\) 300412. 166714.i 1.43214 0.794769i
\(459\) 0 0
\(460\) 151547. + 94490.7i 0.716197 + 0.446554i
\(461\) −194152. −0.913565 −0.456783 0.889578i \(-0.650998\pi\)
−0.456783 + 0.889578i \(0.650998\pi\)
\(462\) 0 0
\(463\) 99567.3i 0.464467i −0.972660 0.232234i \(-0.925397\pi\)
0.972660 0.232234i \(-0.0746034\pi\)
\(464\) 80532.7 + 164298.i 0.374056 + 0.763125i
\(465\) 0 0
\(466\) 44677.6 24793.8i 0.205740 0.114175i
\(467\) 126990.i 0.582287i 0.956679 + 0.291144i \(0.0940358\pi\)
−0.956679 + 0.291144i \(0.905964\pi\)
\(468\) 0 0
\(469\) 29797.6 0.135468
\(470\) −73016.7 131573.i −0.330542 0.595624i
\(471\) 0 0
\(472\) −64836.1 3302.27i −0.291027 0.0148228i
\(473\) 185071. 0.827209
\(474\) 0 0
\(475\) 150534.i 0.667189i
\(476\) 114075. + 71126.6i 0.503474 + 0.313919i
\(477\) 0 0
\(478\) 205628. + 370535.i 0.899969 + 1.62171i
\(479\) 55931.1i 0.243771i −0.992544 0.121886i \(-0.961106\pi\)
0.992544 0.121886i \(-0.0388941\pi\)
\(480\) 0 0
\(481\) −305600. −1.32088
\(482\) 35602.9 19757.9i 0.153247 0.0850445i
\(483\) 0 0
\(484\) 78270.0 125532.i 0.334122 0.535875i
\(485\) −423105. −1.79872
\(486\) 0 0
\(487\) 274913.i 1.15914i −0.814921 0.579572i \(-0.803220\pi\)
0.814921 0.579572i \(-0.196780\pi\)
\(488\) −2801.68 + 55007.6i −0.0117647 + 0.230985i
\(489\) 0 0
\(490\) 31405.1 17428.3i 0.130800 0.0725876i
\(491\) 32375.0i 0.134291i −0.997743 0.0671455i \(-0.978611\pi\)
0.997743 0.0671455i \(-0.0213892\pi\)
\(492\) 0 0
\(493\) 130096. 0.535267
\(494\) −184817. 333033.i −0.757334 1.36469i
\(495\) 0 0
\(496\) 261500. 128178.i 1.06294 0.521013i
\(497\) 441656. 1.78802
\(498\) 0 0
\(499\) 290345.i 1.16604i 0.812458 + 0.583019i \(0.198129\pi\)
−0.812458 + 0.583019i \(0.801871\pi\)
\(500\) 41045.0 65829.4i 0.164180 0.263317i
\(501\) 0 0
\(502\) 42406.2 + 76414.4i 0.168276 + 0.303227i
\(503\) 9486.90i 0.0374963i −0.999824 0.0187481i \(-0.994032\pi\)
0.999824 0.0187481i \(-0.00596807\pi\)
\(504\) 0 0
\(505\) 456761. 1.79104
\(506\) −86298.5 + 47891.4i −0.337056 + 0.187049i
\(507\) 0 0
\(508\) 96716.5 + 60303.4i 0.374777 + 0.233676i
\(509\) −292751. −1.12996 −0.564980 0.825104i \(-0.691116\pi\)
−0.564980 + 0.825104i \(0.691116\pi\)
\(510\) 0 0
\(511\) 87663.1i 0.335718i
\(512\) 39865.2 259095.i 0.152074 0.988369i
\(513\) 0 0
\(514\) −194328. + 107842.i −0.735544 + 0.408190i
\(515\) 431697.i 1.62766i
\(516\) 0 0
\(517\) 83158.6 0.311119
\(518\) 90351.9 + 162811.i 0.336727 + 0.606769i
\(519\) 0 0
\(520\) −32780.3 + 643601.i −0.121229 + 2.38018i
\(521\) −344253. −1.26824 −0.634120 0.773234i \(-0.718638\pi\)
−0.634120 + 0.773234i \(0.718638\pi\)
\(522\) 0 0
\(523\) 79326.1i 0.290010i −0.989431 0.145005i \(-0.953680\pi\)
0.989431 0.145005i \(-0.0463198\pi\)
\(524\) −94490.5 58915.4i −0.344132 0.214569i
\(525\) 0 0
\(526\) −48840.8 88009.3i −0.176527 0.318095i
\(527\) 207064.i 0.745561i
\(528\) 0 0
\(529\) 166996. 0.596753
\(530\) −122929. + 68219.5i −0.437625 + 0.242860i
\(531\) 0 0
\(532\) −122784. + 196925.i −0.433830 + 0.695790i
\(533\) −337921. −1.18949
\(534\) 0 0
\(535\) 494821.i 1.72878i
\(536\) −41260.1 2101.49i −0.143615 0.00731471i
\(537\) 0 0
\(538\) −189405. + 105110.i −0.654375 + 0.363146i
\(539\) 19849.0i 0.0683223i
\(540\) 0 0
\(541\) 167330. 0.571715 0.285857 0.958272i \(-0.407722\pi\)
0.285857 + 0.958272i \(0.407722\pi\)
\(542\) 184279. + 332064.i 0.627303 + 1.13038i
\(543\) 0 0
\(544\) −152941. 106533.i −0.516805 0.359986i
\(545\) −250504. −0.843378
\(546\) 0 0
\(547\) 285069.i 0.952743i 0.879244 + 0.476372i \(0.158048\pi\)
−0.879244 + 0.476372i \(0.841952\pi\)
\(548\) −71861.5 + 115254.i −0.239296 + 0.383790i
\(549\) 0 0
\(550\) −68300.6 123075.i −0.225787 0.406860i
\(551\) 224582.i 0.739728i
\(552\) 0 0
\(553\) 360749. 1.17965
\(554\) −377871. + 209700.i −1.23119 + 0.683248i
\(555\) 0 0
\(556\) −289780. 180680.i −0.937387 0.584467i
\(557\) 51271.9 0.165260 0.0826302 0.996580i \(-0.473668\pi\)
0.0826302 + 0.996580i \(0.473668\pi\)
\(558\) 0 0
\(559\) 763547.i 2.44350i
\(560\) 352575. 172819.i 1.12428 0.551082i
\(561\) 0 0
\(562\) 241071. 133782.i 0.763259 0.423571i
\(563\) 2873.82i 0.00906656i −0.999990 0.00453328i \(-0.998557\pi\)
0.999990 0.00453328i \(-0.00144299\pi\)
\(564\) 0 0
\(565\) 32971.2 0.103285
\(566\) 87753.2 + 158128.i 0.273924 + 0.493601i
\(567\) 0 0
\(568\) −611552. 31148.0i −1.89556 0.0965458i
\(569\) −113753. −0.351350 −0.175675 0.984448i \(-0.556211\pi\)
−0.175675 + 0.984448i \(0.556211\pi\)
\(570\) 0 0
\(571\) 31475.3i 0.0965379i −0.998834 0.0482689i \(-0.984630\pi\)
0.998834 0.0482689i \(-0.0153705\pi\)
\(572\) −302208. 188429.i −0.923664 0.575910i
\(573\) 0 0
\(574\) 99907.7 + 180030.i 0.303232 + 0.546413i
\(575\) 160935.i 0.486760i
\(576\) 0 0
\(577\) −654654. −1.96635 −0.983174 0.182671i \(-0.941526\pi\)
−0.983174 + 0.182671i \(0.941526\pi\)
\(578\) 176241. 97804.9i 0.527534 0.292755i
\(579\) 0 0
\(580\) 201046. 322444.i 0.597640 0.958515i
\(581\) 375910. 1.11361
\(582\) 0 0
\(583\) 77695.1i 0.228590i
\(584\) −6182.48 + 121385.i −0.0181275 + 0.355910i
\(585\) 0 0
\(586\) 250798. 139180.i 0.730346 0.405306i
\(587\) 643491.i 1.86753i −0.357893 0.933763i \(-0.616505\pi\)
0.357893 0.933763i \(-0.383495\pi\)
\(588\) 0 0
\(589\) 357450. 1.03035
\(590\) 65420.6 + 117886.i 0.187936 + 0.338654i
\(591\) 0 0
\(592\) −113626. 231813.i −0.324216 0.661446i
\(593\) −183090. −0.520661 −0.260330 0.965520i \(-0.583831\pi\)
−0.260330 + 0.965520i \(0.583831\pi\)
\(594\) 0 0
\(595\) 279180.i 0.788589i
\(596\) −107795. + 172885.i −0.303462 + 0.486703i
\(597\) 0 0
\(598\) −197586. 356042.i −0.552527 0.995633i
\(599\) 27833.2i 0.0775728i 0.999248 + 0.0387864i \(0.0123492\pi\)
−0.999248 + 0.0387864i \(0.987651\pi\)
\(600\) 0 0
\(601\) −271528. −0.751736 −0.375868 0.926673i \(-0.622655\pi\)
−0.375868 + 0.926673i \(0.622655\pi\)
\(602\) 406786. 225746.i 1.12247 0.622912i
\(603\) 0 0
\(604\) 48001.8 + 29929.5i 0.131578 + 0.0820399i
\(605\) −307219. −0.839339
\(606\) 0 0
\(607\) 100450.i 0.272628i 0.990666 + 0.136314i \(0.0435256\pi\)
−0.990666 + 0.136314i \(0.956474\pi\)
\(608\) 183905. 264019.i 0.497493 0.714214i
\(609\) 0 0
\(610\) 100015. 55503.6i 0.268786 0.149163i
\(611\) 343088.i 0.919015i
\(612\) 0 0
\(613\) 458408. 1.21992 0.609960 0.792432i \(-0.291185\pi\)
0.609960 + 0.792432i \(0.291185\pi\)
\(614\) −186073. 335297.i −0.493568 0.889391i
\(615\) 0 0
\(616\) −11037.8 + 216714.i −0.0290885 + 0.571116i
\(617\) −474635. −1.24678 −0.623389 0.781912i \(-0.714245\pi\)
−0.623389 + 0.781912i \(0.714245\pi\)
\(618\) 0 0
\(619\) 6598.31i 0.0172207i 0.999963 + 0.00861036i \(0.00274080\pi\)
−0.999963 + 0.00861036i \(0.997259\pi\)
\(620\) −513209. 319989.i −1.33509 0.832438i
\(621\) 0 0
\(622\) −46715.9 84180.4i −0.120749 0.217586i
\(623\) 353282.i 0.910218i
\(624\) 0 0
\(625\) −460532. −1.17896
\(626\) 347336. 192754.i 0.886342 0.491876i
\(627\) 0 0
\(628\) 251770. 403797.i 0.638389 1.02387i
\(629\) −183557. −0.463948
\(630\) 0 0
\(631\) 102946.i 0.258553i −0.991609 0.129277i \(-0.958734\pi\)
0.991609 0.129277i \(-0.0412655\pi\)
\(632\) −499521. 25442.0i −1.25060 0.0636966i
\(633\) 0 0
\(634\) −207897. + 115372.i −0.517212 + 0.287027i
\(635\) 236698.i 0.587012i
\(636\) 0 0
\(637\) −81891.3 −0.201818
\(638\) 101898. + 183616.i 0.250336 + 0.451096i
\(639\) 0 0
\(640\) −500392. + 214434.i −1.22166 + 0.523521i
\(641\) 404806. 0.985215 0.492607 0.870252i \(-0.336044\pi\)
0.492607 + 0.870252i \(0.336044\pi\)
\(642\) 0 0
\(643\) 492031.i 1.19006i −0.803702 0.595032i \(-0.797139\pi\)
0.803702 0.595032i \(-0.202861\pi\)
\(644\) −131267. + 210531.i −0.316508 + 0.507626i
\(645\) 0 0
\(646\) −111009. 200035.i −0.266008 0.479336i
\(647\) 306912.i 0.733171i −0.930384 0.366586i \(-0.880527\pi\)
0.930384 0.366586i \(-0.119473\pi\)
\(648\) 0 0
\(649\) −74507.5 −0.176893
\(650\) 507772. 281788.i 1.20183 0.666954i
\(651\) 0 0
\(652\) −80158.6 49979.4i −0.188562 0.117570i
\(653\) 195324. 0.458066 0.229033 0.973419i \(-0.426444\pi\)
0.229033 + 0.973419i \(0.426444\pi\)
\(654\) 0 0
\(655\) 231250.i 0.539013i
\(656\) −125644. 256330.i −0.291966 0.595651i
\(657\) 0 0
\(658\) 182783. 101435.i 0.422166 0.234281i
\(659\) 783894.i 1.80504i 0.430650 + 0.902519i \(0.358284\pi\)
−0.430650 + 0.902519i \(0.641716\pi\)
\(660\) 0 0
\(661\) 742150. 1.69859 0.849295 0.527918i \(-0.177027\pi\)
0.849295 + 0.527918i \(0.177027\pi\)
\(662\) −178966. 322490.i −0.408371 0.735869i
\(663\) 0 0
\(664\) −520515. 26511.2i −1.18059 0.0601304i
\(665\) 481943. 1.08981
\(666\) 0 0
\(667\) 240099.i 0.539682i
\(668\) −279227. 174100.i −0.625754 0.390162i
\(669\) 0 0
\(670\) 41632.1 + 75019.6i 0.0927426 + 0.167119i
\(671\) 63212.9i 0.140398i
\(672\) 0 0
\(673\) 423202. 0.934366 0.467183 0.884161i \(-0.345269\pi\)
0.467183 + 0.884161i \(0.345269\pi\)
\(674\) −160566. + 89106.0i −0.353454 + 0.196149i
\(675\) 0 0
\(676\) 535621. 859046.i 1.17210 1.87985i
\(677\) 308244. 0.672538 0.336269 0.941766i \(-0.390835\pi\)
0.336269 + 0.941766i \(0.390835\pi\)
\(678\) 0 0
\(679\) 587781.i 1.27490i
\(680\) −19689.3 + 386576.i −0.0425807 + 0.836020i
\(681\) 0 0
\(682\) 292247. 162182.i 0.628320 0.348686i
\(683\) 760287.i 1.62981i −0.579597 0.814903i \(-0.696790\pi\)
0.579597 0.814903i \(-0.303210\pi\)
\(684\) 0 0
\(685\) 282065. 0.601130
\(686\) 239329. + 431262.i 0.508565 + 0.916416i
\(687\) 0 0
\(688\) −579189. + 283897.i −1.22361 + 0.599769i
\(689\) 320547. 0.675232
\(690\) 0 0
\(691\) 361693.i 0.757501i 0.925499 + 0.378751i \(0.123646\pi\)
−0.925499 + 0.378751i \(0.876354\pi\)
\(692\) 51723.4 82955.6i 0.108013 0.173234i
\(693\) 0 0
\(694\) −294978. 531539.i −0.612450 1.10361i
\(695\) 709190.i 1.46823i
\(696\) 0 0
\(697\) −202970. −0.417798
\(698\) 655056. 363524.i 1.34452 0.746143i
\(699\) 0 0
\(700\) −300250. 187208.i −0.612755 0.382057i
\(701\) 878492. 1.78773 0.893864 0.448337i \(-0.147984\pi\)
0.893864 + 0.448337i \(0.147984\pi\)
\(702\) 0 0
\(703\) 316870.i 0.641167i
\(704\) 30567.7 299301.i 0.0616761 0.603896i
\(705\) 0 0
\(706\) −158842. + 88149.6i −0.318681 + 0.176852i
\(707\) 634537.i 1.26946i
\(708\) 0 0
\(709\) 862381. 1.71556 0.857781 0.514015i \(-0.171842\pi\)
0.857781 + 0.514015i \(0.171842\pi\)
\(710\) 617066. + 1.11193e6i 1.22409 + 2.20577i
\(711\) 0 0
\(712\) −24915.4 + 489183.i −0.0491482 + 0.964964i
\(713\) 382146. 0.751710
\(714\) 0 0
\(715\) 739605.i 1.44673i
\(716\) −156609. 97646.6i −0.305485 0.190472i
\(717\) 0 0
\(718\) −138786. 250088.i −0.269214 0.485114i
\(719\) 424008.i 0.820193i 0.912042 + 0.410097i \(0.134505\pi\)
−0.912042 + 0.410097i \(0.865495\pi\)
\(720\) 0 0
\(721\) 599717. 1.15365
\(722\) −110486. + 61314.3i −0.211950 + 0.117622i
\(723\) 0 0
\(724\) −216242. + 346816.i −0.412536 + 0.661639i
\(725\) −342418. −0.651449
\(726\) 0 0
\(727\) 91032.9i 0.172238i −0.996285 0.0861191i \(-0.972553\pi\)
0.996285 0.0861191i \(-0.0274466\pi\)
\(728\) −894096. 45538.7i −1.68702 0.0859247i
\(729\) 0 0
\(730\) 220704. 122480.i 0.414157 0.229836i
\(731\) 458620.i 0.858259i
\(732\) 0 0
\(733\) −13278.0 −0.0247129 −0.0123565 0.999924i \(-0.503933\pi\)
−0.0123565 + 0.999924i \(0.503933\pi\)
\(734\) −128659. 231840.i −0.238808 0.430324i
\(735\) 0 0
\(736\) 196611. 282260.i 0.362955 0.521068i
\(737\) −47414.8 −0.0872929
\(738\) 0 0
\(739\) 622195.i 1.13930i 0.821888 + 0.569650i \(0.192921\pi\)
−0.821888 + 0.569650i \(0.807079\pi\)
\(740\) −283662. + 454947.i −0.518010 + 0.830802i
\(741\) 0 0
\(742\) −94771.1 170774.i −0.172135 0.310180i
\(743\) 700428.i 1.26878i 0.773014 + 0.634389i \(0.218748\pi\)
−0.773014 + 0.634389i \(0.781252\pi\)
\(744\) 0 0
\(745\) 423107. 0.762321
\(746\) −502135. + 278660.i −0.902283 + 0.500722i
\(747\) 0 0
\(748\) −181520. 113179.i −0.324430 0.202284i
\(749\) −687409. −1.22533
\(750\) 0 0
\(751\) 85133.1i 0.150945i −0.997148 0.0754725i \(-0.975953\pi\)
0.997148 0.0754725i \(-0.0240465\pi\)
\(752\) −260250. + 127565.i −0.460208 + 0.225577i
\(753\) 0 0
\(754\) −757544. + 420399.i −1.33249 + 0.739468i
\(755\) 117477.i 0.206091i
\(756\) 0 0
\(757\) 319528. 0.557592 0.278796 0.960350i \(-0.410065\pi\)
0.278796 + 0.960350i \(0.410065\pi\)
\(758\) −355540. 640669.i −0.618799 1.11505i
\(759\) 0 0
\(760\) −667337. 33989.3i −1.15536 0.0588457i
\(761\) 753777. 1.30159 0.650794 0.759255i \(-0.274436\pi\)
0.650794 + 0.759255i \(0.274436\pi\)
\(762\) 0 0
\(763\) 348003.i 0.597770i
\(764\) 530426. + 330724.i 0.908737 + 0.566604i
\(765\) 0 0
\(766\) −34012.4 61289.2i −0.0579669 0.104454i
\(767\) 307396.i 0.522525i
\(768\) 0 0
\(769\) 850312. 1.43789 0.718945 0.695067i \(-0.244625\pi\)
0.718945 + 0.695067i \(0.244625\pi\)
\(770\) 394031. 218668.i 0.664582 0.368810i
\(771\) 0 0
\(772\) 235595. 377855.i 0.395304 0.634001i
\(773\) 13034.7 0.0218143 0.0109071 0.999941i \(-0.496528\pi\)
0.0109071 + 0.999941i \(0.496528\pi\)
\(774\) 0 0
\(775\) 545000.i 0.907388i
\(776\) −41453.6 + 813889.i −0.0688396 + 1.35158i
\(777\) 0 0
\(778\) −268825. + 149185.i −0.444131 + 0.246471i
\(779\) 350383.i 0.577389i
\(780\) 0 0
\(781\) −702776. −1.15217
\(782\) −118679. 213855.i −0.194071 0.349708i
\(783\) 0 0
\(784\) −30448.3 62118.7i −0.0495372 0.101063i
\(785\) −988229. −1.60368
\(786\) 0 0
\(787\)