Properties

Label 864.2.w.a.107.9
Level $864$
Weight $2$
Character 864.107
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 107.9
Character \(\chi\) \(=\) 864.107
Dual form 864.2.w.a.323.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.948429 - 1.04904i) q^{2} +(-0.200965 + 1.98988i) q^{4} +(1.78263 + 0.738390i) q^{5} +(-0.622002 + 0.622002i) q^{7} +(2.27806 - 1.67644i) q^{8} +O(q^{10})\) \(q+(-0.948429 - 1.04904i) q^{2} +(-0.200965 + 1.98988i) q^{4} +(1.78263 + 0.738390i) q^{5} +(-0.622002 + 0.622002i) q^{7} +(2.27806 - 1.67644i) q^{8} +(-0.916100 - 2.57036i) q^{10} +(0.156498 + 0.0648236i) q^{11} +(1.19856 + 2.89359i) q^{13} +(1.24243 + 0.0625795i) q^{14} +(-3.91923 - 0.799791i) q^{16} +4.81317 q^{17} +(-3.67470 + 1.52211i) q^{19} +(-1.82755 + 3.39883i) q^{20} +(-0.0804248 - 0.225653i) q^{22} +(1.56750 - 1.56750i) q^{23} +(-0.902976 - 0.902976i) q^{25} +(1.89874 - 4.00171i) q^{26} +(-1.11271 - 1.36271i) q^{28} +(1.08392 + 2.61682i) q^{29} +2.74627i q^{31} +(2.87810 + 4.86997i) q^{32} +(-4.56495 - 5.04920i) q^{34} +(-1.56808 + 0.649520i) q^{35} +(-1.96490 + 4.74369i) q^{37} +(5.08195 + 2.41129i) q^{38} +(5.29881 - 1.30637i) q^{40} +(3.95321 + 3.95321i) q^{41} +(-0.627273 + 1.51437i) q^{43} +(-0.160442 + 0.298385i) q^{44} +(-3.13103 - 0.157706i) q^{46} +9.33089i q^{47} +6.22623i q^{49} +(-0.0908483 + 1.80367i) q^{50} +(-5.99876 + 1.80349i) q^{52} +(0.182908 - 0.441579i) q^{53} +(0.231113 + 0.231113i) q^{55} +(-0.374210 + 2.45971i) q^{56} +(1.71712 - 3.61895i) q^{58} +(3.02418 - 7.30102i) q^{59} +(11.6637 - 4.83126i) q^{61} +(2.88094 - 2.60464i) q^{62} +(2.37911 - 7.63805i) q^{64} +6.04322i q^{65} +(4.45039 + 10.7442i) q^{67} +(-0.967277 + 9.57761i) q^{68} +(2.16859 + 1.02895i) q^{70} +(-6.22714 - 6.22714i) q^{71} +(-0.573022 + 0.573022i) q^{73} +(6.83988 - 2.43779i) q^{74} +(-2.29033 - 7.61810i) q^{76} +(-0.137662 + 0.0570216i) q^{77} +12.6432 q^{79} +(-6.39598 - 4.31965i) q^{80} +(0.397731 - 7.89640i) q^{82} +(-4.21199 - 10.1686i) q^{83} +(8.58010 + 3.55400i) q^{85} +(2.18356 - 0.778239i) q^{86} +(0.465184 - 0.114687i) q^{88} +(6.68154 - 6.68154i) q^{89} +(-2.54533 - 1.05431i) q^{91} +(2.80412 + 3.43415i) q^{92} +(9.78847 - 8.84969i) q^{94} -7.67456 q^{95} -5.92342 q^{97} +(6.53155 - 5.90513i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.948429 1.04904i −0.670641 0.741782i
\(3\) 0 0
\(4\) −0.200965 + 1.98988i −0.100482 + 0.994939i
\(5\) 1.78263 + 0.738390i 0.797217 + 0.330218i 0.743841 0.668356i \(-0.233002\pi\)
0.0533761 + 0.998574i \(0.483002\pi\)
\(6\) 0 0
\(7\) −0.622002 + 0.622002i −0.235095 + 0.235095i −0.814815 0.579721i \(-0.803162\pi\)
0.579721 + 0.814815i \(0.303162\pi\)
\(8\) 2.27806 1.67644i 0.805416 0.592710i
\(9\) 0 0
\(10\) −0.916100 2.57036i −0.289696 0.812820i
\(11\) 0.156498 + 0.0648236i 0.0471859 + 0.0195450i 0.406152 0.913806i \(-0.366870\pi\)
−0.358966 + 0.933351i \(0.616870\pi\)
\(12\) 0 0
\(13\) 1.19856 + 2.89359i 0.332422 + 0.802538i 0.998399 + 0.0565653i \(0.0180149\pi\)
−0.665977 + 0.745972i \(0.731985\pi\)
\(14\) 1.24243 + 0.0625795i 0.332053 + 0.0167251i
\(15\) 0 0
\(16\) −3.91923 0.799791i −0.979807 0.199948i
\(17\) 4.81317 1.16736 0.583682 0.811982i \(-0.301611\pi\)
0.583682 + 0.811982i \(0.301611\pi\)
\(18\) 0 0
\(19\) −3.67470 + 1.52211i −0.843035 + 0.349196i −0.762049 0.647519i \(-0.775807\pi\)
−0.0809854 + 0.996715i \(0.525807\pi\)
\(20\) −1.82755 + 3.39883i −0.408653 + 0.760001i
\(21\) 0 0
\(22\) −0.0804248 0.225653i −0.0171466 0.0481094i
\(23\) 1.56750 1.56750i 0.326846 0.326846i −0.524540 0.851386i \(-0.675763\pi\)
0.851386 + 0.524540i \(0.175763\pi\)
\(24\) 0 0
\(25\) −0.902976 0.902976i −0.180595 0.180595i
\(26\) 1.89874 4.00171i 0.372373 0.784799i
\(27\) 0 0
\(28\) −1.11271 1.36271i −0.210282 0.257528i
\(29\) 1.08392 + 2.61682i 0.201279 + 0.485932i 0.991999 0.126247i \(-0.0402932\pi\)
−0.790719 + 0.612179i \(0.790293\pi\)
\(30\) 0 0
\(31\) 2.74627i 0.493245i 0.969112 + 0.246622i \(0.0793207\pi\)
−0.969112 + 0.246622i \(0.920679\pi\)
\(32\) 2.87810 + 4.86997i 0.508780 + 0.860896i
\(33\) 0 0
\(34\) −4.56495 5.04920i −0.782882 0.865930i
\(35\) −1.56808 + 0.649520i −0.265054 + 0.109789i
\(36\) 0 0
\(37\) −1.96490 + 4.74369i −0.323028 + 0.779857i 0.676048 + 0.736858i \(0.263691\pi\)
−0.999075 + 0.0429995i \(0.986309\pi\)
\(38\) 5.08195 + 2.41129i 0.824401 + 0.391163i
\(39\) 0 0
\(40\) 5.29881 1.30637i 0.837815 0.206556i
\(41\) 3.95321 + 3.95321i 0.617387 + 0.617387i 0.944860 0.327473i \(-0.106197\pi\)
−0.327473 + 0.944860i \(0.606197\pi\)
\(42\) 0 0
\(43\) −0.627273 + 1.51437i −0.0956582 + 0.230939i −0.964464 0.264213i \(-0.914888\pi\)
0.868806 + 0.495152i \(0.164888\pi\)
\(44\) −0.160442 + 0.298385i −0.0241875 + 0.0449832i
\(45\) 0 0
\(46\) −3.13103 0.157706i −0.461645 0.0232525i
\(47\) 9.33089i 1.36105i 0.732725 + 0.680525i \(0.238248\pi\)
−0.732725 + 0.680525i \(0.761752\pi\)
\(48\) 0 0
\(49\) 6.22623i 0.889461i
\(50\) −0.0908483 + 1.80367i −0.0128479 + 0.255077i
\(51\) 0 0
\(52\) −5.99876 + 1.80349i −0.831878 + 0.250099i
\(53\) 0.182908 0.441579i 0.0251243 0.0606555i −0.910819 0.412805i \(-0.864549\pi\)
0.935944 + 0.352149i \(0.114549\pi\)
\(54\) 0 0
\(55\) 0.231113 + 0.231113i 0.0311633 + 0.0311633i
\(56\) −0.374210 + 2.45971i −0.0500059 + 0.328692i
\(57\) 0 0
\(58\) 1.71712 3.61895i 0.225469 0.475191i
\(59\) 3.02418 7.30102i 0.393715 0.950512i −0.595408 0.803423i \(-0.703010\pi\)
0.989123 0.147089i \(-0.0469904\pi\)
\(60\) 0 0
\(61\) 11.6637 4.83126i 1.49338 0.618580i 0.521334 0.853353i \(-0.325435\pi\)
0.972050 + 0.234773i \(0.0754346\pi\)
\(62\) 2.88094 2.60464i 0.365880 0.330790i
\(63\) 0 0
\(64\) 2.37911 7.63805i 0.297389 0.954756i
\(65\) 6.04322i 0.749569i
\(66\) 0 0
\(67\) 4.45039 + 10.7442i 0.543701 + 1.31261i 0.922094 + 0.386966i \(0.126477\pi\)
−0.378393 + 0.925645i \(0.623523\pi\)
\(68\) −0.967277 + 9.57761i −0.117300 + 1.16146i
\(69\) 0 0
\(70\) 2.16859 + 1.02895i 0.259196 + 0.122984i
\(71\) −6.22714 6.22714i −0.739025 0.739025i 0.233364 0.972389i \(-0.425027\pi\)
−0.972389 + 0.233364i \(0.925027\pi\)
\(72\) 0 0
\(73\) −0.573022 + 0.573022i −0.0670672 + 0.0670672i −0.739845 0.672778i \(-0.765101\pi\)
0.672778 + 0.739845i \(0.265101\pi\)
\(74\) 6.83988 2.43779i 0.795120 0.283388i
\(75\) 0 0
\(76\) −2.29033 7.61810i −0.262719 0.873856i
\(77\) −0.137662 + 0.0570216i −0.0156881 + 0.00649822i
\(78\) 0 0
\(79\) 12.6432 1.42247 0.711233 0.702956i \(-0.248137\pi\)
0.711233 + 0.702956i \(0.248137\pi\)
\(80\) −6.39598 4.31965i −0.715092 0.482952i
\(81\) 0 0
\(82\) 0.397731 7.89640i 0.0439221 0.872012i
\(83\) −4.21199 10.1686i −0.462326 1.11615i −0.967440 0.253101i \(-0.918550\pi\)
0.505114 0.863053i \(-0.331450\pi\)
\(84\) 0 0
\(85\) 8.58010 + 3.55400i 0.930643 + 0.385485i
\(86\) 2.18356 0.778239i 0.235459 0.0839197i
\(87\) 0 0
\(88\) 0.465184 0.114687i 0.0495888 0.0122257i
\(89\) 6.68154 6.68154i 0.708241 0.708241i −0.257924 0.966165i \(-0.583038\pi\)
0.966165 + 0.257924i \(0.0830384\pi\)
\(90\) 0 0
\(91\) −2.54533 1.05431i −0.266823 0.110522i
\(92\) 2.80412 + 3.43415i 0.292350 + 0.358034i
\(93\) 0 0
\(94\) 9.78847 8.84969i 1.00960 0.912776i
\(95\) −7.67456 −0.787393
\(96\) 0 0
\(97\) −5.92342 −0.601432 −0.300716 0.953714i \(-0.597226\pi\)
−0.300716 + 0.953714i \(0.597226\pi\)
\(98\) 6.53155 5.90513i 0.659787 0.596509i
\(99\) 0 0
\(100\) 1.97828 1.61535i 0.197828 0.161535i
\(101\) 4.59423 + 1.90299i 0.457143 + 0.189355i 0.599358 0.800481i \(-0.295423\pi\)
−0.142215 + 0.989836i \(0.545423\pi\)
\(102\) 0 0
\(103\) 0.254297 0.254297i 0.0250566 0.0250566i −0.694467 0.719524i \(-0.744360\pi\)
0.719524 + 0.694467i \(0.244360\pi\)
\(104\) 7.58133 + 4.58245i 0.743410 + 0.449347i
\(105\) 0 0
\(106\) −0.636709 + 0.226929i −0.0618426 + 0.0220413i
\(107\) −4.13143 1.71129i −0.399401 0.165437i 0.173936 0.984757i \(-0.444351\pi\)
−0.573337 + 0.819320i \(0.694351\pi\)
\(108\) 0 0
\(109\) 4.89484 + 11.8172i 0.468840 + 1.13188i 0.964670 + 0.263461i \(0.0848640\pi\)
−0.495830 + 0.868420i \(0.665136\pi\)
\(110\) 0.0232523 0.461641i 0.00221702 0.0440158i
\(111\) 0 0
\(112\) 2.93524 1.94029i 0.277354 0.183341i
\(113\) 12.6188 1.18708 0.593538 0.804806i \(-0.297731\pi\)
0.593538 + 0.804806i \(0.297731\pi\)
\(114\) 0 0
\(115\) 3.95170 1.63685i 0.368498 0.152637i
\(116\) −5.42499 + 1.63099i −0.503697 + 0.151433i
\(117\) 0 0
\(118\) −10.5273 + 3.75202i −0.969115 + 0.345401i
\(119\) −2.99380 + 2.99380i −0.274441 + 0.274441i
\(120\) 0 0
\(121\) −7.75789 7.75789i −0.705262 0.705262i
\(122\) −16.1304 7.65357i −1.46038 0.692921i
\(123\) 0 0
\(124\) −5.46474 0.551904i −0.490748 0.0495624i
\(125\) −4.63488 11.1896i −0.414556 1.00083i
\(126\) 0 0
\(127\) 17.0615i 1.51396i −0.653438 0.756980i \(-0.726674\pi\)
0.653438 0.756980i \(-0.273326\pi\)
\(128\) −10.2690 + 4.74837i −0.907663 + 0.419700i
\(129\) 0 0
\(130\) 6.33957 5.73156i 0.556017 0.502691i
\(131\) −11.9542 + 4.95158i −1.04444 + 0.432621i −0.837904 0.545818i \(-0.816219\pi\)
−0.206536 + 0.978439i \(0.566219\pi\)
\(132\) 0 0
\(133\) 1.33892 3.23243i 0.116099 0.280287i
\(134\) 7.05019 14.8587i 0.609044 1.28360i
\(135\) 0 0
\(136\) 10.9647 8.06897i 0.940213 0.691909i
\(137\) 0.560971 + 0.560971i 0.0479270 + 0.0479270i 0.730664 0.682737i \(-0.239211\pi\)
−0.682737 + 0.730664i \(0.739211\pi\)
\(138\) 0 0
\(139\) −4.35315 + 10.5094i −0.369229 + 0.891398i 0.624648 + 0.780907i \(0.285243\pi\)
−0.993877 + 0.110492i \(0.964757\pi\)
\(140\) −0.977337 3.25082i −0.0826001 0.274744i
\(141\) 0 0
\(142\) −0.626511 + 12.4385i −0.0525757 + 1.04382i
\(143\) 0.530536i 0.0443657i
\(144\) 0 0
\(145\) 5.46519i 0.453859i
\(146\) 1.14459 + 0.0576517i 0.0947272 + 0.00477128i
\(147\) 0 0
\(148\) −9.04448 4.86322i −0.743452 0.399755i
\(149\) −7.37477 + 17.8043i −0.604164 + 1.45858i 0.265093 + 0.964223i \(0.414597\pi\)
−0.869258 + 0.494359i \(0.835403\pi\)
\(150\) 0 0
\(151\) 2.98204 + 2.98204i 0.242675 + 0.242675i 0.817956 0.575281i \(-0.195107\pi\)
−0.575281 + 0.817956i \(0.695107\pi\)
\(152\) −5.81947 + 9.62787i −0.472021 + 0.780924i
\(153\) 0 0
\(154\) 0.190381 + 0.0903323i 0.0153413 + 0.00727918i
\(155\) −2.02782 + 4.89559i −0.162878 + 0.393223i
\(156\) 0 0
\(157\) −3.24732 + 1.34508i −0.259164 + 0.107349i −0.508483 0.861072i \(-0.669793\pi\)
0.249318 + 0.968422i \(0.419793\pi\)
\(158\) −11.9911 13.2632i −0.953964 1.05516i
\(159\) 0 0
\(160\) 1.53465 + 10.8065i 0.121325 + 0.854330i
\(161\) 1.94998i 0.153680i
\(162\) 0 0
\(163\) 6.91012 + 16.6825i 0.541242 + 1.30667i 0.923847 + 0.382762i \(0.125027\pi\)
−0.382605 + 0.923912i \(0.624973\pi\)
\(164\) −8.66085 + 7.07194i −0.676299 + 0.552226i
\(165\) 0 0
\(166\) −6.67253 + 14.0628i −0.517889 + 1.09148i
\(167\) −11.6859 11.6859i −0.904286 0.904286i 0.0915178 0.995803i \(-0.470828\pi\)
−0.995803 + 0.0915178i \(0.970828\pi\)
\(168\) 0 0
\(169\) 2.25608 2.25608i 0.173545 0.173545i
\(170\) −4.40934 12.3716i −0.338181 0.948856i
\(171\) 0 0
\(172\) −2.88735 1.55253i −0.220158 0.118379i
\(173\) 20.9504 8.67794i 1.59283 0.659772i 0.602451 0.798156i \(-0.294191\pi\)
0.990379 + 0.138384i \(0.0441908\pi\)
\(174\) 0 0
\(175\) 1.12331 0.0849140
\(176\) −0.561506 0.379224i −0.0423251 0.0285851i
\(177\) 0 0
\(178\) −13.3462 0.672228i −1.00034 0.0503856i
\(179\) −0.893419 2.15690i −0.0667773 0.161215i 0.886968 0.461831i \(-0.152807\pi\)
−0.953745 + 0.300617i \(0.902807\pi\)
\(180\) 0 0
\(181\) −8.91096 3.69104i −0.662347 0.274353i 0.0260791 0.999660i \(-0.491698\pi\)
−0.688426 + 0.725307i \(0.741698\pi\)
\(182\) 1.30805 + 3.67009i 0.0969592 + 0.272045i
\(183\) 0 0
\(184\) 0.943043 6.19868i 0.0695220 0.456972i
\(185\) −7.00539 + 7.00539i −0.515046 + 0.515046i
\(186\) 0 0
\(187\) 0.753251 + 0.312007i 0.0550831 + 0.0228162i
\(188\) −18.5673 1.87518i −1.35416 0.136762i
\(189\) 0 0
\(190\) 7.27877 + 8.05091i 0.528058 + 0.584074i
\(191\) 2.43569 0.176240 0.0881200 0.996110i \(-0.471914\pi\)
0.0881200 + 0.996110i \(0.471914\pi\)
\(192\) 0 0
\(193\) −23.6589 −1.70301 −0.851504 0.524349i \(-0.824309\pi\)
−0.851504 + 0.524349i \(0.824309\pi\)
\(194\) 5.61795 + 6.21390i 0.403345 + 0.446132i
\(195\) 0 0
\(196\) −12.3894 1.25125i −0.884959 0.0893752i
\(197\) 3.36182 + 1.39251i 0.239520 + 0.0992122i 0.499214 0.866478i \(-0.333622\pi\)
−0.259695 + 0.965691i \(0.583622\pi\)
\(198\) 0 0
\(199\) 4.56361 4.56361i 0.323506 0.323506i −0.526604 0.850110i \(-0.676535\pi\)
0.850110 + 0.526604i \(0.176535\pi\)
\(200\) −3.57082 0.543250i −0.252495 0.0384136i
\(201\) 0 0
\(202\) −2.36099 6.62438i −0.166119 0.466090i
\(203\) −2.30187 0.953466i −0.161560 0.0669202i
\(204\) 0 0
\(205\) 4.12810 + 9.96612i 0.288319 + 0.696064i
\(206\) −0.507950 0.0255847i −0.0353905 0.00178257i
\(207\) 0 0
\(208\) −2.38318 12.2992i −0.165244 0.852799i
\(209\) −0.673752 −0.0466044
\(210\) 0 0
\(211\) −3.67647 + 1.52284i −0.253098 + 0.104837i −0.505626 0.862753i \(-0.668738\pi\)
0.252527 + 0.967590i \(0.418738\pi\)
\(212\) 0.841930 + 0.452706i 0.0578240 + 0.0310920i
\(213\) 0 0
\(214\) 2.12315 + 5.95707i 0.145136 + 0.407217i
\(215\) −2.23639 + 2.23639i −0.152521 + 0.152521i
\(216\) 0 0
\(217\) −1.70819 1.70819i −0.115959 0.115959i
\(218\) 7.75428 16.3426i 0.525186 1.10686i
\(219\) 0 0
\(220\) −0.506333 + 0.413441i −0.0341369 + 0.0278742i
\(221\) 5.76889 + 13.9273i 0.388057 + 0.936854i
\(222\) 0 0
\(223\) 15.1287i 1.01309i −0.862213 0.506545i \(-0.830922\pi\)
0.862213 0.506545i \(-0.169078\pi\)
\(224\) −4.81931 1.23895i −0.322004 0.0827806i
\(225\) 0 0
\(226\) −11.9680 13.2376i −0.796102 0.880552i
\(227\) −14.4739 + 5.99529i −0.960666 + 0.397921i −0.807230 0.590237i \(-0.799034\pi\)
−0.153437 + 0.988158i \(0.549034\pi\)
\(228\) 0 0
\(229\) −2.24557 + 5.42129i −0.148391 + 0.358249i −0.980544 0.196298i \(-0.937108\pi\)
0.832153 + 0.554546i \(0.187108\pi\)
\(230\) −5.46503 2.59306i −0.360353 0.170981i
\(231\) 0 0
\(232\) 6.85618 + 4.14415i 0.450130 + 0.272077i
\(233\) −21.4875 21.4875i −1.40769 1.40769i −0.771675 0.636017i \(-0.780581\pi\)
−0.636017 0.771675i \(-0.719419\pi\)
\(234\) 0 0
\(235\) −6.88984 + 16.6336i −0.449444 + 1.08505i
\(236\) 13.9204 + 7.48500i 0.906140 + 0.487232i
\(237\) 0 0
\(238\) 5.98002 + 0.301205i 0.387627 + 0.0195243i
\(239\) 15.5320i 1.00468i −0.864671 0.502339i \(-0.832473\pi\)
0.864671 0.502339i \(-0.167527\pi\)
\(240\) 0 0
\(241\) 25.7287i 1.65733i −0.559743 0.828666i \(-0.689100\pi\)
0.559743 0.828666i \(-0.310900\pi\)
\(242\) −0.780519 + 15.4961i −0.0501737 + 0.996129i
\(243\) 0 0
\(244\) 7.26963 + 24.1803i 0.465390 + 1.54798i
\(245\) −4.59739 + 11.0991i −0.293716 + 0.709094i
\(246\) 0 0
\(247\) −8.80874 8.80874i −0.560487 0.560487i
\(248\) 4.60395 + 6.25617i 0.292351 + 0.397267i
\(249\) 0 0
\(250\) −7.34246 + 15.4747i −0.464378 + 0.978706i
\(251\) 0.0305865 0.0738424i 0.00193060 0.00466089i −0.922911 0.385013i \(-0.874197\pi\)
0.924842 + 0.380352i \(0.124197\pi\)
\(252\) 0 0
\(253\) 0.346922 0.143700i 0.0218108 0.00903432i
\(254\) −17.8981 + 16.1816i −1.12303 + 1.01532i
\(255\) 0 0
\(256\) 14.7207 + 6.26912i 0.920042 + 0.391820i
\(257\) 27.2896i 1.70228i 0.524938 + 0.851141i \(0.324089\pi\)
−0.524938 + 0.851141i \(0.675911\pi\)
\(258\) 0 0
\(259\) −1.72841 4.17275i −0.107398 0.259282i
\(260\) −12.0253 1.21447i −0.745775 0.0753185i
\(261\) 0 0
\(262\) 16.5321 + 7.84416i 1.02136 + 0.484614i
\(263\) −14.9965 14.9965i −0.924725 0.924725i 0.0726334 0.997359i \(-0.476860\pi\)
−0.997359 + 0.0726334i \(0.976860\pi\)
\(264\) 0 0
\(265\) 0.652115 0.652115i 0.0400591 0.0400591i
\(266\) −4.66081 + 1.66115i −0.285773 + 0.101852i
\(267\) 0 0
\(268\) −22.2740 + 6.69652i −1.36060 + 0.409055i
\(269\) 19.0608 7.89523i 1.16216 0.481381i 0.283564 0.958953i \(-0.408483\pi\)
0.878592 + 0.477573i \(0.158483\pi\)
\(270\) 0 0
\(271\) 6.04647 0.367297 0.183648 0.982992i \(-0.441209\pi\)
0.183648 + 0.982992i \(0.441209\pi\)
\(272\) −18.8639 3.84953i −1.14379 0.233412i
\(273\) 0 0
\(274\) 0.0564392 1.12052i 0.00340962 0.0676932i
\(275\) −0.0827798 0.199848i −0.00499181 0.0120513i
\(276\) 0 0
\(277\) 17.5872 + 7.28485i 1.05671 + 0.437704i 0.842283 0.539036i \(-0.181211\pi\)
0.214428 + 0.976740i \(0.431211\pi\)
\(278\) 15.1535 5.40083i 0.908844 0.323920i
\(279\) 0 0
\(280\) −2.48330 + 4.10844i −0.148406 + 0.245526i
\(281\) −3.99083 + 3.99083i −0.238073 + 0.238073i −0.816052 0.577979i \(-0.803842\pi\)
0.577979 + 0.816052i \(0.303842\pi\)
\(282\) 0 0
\(283\) −23.8200 9.86659i −1.41595 0.586508i −0.462114 0.886821i \(-0.652909\pi\)
−0.953841 + 0.300313i \(0.902909\pi\)
\(284\) 13.6427 11.1398i 0.809544 0.661026i
\(285\) 0 0
\(286\) 0.556553 0.503176i 0.0329097 0.0297534i
\(287\) −4.91780 −0.290289
\(288\) 0 0
\(289\) 6.16656 0.362739
\(290\) 5.73320 5.18335i 0.336665 0.304377i
\(291\) 0 0
\(292\) −1.02509 1.25540i −0.0599887 0.0734668i
\(293\) 2.98858 + 1.23791i 0.174595 + 0.0723195i 0.468269 0.883586i \(-0.344878\pi\)
−0.293674 + 0.955906i \(0.594878\pi\)
\(294\) 0 0
\(295\) 10.7820 10.7820i 0.627753 0.627753i
\(296\) 3.47634 + 14.1004i 0.202058 + 0.819571i
\(297\) 0 0
\(298\) 25.6718 9.14966i 1.48713 0.530026i
\(299\) 6.41445 + 2.65695i 0.370957 + 0.153656i
\(300\) 0 0
\(301\) −0.551776 1.33211i −0.0318039 0.0767813i
\(302\) 0.300022 5.95652i 0.0172643 0.342759i
\(303\) 0 0
\(304\) 15.6194 3.02651i 0.895832 0.173582i
\(305\) 24.3595 1.39482
\(306\) 0 0
\(307\) −27.9645 + 11.5833i −1.59602 + 0.661092i −0.990845 0.135002i \(-0.956896\pi\)
−0.605173 + 0.796094i \(0.706896\pi\)
\(308\) −0.0858008 0.285391i −0.00488895 0.0162616i
\(309\) 0 0
\(310\) 7.05891 2.51586i 0.400919 0.142891i
\(311\) 19.5213 19.5213i 1.10695 1.10695i 0.113401 0.993549i \(-0.463826\pi\)
0.993549 0.113401i \(-0.0361745\pi\)
\(312\) 0 0
\(313\) −15.3194 15.3194i −0.865901 0.865901i 0.126114 0.992016i \(-0.459749\pi\)
−0.992016 + 0.126114i \(0.959749\pi\)
\(314\) 4.49090 + 2.13085i 0.253436 + 0.120251i
\(315\) 0 0
\(316\) −2.54083 + 25.1583i −0.142933 + 1.41527i
\(317\) −8.07700 19.4996i −0.453649 1.09521i −0.970924 0.239387i \(-0.923053\pi\)
0.517275 0.855819i \(-0.326947\pi\)
\(318\) 0 0
\(319\) 0.479791i 0.0268631i
\(320\) 9.88095 11.8591i 0.552362 0.662945i
\(321\) 0 0
\(322\) 2.04560 1.84941i 0.113997 0.103064i
\(323\) −17.6870 + 7.32618i −0.984129 + 0.407639i
\(324\) 0 0
\(325\) 1.53057 3.69512i 0.0849007 0.204968i
\(326\) 10.9468 23.0711i 0.606289 1.27779i
\(327\) 0 0
\(328\) 15.6329 + 2.37834i 0.863185 + 0.131322i
\(329\) −5.80383 5.80383i −0.319976 0.319976i
\(330\) 0 0
\(331\) 8.08547 19.5200i 0.444417 1.07292i −0.529965 0.848020i \(-0.677795\pi\)
0.974382 0.224899i \(-0.0722052\pi\)
\(332\) 21.0808 6.33781i 1.15696 0.347832i
\(333\) 0 0
\(334\) −1.17572 + 23.3423i −0.0643326 + 1.27723i
\(335\) 22.4391i 1.22598i
\(336\) 0 0
\(337\) 7.13608i 0.388727i 0.980930 + 0.194364i \(0.0622642\pi\)
−0.980930 + 0.194364i \(0.937736\pi\)
\(338\) −4.50645 0.226984i −0.245118 0.0123463i
\(339\) 0 0
\(340\) −8.79632 + 16.3591i −0.477047 + 0.887198i
\(341\) −0.178023 + 0.429786i −0.00964049 + 0.0232742i
\(342\) 0 0
\(343\) −8.22674 8.22674i −0.444202 0.444202i
\(344\) 1.10978 + 4.50141i 0.0598355 + 0.242700i
\(345\) 0 0
\(346\) −28.9735 13.7474i −1.55762 0.739064i
\(347\) 10.8574 26.2122i 0.582858 1.40714i −0.307354 0.951595i \(-0.599443\pi\)
0.890211 0.455548i \(-0.150557\pi\)
\(348\) 0 0
\(349\) 21.7373 9.00387i 1.16357 0.481966i 0.284508 0.958674i \(-0.408170\pi\)
0.879062 + 0.476707i \(0.158170\pi\)
\(350\) −1.06538 1.17839i −0.0569467 0.0629877i
\(351\) 0 0
\(352\) 0.134728 + 0.948708i 0.00718100 + 0.0505663i
\(353\) 20.0677i 1.06810i −0.845454 0.534048i \(-0.820670\pi\)
0.845454 0.534048i \(-0.179330\pi\)
\(354\) 0 0
\(355\) −6.50264 15.6988i −0.345124 0.833204i
\(356\) 11.9527 + 14.6382i 0.633491 + 0.775823i
\(357\) 0 0
\(358\) −1.41533 + 2.98290i −0.0748026 + 0.157651i
\(359\) 2.29736 + 2.29736i 0.121250 + 0.121250i 0.765128 0.643878i \(-0.222676\pi\)
−0.643878 + 0.765128i \(0.722676\pi\)
\(360\) 0 0
\(361\) −2.24841 + 2.24841i −0.118337 + 0.118337i
\(362\) 4.57937 + 12.8486i 0.240686 + 0.675309i
\(363\) 0 0
\(364\) 2.60947 4.85301i 0.136773 0.254367i
\(365\) −1.44460 + 0.598374i −0.0756139 + 0.0313203i
\(366\) 0 0
\(367\) −7.23365 −0.377594 −0.188797 0.982016i \(-0.560459\pi\)
−0.188797 + 0.982016i \(0.560459\pi\)
\(368\) −7.39706 + 4.88972i −0.385598 + 0.254894i
\(369\) 0 0
\(370\) 13.9930 + 0.704811i 0.727463 + 0.0366414i
\(371\) 0.160894 + 0.388432i 0.00835319 + 0.0201664i
\(372\) 0 0
\(373\) 16.5680 + 6.86267i 0.857856 + 0.355336i 0.767869 0.640607i \(-0.221317\pi\)
0.0899875 + 0.995943i \(0.471317\pi\)
\(374\) −0.387098 1.08611i −0.0200163 0.0561612i
\(375\) 0 0
\(376\) 15.6427 + 21.2563i 0.806709 + 1.09621i
\(377\) −6.27286 + 6.27286i −0.323069 + 0.323069i
\(378\) 0 0
\(379\) 20.4951 + 8.48935i 1.05276 + 0.436069i 0.840877 0.541226i \(-0.182040\pi\)
0.211885 + 0.977295i \(0.432040\pi\)
\(380\) 1.54232 15.2714i 0.0791192 0.783408i
\(381\) 0 0
\(382\) −2.31008 2.55513i −0.118194 0.130732i
\(383\) −2.58370 −0.132021 −0.0660103 0.997819i \(-0.521027\pi\)
−0.0660103 + 0.997819i \(0.521027\pi\)
\(384\) 0 0
\(385\) −0.287506 −0.0146526
\(386\) 22.4388 + 24.8191i 1.14211 + 1.26326i
\(387\) 0 0
\(388\) 1.19040 11.7869i 0.0604334 0.598388i
\(389\) −4.93427 2.04384i −0.250177 0.103627i 0.254071 0.967186i \(-0.418230\pi\)
−0.504248 + 0.863559i \(0.668230\pi\)
\(390\) 0 0
\(391\) 7.54464 7.54464i 0.381549 0.381549i
\(392\) 10.4379 + 14.1837i 0.527193 + 0.716386i
\(393\) 0 0
\(394\) −1.72765 4.84737i −0.0870376 0.244207i
\(395\) 22.5381 + 9.33559i 1.13402 + 0.469725i
\(396\) 0 0
\(397\) −6.50861 15.7132i −0.326658 0.788622i −0.998836 0.0482326i \(-0.984641\pi\)
0.672178 0.740389i \(-0.265359\pi\)
\(398\) −9.11567 0.459144i −0.456927 0.0230148i
\(399\) 0 0
\(400\) 2.81678 + 4.26116i 0.140839 + 0.213058i
\(401\) 13.5140 0.674856 0.337428 0.941351i \(-0.390443\pi\)
0.337428 + 0.941351i \(0.390443\pi\)
\(402\) 0 0
\(403\) −7.94658 + 3.29158i −0.395847 + 0.163965i
\(404\) −4.71000 + 8.75952i −0.234331 + 0.435802i
\(405\) 0 0
\(406\) 1.18294 + 3.31905i 0.0587082 + 0.164722i
\(407\) −0.615006 + 0.615006i −0.0304847 + 0.0304847i
\(408\) 0 0
\(409\) −15.3092 15.3092i −0.756990 0.756990i 0.218783 0.975773i \(-0.429791\pi\)
−0.975773 + 0.218783i \(0.929791\pi\)
\(410\) 6.53964 13.7827i 0.322970 0.680679i
\(411\) 0 0
\(412\) 0.454915 + 0.557124i 0.0224120 + 0.0274475i
\(413\) 2.66020 + 6.42230i 0.130900 + 0.316021i
\(414\) 0 0
\(415\) 21.2370i 1.04249i
\(416\) −10.6421 + 14.1650i −0.521772 + 0.694496i
\(417\) 0 0
\(418\) 0.639006 + 0.706792i 0.0312548 + 0.0345703i
\(419\) −7.00151 + 2.90012i −0.342046 + 0.141680i −0.547093 0.837072i \(-0.684265\pi\)
0.205046 + 0.978752i \(0.434265\pi\)
\(420\) 0 0
\(421\) 4.44827 10.7391i 0.216796 0.523391i −0.777643 0.628706i \(-0.783585\pi\)
0.994439 + 0.105315i \(0.0335850\pi\)
\(422\) 5.08439 + 2.41245i 0.247504 + 0.117436i
\(423\) 0 0
\(424\) −0.323604 1.31258i −0.0157156 0.0637444i
\(425\) −4.34617 4.34617i −0.210820 0.210820i
\(426\) 0 0
\(427\) −4.24979 + 10.2599i −0.205662 + 0.496511i
\(428\) 4.23554 7.87713i 0.204733 0.380756i
\(429\) 0 0
\(430\) 4.46712 + 0.225003i 0.215424 + 0.0108506i
\(431\) 35.7388i 1.72148i 0.509046 + 0.860739i \(0.329998\pi\)
−0.509046 + 0.860739i \(0.670002\pi\)
\(432\) 0 0
\(433\) 36.2711i 1.74308i −0.490326 0.871539i \(-0.663122\pi\)
0.490326 0.871539i \(-0.336878\pi\)
\(434\) −0.171860 + 3.41205i −0.00824955 + 0.163783i
\(435\) 0 0
\(436\) −24.4984 + 7.36529i −1.17326 + 0.352733i
\(437\) −3.37419 + 8.14601i −0.161409 + 0.389676i
\(438\) 0 0
\(439\) −4.44721 4.44721i −0.212254 0.212254i 0.592970 0.805224i \(-0.297955\pi\)
−0.805224 + 0.592970i \(0.797955\pi\)
\(440\) 0.913937 + 0.139043i 0.0435702 + 0.00662861i
\(441\) 0 0
\(442\) 9.13893 19.2609i 0.434694 0.916146i
\(443\) −0.302597 + 0.730534i −0.0143768 + 0.0347087i −0.930905 0.365262i \(-0.880980\pi\)
0.916528 + 0.399970i \(0.130980\pi\)
\(444\) 0 0
\(445\) 16.8443 6.97714i 0.798497 0.330748i
\(446\) −15.8706 + 14.3485i −0.751493 + 0.679420i
\(447\) 0 0
\(448\) 3.27107 + 6.23070i 0.154544 + 0.294373i
\(449\) 9.45413i 0.446168i 0.974799 + 0.223084i \(0.0716124\pi\)
−0.974799 + 0.223084i \(0.928388\pi\)
\(450\) 0 0
\(451\) 0.362408 + 0.874930i 0.0170651 + 0.0411988i
\(452\) −2.53593 + 25.1099i −0.119280 + 1.18107i
\(453\) 0 0
\(454\) 20.0168 + 9.49758i 0.939433 + 0.445744i
\(455\) −3.75889 3.75889i −0.176220 0.176220i
\(456\) 0 0
\(457\) −8.41071 + 8.41071i −0.393437 + 0.393437i −0.875910 0.482474i \(-0.839738\pi\)
0.482474 + 0.875910i \(0.339738\pi\)
\(458\) 7.81690 2.78601i 0.365260 0.130182i
\(459\) 0 0
\(460\) 2.46298 + 8.19236i 0.114837 + 0.381971i
\(461\) 22.6364 9.37632i 1.05428 0.436699i 0.212865 0.977082i \(-0.431721\pi\)
0.841419 + 0.540383i \(0.181721\pi\)
\(462\) 0 0
\(463\) 2.98464 0.138708 0.0693541 0.997592i \(-0.477906\pi\)
0.0693541 + 0.997592i \(0.477906\pi\)
\(464\) −2.15523 11.1228i −0.100054 0.516364i
\(465\) 0 0
\(466\) −2.16185 + 42.9206i −0.100146 + 1.98826i
\(467\) 14.7083 + 35.5089i 0.680618 + 1.64316i 0.762874 + 0.646547i \(0.223788\pi\)
−0.0822559 + 0.996611i \(0.526212\pi\)
\(468\) 0 0
\(469\) −9.45105 3.91475i −0.436409 0.180767i
\(470\) 23.9838 8.54803i 1.10629 0.394291i
\(471\) 0 0
\(472\) −5.35044 21.7020i −0.246274 0.998917i
\(473\) −0.196334 + 0.196334i −0.00902744 + 0.00902744i
\(474\) 0 0
\(475\) 4.69260 + 1.94374i 0.215311 + 0.0891849i
\(476\) −5.35564 6.55894i −0.245476 0.300629i
\(477\) 0 0
\(478\) −16.2936 + 14.7310i −0.745253 + 0.673778i
\(479\) 39.8284 1.81980 0.909902 0.414823i \(-0.136156\pi\)
0.909902 + 0.414823i \(0.136156\pi\)
\(480\) 0 0
\(481\) −16.0813 −0.733246
\(482\) −26.9904 + 24.4019i −1.22938 + 1.11147i
\(483\) 0 0
\(484\) 16.9963 13.8782i 0.772559 0.630826i
\(485\) −10.5593 4.37380i −0.479472 0.198604i
\(486\) 0 0
\(487\) 21.5914 21.5914i 0.978400 0.978400i −0.0213713 0.999772i \(-0.506803\pi\)
0.999772 + 0.0213713i \(0.00680320\pi\)
\(488\) 18.4713 30.5594i 0.836156 1.38336i
\(489\) 0 0
\(490\) 16.0037 5.70385i 0.722971 0.257674i
\(491\) 26.9379 + 11.1580i 1.21569 + 0.503555i 0.896037 0.443980i \(-0.146434\pi\)
0.319652 + 0.947535i \(0.396434\pi\)
\(492\) 0 0
\(493\) 5.21710 + 12.5952i 0.234966 + 0.567259i
\(494\) −0.886245 + 17.5952i −0.0398741 + 0.791644i
\(495\) 0 0
\(496\) 2.19644 10.7633i 0.0986232 0.483284i
\(497\) 7.74658 0.347482
\(498\) 0 0
\(499\) 11.3562 4.70388i 0.508372 0.210575i −0.113729 0.993512i \(-0.536279\pi\)
0.622101 + 0.782937i \(0.286279\pi\)
\(500\) 23.1974 6.97413i 1.03742 0.311892i
\(501\) 0 0
\(502\) −0.106473 + 0.0379478i −0.00475211 + 0.00169369i
\(503\) 8.97393 8.97393i 0.400128 0.400128i −0.478150 0.878278i \(-0.658693\pi\)
0.878278 + 0.478150i \(0.158693\pi\)
\(504\) 0 0
\(505\) 6.78467 + 6.78467i 0.301914 + 0.301914i
\(506\) −0.479777 0.227645i −0.0213287 0.0101201i
\(507\) 0 0
\(508\) 33.9502 + 3.42876i 1.50630 + 0.152126i
\(509\) −2.41200 5.82308i −0.106910 0.258104i 0.861367 0.507983i \(-0.169609\pi\)
−0.968277 + 0.249880i \(0.919609\pi\)
\(510\) 0 0
\(511\) 0.712842i 0.0315343i
\(512\) −7.38496 21.3884i −0.326372 0.945241i
\(513\) 0 0
\(514\) 28.6279 25.8823i 1.26272 1.14162i
\(515\) 0.641088 0.265547i 0.0282497 0.0117014i
\(516\) 0 0
\(517\) −0.604862 + 1.46027i −0.0266018 + 0.0642224i
\(518\) −2.73811 + 5.77073i −0.120305 + 0.253551i
\(519\) 0 0
\(520\) 10.1311 + 13.7668i 0.444277 + 0.603714i
\(521\) −0.969806 0.969806i −0.0424880 0.0424880i 0.685544 0.728032i \(-0.259565\pi\)
−0.728032 + 0.685544i \(0.759565\pi\)
\(522\) 0 0
\(523\) −13.6100 + 32.8575i −0.595125 + 1.43676i 0.283372 + 0.959010i \(0.408547\pi\)
−0.878497 + 0.477748i \(0.841453\pi\)
\(524\) −7.45067 24.7824i −0.325484 1.08263i
\(525\) 0 0
\(526\) −1.50880 + 29.9551i −0.0657867 + 1.30610i
\(527\) 13.2183i 0.575796i
\(528\) 0 0
\(529\) 18.0859i 0.786343i
\(530\) −1.30258 0.0656092i −0.0565804 0.00284988i
\(531\) 0 0
\(532\) 6.16306 + 3.31388i 0.267203 + 0.143675i
\(533\) −6.70079 + 16.1771i −0.290243 + 0.700709i
\(534\) 0 0
\(535\) −6.10122 6.10122i −0.263779 0.263779i
\(536\) 28.1502 + 17.0151i 1.21590 + 0.734940i
\(537\) 0 0
\(538\) −26.3602 12.5074i −1.13647 0.539233i
\(539\) −0.403606 + 0.974392i −0.0173846 + 0.0419700i
\(540\) 0 0
\(541\) −22.0030 + 9.11394i −0.945983 + 0.391839i −0.801720 0.597700i \(-0.796081\pi\)
−0.144263 + 0.989539i \(0.546081\pi\)
\(542\) −5.73464 6.34298i −0.246324 0.272454i
\(543\) 0 0
\(544\) 13.8528 + 23.4399i 0.593932 + 1.00498i
\(545\) 24.6800i 1.05717i
\(546\) 0 0
\(547\) −2.89886 6.99847i −0.123946 0.299233i 0.849711 0.527248i \(-0.176776\pi\)
−0.973657 + 0.228016i \(0.926776\pi\)
\(548\) −1.22900 + 1.00353i −0.0525003 + 0.0428686i
\(549\) 0 0
\(550\) −0.131138 + 0.276381i −0.00559173 + 0.0117849i
\(551\) −7.96619 7.96619i −0.339371 0.339371i
\(552\) 0 0
\(553\) −7.86407 + 7.86407i −0.334414 + 0.334414i
\(554\) −9.03810 25.3588i −0.383992 1.07739i
\(555\) 0 0
\(556\) −20.0377 10.7743i −0.849786 0.456930i
\(557\) −5.71563 + 2.36749i −0.242179 + 0.100314i −0.500472 0.865753i \(-0.666840\pi\)
0.258293 + 0.966067i \(0.416840\pi\)
\(558\) 0 0
\(559\) −5.13379 −0.217136
\(560\) 6.66515 1.29148i 0.281654 0.0545750i
\(561\) 0 0
\(562\) 7.97156 + 0.401517i 0.336260 + 0.0169370i
\(563\) −11.5978 27.9995i −0.488787 1.18004i −0.955331 0.295538i \(-0.904501\pi\)
0.466544 0.884498i \(-0.345499\pi\)
\(564\) 0 0
\(565\) 22.4947 + 9.31760i 0.946358 + 0.391994i
\(566\) 12.2412 + 34.3459i 0.514536 + 1.44367i
\(567\) 0 0
\(568\) −24.6252 3.74638i −1.03325 0.157195i
\(569\) −8.09693 + 8.09693i −0.339441 + 0.339441i −0.856157 0.516716i \(-0.827154\pi\)
0.516716 + 0.856157i \(0.327154\pi\)
\(570\) 0 0
\(571\) 2.74000 + 1.13495i 0.114666 + 0.0474960i 0.439279 0.898351i \(-0.355234\pi\)
−0.324613 + 0.945847i \(0.605234\pi\)
\(572\) −1.05570 0.106619i −0.0441411 0.00445797i
\(573\) 0 0
\(574\) 4.66419 + 5.15897i 0.194679 + 0.215331i
\(575\) −2.83083 −0.118054
\(576\) 0 0
\(577\) 6.87235 0.286100 0.143050 0.989715i \(-0.454309\pi\)
0.143050 + 0.989715i \(0.454309\pi\)
\(578\) −5.84855 6.46896i −0.243267 0.269073i
\(579\) 0 0
\(580\) −10.8751 1.09831i −0.451562 0.0456049i
\(581\) 8.94478 + 3.70505i 0.371092 + 0.153711i
\(582\) 0 0
\(583\) 0.0572495 0.0572495i 0.00237103 0.00237103i
\(584\) −0.344743 + 2.26601i −0.0142656 + 0.0937684i
\(585\) 0 0
\(586\) −1.53584 4.30920i −0.0634449 0.178012i
\(587\) 38.8656 + 16.0987i 1.60415 + 0.664463i 0.991996 0.126272i \(-0.0403012\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(588\) 0 0
\(589\) −4.18013 10.0917i −0.172239 0.415822i
\(590\) −21.5367 1.08478i −0.886653 0.0446595i
\(591\) 0 0
\(592\) 11.4948 17.0201i 0.472435 0.699521i
\(593\) −3.82382 −0.157025 −0.0785126 0.996913i \(-0.525017\pi\)
−0.0785126 + 0.996913i \(0.525017\pi\)
\(594\) 0 0
\(595\) −7.54743 + 3.12625i −0.309415 + 0.128164i
\(596\) −33.9462 18.2529i −1.39049 0.747668i
\(597\) 0 0
\(598\) −3.29641 9.24894i −0.134800 0.378217i
\(599\) 24.3269 24.3269i 0.993971 0.993971i −0.00601064 0.999982i \(-0.501913\pi\)
0.999982 + 0.00601064i \(0.00191326\pi\)
\(600\) 0 0
\(601\) −11.3481 11.3481i −0.462899 0.462899i 0.436706 0.899604i \(-0.356145\pi\)
−0.899604 + 0.436706i \(0.856145\pi\)
\(602\) −0.874110 + 1.84224i −0.0356261 + 0.0750842i
\(603\) 0 0
\(604\) −6.53317 + 5.33460i −0.265831 + 0.217062i
\(605\) −8.10111 19.5578i −0.329357 0.795138i
\(606\) 0 0
\(607\) 33.7633i 1.37041i 0.728349 + 0.685206i \(0.240288\pi\)
−0.728349 + 0.685206i \(0.759712\pi\)
\(608\) −17.9888 13.5149i −0.729541 0.548101i
\(609\) 0 0
\(610\) −23.1032 25.5540i −0.935422 1.03465i
\(611\) −26.9998 + 11.1837i −1.09229 + 0.452443i
\(612\) 0 0
\(613\) −4.90460 + 11.8407i −0.198095 + 0.478243i −0.991445 0.130522i \(-0.958335\pi\)
0.793351 + 0.608765i \(0.208335\pi\)
\(614\) 38.6736 + 18.3499i 1.56074 + 0.740543i
\(615\) 0 0
\(616\) −0.218010 + 0.360681i −0.00878387 + 0.0145323i
\(617\) −34.8951 34.8951i −1.40482 1.40482i −0.783760 0.621064i \(-0.786701\pi\)
−0.621064 0.783760i \(-0.713299\pi\)
\(618\) 0 0
\(619\) 4.75222 11.4729i 0.191008 0.461134i −0.799142 0.601142i \(-0.794713\pi\)
0.990150 + 0.140008i \(0.0447127\pi\)
\(620\) −9.33411 5.01896i −0.374867 0.201566i
\(621\) 0 0
\(622\) −38.9931 1.96403i −1.56348 0.0787505i
\(623\) 8.31186i 0.333008i
\(624\) 0 0
\(625\) 16.9843i 0.679370i
\(626\) −1.54128 + 30.5999i −0.0616018 + 1.22302i
\(627\) 0 0
\(628\) −2.02396 6.73209i −0.0807647 0.268640i
\(629\) −9.45739 + 22.8322i −0.377091 + 0.910378i
\(630\) 0 0
\(631\) −2.46865 2.46865i −0.0982753 0.0982753i 0.656260 0.754535i \(-0.272138\pi\)
−0.754535 + 0.656260i \(0.772138\pi\)
\(632\) 28.8019 21.1955i 1.14568 0.843111i
\(633\) 0 0
\(634\) −12.7954 + 26.9671i −0.508169 + 1.07100i
\(635\) 12.5980 30.4143i 0.499937 1.20696i
\(636\) 0 0
\(637\) −18.0162 + 7.46253i −0.713826 + 0.295676i
\(638\) 0.503320 0.455048i 0.0199266 0.0180155i
\(639\) 0 0
\(640\) −21.8121 + 0.882038i −0.862197 + 0.0348656i
\(641\) 38.1577i 1.50714i −0.657368 0.753570i \(-0.728330\pi\)
0.657368 0.753570i \(-0.271670\pi\)
\(642\) 0 0
\(643\) 1.23595 + 2.98384i 0.0487411 + 0.117671i 0.946375 0.323071i \(-0.104715\pi\)
−0.897634 + 0.440742i \(0.854715\pi\)
\(644\) −3.88021 0.391877i −0.152902 0.0154421i
\(645\) 0 0
\(646\) 24.4603 + 11.6059i 0.962376 + 0.456630i
\(647\) 21.3045 + 21.3045i 0.837567 + 0.837567i 0.988538 0.150971i \(-0.0482401\pi\)
−0.150971 + 0.988538i \(0.548240\pi\)
\(648\) 0 0
\(649\) 0.946557 0.946557i 0.0371556 0.0371556i
\(650\) −5.32796 + 1.89893i −0.208980 + 0.0744823i
\(651\) 0 0
\(652\) −34.5848 + 10.3977i −1.35445 + 0.407205i
\(653\) −13.2549 + 5.49034i −0.518703 + 0.214854i −0.626647 0.779303i \(-0.715573\pi\)
0.107944 + 0.994157i \(0.465573\pi\)
\(654\) 0 0
\(655\) −24.9661 −0.975506
\(656\) −12.3318 18.6553i −0.481475 0.728365i
\(657\) 0 0
\(658\) −0.583923 + 11.5930i −0.0227637 + 0.451941i
\(659\) −11.5078 27.7824i −0.448282 1.08225i −0.972965 0.230951i \(-0.925816\pi\)
0.524683 0.851297i \(-0.324184\pi\)
\(660\) 0 0
\(661\) 28.8418 + 11.9467i 1.12182 + 0.464671i 0.864991 0.501787i \(-0.167324\pi\)
0.256824 + 0.966458i \(0.417324\pi\)
\(662\) −28.1458 + 10.0314i −1.09392 + 0.389882i
\(663\) 0 0
\(664\) −26.6423 16.1036i −1.03392 0.624942i
\(665\) 4.77359 4.77359i 0.185112 0.185112i
\(666\) 0 0
\(667\) 5.80092 + 2.40282i 0.224612 + 0.0930375i
\(668\) 25.6021 20.9051i 0.990574 0.808844i
\(669\) 0 0
\(670\) 23.5394 21.2818i 0.909408 0.822190i
\(671\) 2.13853 0.0825569
\(672\) 0 0
\(673\) −40.9502 −1.57851 −0.789257 0.614063i \(-0.789534\pi\)
−0.789257 + 0.614063i \(0.789534\pi\)
\(674\) 7.48603 6.76807i 0.288351 0.260696i
\(675\) 0 0
\(676\) 4.03593 + 4.94272i 0.155228 + 0.190104i
\(677\) −38.6124 15.9938i −1.48399 0.614690i −0.513994 0.857794i \(-0.671834\pi\)
−0.970000 + 0.243104i \(0.921834\pi\)
\(678\) 0 0
\(679\) 3.68438 3.68438i 0.141394 0.141394i
\(680\) 25.5040 6.28780i 0.978035 0.241126i
\(681\) 0 0
\(682\) 0.619704 0.220868i 0.0237297 0.00845748i
\(683\) 19.6686 + 8.14698i 0.752596 + 0.311736i 0.725800 0.687905i \(-0.241470\pi\)
0.0267959 + 0.999641i \(0.491470\pi\)
\(684\) 0 0
\(685\) 0.585790 + 1.41422i 0.0223819 + 0.0540346i
\(686\) −0.827691 + 16.4326i −0.0316014 + 0.627401i
\(687\) 0 0
\(688\) 3.66960 5.43347i 0.139902 0.207149i
\(689\) 1.49698 0.0570302
\(690\) 0 0
\(691\) −0.338658 + 0.140277i −0.0128832 + 0.00533638i −0.389116 0.921189i \(-0.627219\pi\)
0.376233 + 0.926525i \(0.377219\pi\)
\(692\) 13.0577 + 43.4327i 0.496381 + 1.65106i
\(693\) 0 0
\(694\) −37.7951 + 13.4705i −1.43468 + 0.511334i
\(695\) −15.5201 + 15.5201i −0.588712 + 0.588712i
\(696\) 0 0
\(697\) 19.0274 + 19.0274i 0.720716 + 0.720716i
\(698\) −30.0617 14.2637i −1.13785 0.539889i
\(699\) 0 0
\(700\) −0.225745 + 2.23524i −0.00853236 + 0.0844842i
\(701\) −17.6750 42.6712i −0.667575 1.61167i −0.785655 0.618665i \(-0.787674\pi\)
0.118080 0.993004i \(-0.462326\pi\)
\(702\) 0 0
\(703\) 20.4224i 0.770247i
\(704\) 0.867452 1.04112i 0.0326933 0.0392386i
\(705\) 0 0
\(706\) −21.0518 + 19.0328i −0.792295 + 0.716309i
\(707\) −4.04128 + 1.67395i −0.151988 + 0.0629555i
\(708\) 0 0
\(709\) 5.95722 14.3820i 0.223728 0.540127i −0.771663 0.636032i \(-0.780575\pi\)
0.995390 + 0.0959051i \(0.0305745\pi\)
\(710\) −10.3013 + 21.7107i −0.386601 + 0.814787i
\(711\) 0 0
\(712\) 4.01976 26.4221i 0.150647 0.990211i
\(713\) 4.30478 + 4.30478i 0.161215 + 0.161215i
\(714\) 0 0
\(715\) −0.391743 + 0.945751i −0.0146504 + 0.0353691i
\(716\) 4.47152 1.34433i 0.167109 0.0502401i
\(717\) 0 0
\(718\) 0.231137 4.58891i 0.00862596 0.171256i
\(719\) 26.6063i 0.992249i 0.868251 + 0.496124i \(0.165244\pi\)
−0.868251 + 0.496124i \(0.834756\pi\)
\(720\) 0 0
\(721\) 0.316346i 0.0117813i
\(722\) 4.49112 + 0.226212i 0.167142 + 0.00841873i
\(723\) 0 0
\(724\) 9.13551 16.9900i 0.339519 0.631427i
\(725\) 1.38417 3.34169i 0.0514068 0.124107i
\(726\) 0 0
\(727\) 32.3093 + 32.3093i 1.19828 + 1.19828i 0.974680 + 0.223604i \(0.0717823\pi\)
0.223604 + 0.974680i \(0.428218\pi\)
\(728\) −7.56589 + 1.86530i −0.280411 + 0.0691328i
\(729\) 0 0
\(730\) 1.99782 + 0.947929i 0.0739426 + 0.0350844i
\(731\) −3.01917 + 7.28891i −0.111668 + 0.269590i
\(732\) 0 0
\(733\) −25.7622 + 10.6711i −0.951549 + 0.394145i −0.803813 0.594882i \(-0.797199\pi\)
−0.147736 + 0.989027i \(0.547199\pi\)
\(734\) 6.86060 + 7.58838i 0.253230 + 0.280092i
\(735\) 0 0
\(736\) 12.1451 + 3.12226i 0.447674 + 0.115088i
\(737\) 1.96993i 0.0725634i
\(738\) 0 0
\(739\) 9.64374 + 23.2821i 0.354751 + 0.856444i 0.996020 + 0.0891284i \(0.0284081\pi\)
−0.641269 + 0.767316i \(0.721592\pi\)
\(740\) −12.5320 15.3477i −0.460687 0.564193i
\(741\) 0 0
\(742\) 0.254884 0.537184i 0.00935708 0.0197207i
\(743\) −12.1679 12.1679i −0.446396 0.446396i 0.447759 0.894154i \(-0.352222\pi\)
−0.894154 + 0.447759i \(0.852222\pi\)
\(744\) 0 0
\(745\) −26.2930 + 26.2930i −0.963301 + 0.963301i
\(746\) −8.51432 23.8892i −0.311731 0.874645i
\(747\) 0 0
\(748\) −0.772232 + 1.43617i −0.0282356 + 0.0525117i
\(749\) 3.63419 1.50533i 0.132790 0.0550035i
\(750\) 0 0
\(751\) 21.0598 0.768485 0.384242 0.923232i \(-0.374463\pi\)
0.384242 + 0.923232i \(0.374463\pi\)
\(752\) 7.46276 36.5699i 0.272139 1.33357i
\(753\) 0 0
\(754\) 12.5298 + 0.631111i 0.456310 + 0.0229837i
\(755\) 3.11397 + 7.51778i 0.113329 + 0.273600i
\(756\) 0 0
\(757\) −31.7664 13.1581i −1.15457 0.478238i −0.278505 0.960435i \(-0.589839\pi\)
−0.876063 + 0.482197i \(0.839839\pi\)
\(758\) −10.5325 29.5517i −0.382557 1.07337i
\(759\) 0 0
\(760\) −17.4831 + 12.8659i −0.634179 + 0.466696i
\(761\) −15.4825 + 15.4825i −0.561240 + 0.561240i −0.929660 0.368419i \(-0.879899\pi\)
0.368419 + 0.929660i \(0.379899\pi\)
\(762\) 0 0
\(763\) −10.3949 4.30571i −0.376321 0.155877i
\(764\) −0.489487 + 4.84672i −0.0177090 + 0.175348i
\(765\) 0 0
\(766\) 2.45045 + 2.71040i 0.0885384 + 0.0979306i
\(767\) 24.7509 0.893701
\(768\) 0 0
\(769\) 16.8973 0.609333 0.304666 0.952459i \(-0.401455\pi\)
0.304666 + 0.952459i \(0.401455\pi\)
\(770\) 0.272679 + 0.301605i 0.00982666 + 0.0108691i
\(771\) 0 0
\(772\) 4.75461 47.0784i 0.171122 1.69439i
\(773\) −28.9525 11.9925i −1.04135 0.431341i −0.204553 0.978856i \(-0.565574\pi\)
−0.836796 + 0.547515i \(0.815574\pi\)
\(774\) 0 0
\(775\) 2.47982 2.47982i 0.0890777 0.0890777i
\(776\) −13.4939 + 9.93025i −0.484403 + 0.356475i
\(777\) 0 0
\(778\) 2.53574 + 7.11468i 0.0909105 + 0.255074i
\(779\) −20.5441 8.50964i −0.736068 0.304889i
\(780\) 0 0
\(781\) −0.570869 1.37820i −0.0204273 0.0493159i
\(782\) −15.0702 0.759065i −0.538908 0.0271441i
\(783\) 0 0
\(784\) 4.97968 24.4020i 0.177846 0.871500i
\(785\) −6.78198 −0.242059
\(786\) 0 0
\(787\) 17.7032 7.33292i 0.631052 0.261390i −0.0441479 0.999025i \(-0.514057\pi\)
0.675200 + 0.737635i \(0.264057\pi\)
\(788\) −3.44653 + 6.40976i −0.122778 + 0.228338i