Properties

Label 108.6.h.a.35.14
Level 108
Weight 6
Character 108.35
Analytic conductor 17.321
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 35.14
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.216257 + 5.65272i) q^{2} +(-31.9065 - 2.44488i) q^{4} +(0.143132 - 0.0826372i) q^{5} +(192.634 + 111.217i) q^{7} +(20.7202 - 179.830i) q^{8} +O(q^{10})\) \(q+(-0.216257 + 5.65272i) q^{2} +(-31.9065 - 2.44488i) q^{4} +(0.143132 - 0.0826372i) q^{5} +(192.634 + 111.217i) q^{7} +(20.7202 - 179.830i) q^{8} +(0.436172 + 0.826955i) q^{10} +(329.552 - 570.801i) q^{11} +(43.8997 + 76.0365i) q^{13} +(-670.338 + 1064.85i) q^{14} +(1012.05 + 156.015i) q^{16} +85.1645i q^{17} +2308.11i q^{19} +(-4.76887 + 2.28672i) q^{20} +(3155.31 + 1986.31i) q^{22} +(1327.18 + 2298.74i) q^{23} +(-1562.49 + 2706.31i) q^{25} +(-439.307 + 231.709i) q^{26} +(-5874.36 - 4019.52i) q^{28} +(-1337.58 - 772.253i) q^{29} +(1202.41 - 694.212i) q^{31} +(-1100.77 + 5687.07i) q^{32} +(-481.411 - 18.4174i) q^{34} +36.7627 q^{35} +4404.71 q^{37} +(-13047.1 - 499.144i) q^{38} +(-11.8949 - 27.4516i) q^{40} +(3145.98 - 1816.33i) q^{41} +(2424.30 + 1399.67i) q^{43} +(-11910.4 + 17406.5i) q^{44} +(-13281.1 + 7005.04i) q^{46} +(-4973.66 + 8614.64i) q^{47} +(16335.1 + 28293.2i) q^{49} +(-14960.1 - 9417.55i) q^{50} +(-1214.78 - 2533.39i) q^{52} -15134.7i q^{53} -108.933i q^{55} +(23991.6 - 32336.8i) q^{56} +(4654.59 - 7393.96i) q^{58} +(17228.5 + 29840.7i) q^{59} +(22173.9 - 38406.3i) q^{61} +(3664.16 + 6947.02i) q^{62} +(-31909.3 - 7452.21i) q^{64} +(12.5669 + 7.25550i) q^{65} +(-30386.6 + 17543.7i) q^{67} +(208.217 - 2717.30i) q^{68} +(-7.95019 + 207.809i) q^{70} +6002.26 q^{71} +32902.8 q^{73} +(-952.549 + 24898.6i) q^{74} +(5643.04 - 73643.6i) q^{76} +(126966. - 73303.8i) q^{77} +(23909.7 + 13804.3i) q^{79} +(157.749 - 61.3019i) q^{80} +(9586.86 + 18176.1i) q^{82} +(49118.1 - 85075.0i) q^{83} +(7.03776 + 12.1898i) q^{85} +(-8436.22 + 13401.2i) q^{86} +(-95818.6 - 71090.4i) q^{88} +19178.8i q^{89} +19529.6i q^{91} +(-36725.4 - 76589.3i) q^{92} +(-47620.5 - 29977.7i) q^{94} +(190.736 + 330.364i) q^{95} +(-9697.23 + 16796.1i) q^{97} +(-163466. + 86219.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.216257 + 5.65272i −0.0382292 + 0.999269i
\(3\) 0 0
\(4\) −31.9065 2.44488i −0.997077 0.0764024i
\(5\) 0.143132 0.0826372i 0.00256042 0.00147826i −0.498719 0.866764i \(-0.666196\pi\)
0.501280 + 0.865285i \(0.332863\pi\)
\(6\) 0 0
\(7\) 192.634 + 111.217i 1.48589 + 0.857881i 0.999871 0.0160647i \(-0.00511378\pi\)
0.486023 + 0.873946i \(0.338447\pi\)
\(8\) 20.7202 179.830i 0.114464 0.993427i
\(9\) 0 0
\(10\) 0.436172 + 0.826955i 0.00137930 + 0.00261506i
\(11\) 329.552 570.801i 0.821188 1.42234i −0.0836100 0.996499i \(-0.526645\pi\)
0.904798 0.425841i \(-0.140022\pi\)
\(12\) 0 0
\(13\) 43.8997 + 76.0365i 0.0720449 + 0.124785i 0.899797 0.436308i \(-0.143714\pi\)
−0.827752 + 0.561093i \(0.810381\pi\)
\(14\) −670.338 + 1064.85i −0.914059 + 1.45201i
\(15\) 0 0
\(16\) 1012.05 + 156.015i 0.988325 + 0.152358i
\(17\) 85.1645i 0.0714721i 0.999361 + 0.0357360i \(0.0113776\pi\)
−0.999361 + 0.0357360i \(0.988622\pi\)
\(18\) 0 0
\(19\) 2308.11i 1.46680i 0.679795 + 0.733402i \(0.262069\pi\)
−0.679795 + 0.733402i \(0.737931\pi\)
\(20\) −4.76887 + 2.28672i −0.00266588 + 0.00127832i
\(21\) 0 0
\(22\) 3155.31 + 1986.31i 1.38991 + 0.874963i
\(23\) 1327.18 + 2298.74i 0.523129 + 0.906086i 0.999638 + 0.0269164i \(0.00856881\pi\)
−0.476509 + 0.879170i \(0.658098\pi\)
\(24\) 0 0
\(25\) −1562.49 + 2706.31i −0.499996 + 0.866018i
\(26\) −439.307 + 231.709i −0.127448 + 0.0672218i
\(27\) 0 0
\(28\) −5874.36 4019.52i −1.41601 0.968900i
\(29\) −1337.58 772.253i −0.295342 0.170516i 0.345007 0.938600i \(-0.387877\pi\)
−0.640348 + 0.768085i \(0.721210\pi\)
\(30\) 0 0
\(31\) 1202.41 694.212i 0.224724 0.129744i −0.383412 0.923577i \(-0.625251\pi\)
0.608136 + 0.793833i \(0.291918\pi\)
\(32\) −1100.77 + 5687.07i −0.190030 + 0.981778i
\(33\) 0 0
\(34\) −481.411 18.4174i −0.0714198 0.00273232i
\(35\) 36.7627 0.00507268
\(36\) 0 0
\(37\) 4404.71 0.528948 0.264474 0.964393i \(-0.414802\pi\)
0.264474 + 0.964393i \(0.414802\pi\)
\(38\) −13047.1 499.144i −1.46573 0.0560747i
\(39\) 0 0
\(40\) −11.8949 27.4516i −0.00117547 0.00271280i
\(41\) 3145.98 1816.33i 0.292278 0.168747i −0.346691 0.937979i \(-0.612695\pi\)
0.638969 + 0.769233i \(0.279361\pi\)
\(42\) 0 0
\(43\) 2424.30 + 1399.67i 0.199947 + 0.115440i 0.596631 0.802516i \(-0.296506\pi\)
−0.396684 + 0.917955i \(0.629839\pi\)
\(44\) −11910.4 + 17406.5i −0.927458 + 1.35544i
\(45\) 0 0
\(46\) −13281.1 + 7005.04i −0.925423 + 0.488108i
\(47\) −4973.66 + 8614.64i −0.328422 + 0.568843i −0.982199 0.187844i \(-0.939850\pi\)
0.653777 + 0.756687i \(0.273183\pi\)
\(48\) 0 0
\(49\) 16335.1 + 28293.2i 0.971921 + 1.68342i
\(50\) −14960.1 9417.55i −0.846270 0.532737i
\(51\) 0 0
\(52\) −1214.78 2533.39i −0.0623004 0.129925i
\(53\) 15134.7i 0.740087i −0.929014 0.370044i \(-0.879343\pi\)
0.929014 0.370044i \(-0.120657\pi\)
\(54\) 0 0
\(55\) 108.933i 0.00485572i
\(56\) 23991.6 32336.8i 1.02232 1.37793i
\(57\) 0 0
\(58\) 4654.59 7393.96i 0.181682 0.288607i
\(59\) 17228.5 + 29840.7i 0.644344 + 1.11604i 0.984453 + 0.175651i \(0.0562029\pi\)
−0.340108 + 0.940386i \(0.610464\pi\)
\(60\) 0 0
\(61\) 22173.9 38406.3i 0.762986 1.32153i −0.178318 0.983973i \(-0.557066\pi\)
0.941305 0.337558i \(-0.109601\pi\)
\(62\) 3664.16 + 6947.02i 0.121058 + 0.229519i
\(63\) 0 0
\(64\) −31909.3 7452.21i −0.973796 0.227423i
\(65\) 12.5669 + 7.25550i 0.000368930 + 0.000213002i
\(66\) 0 0
\(67\) −30386.6 + 17543.7i −0.826980 + 0.477457i −0.852817 0.522209i \(-0.825108\pi\)
0.0258378 + 0.999666i \(0.491775\pi\)
\(68\) 208.217 2717.30i 0.00546064 0.0712632i
\(69\) 0 0
\(70\) −7.95019 + 207.809i −0.000193924 + 0.00506898i
\(71\) 6002.26 0.141309 0.0706544 0.997501i \(-0.477491\pi\)
0.0706544 + 0.997501i \(0.477491\pi\)
\(72\) 0 0
\(73\) 32902.8 0.722647 0.361324 0.932441i \(-0.382325\pi\)
0.361324 + 0.932441i \(0.382325\pi\)
\(74\) −952.549 + 24898.6i −0.0202213 + 0.528562i
\(75\) 0 0
\(76\) 5643.04 73643.6i 0.112067 1.46252i
\(77\) 126966. 73303.8i 2.44040 1.40896i
\(78\) 0 0
\(79\) 23909.7 + 13804.3i 0.431029 + 0.248855i 0.699785 0.714354i \(-0.253279\pi\)
−0.268756 + 0.963208i \(0.586613\pi\)
\(80\) 157.749 61.3019i 0.00275575 0.00107090i
\(81\) 0 0
\(82\) 9586.86 + 18176.1i 0.157450 + 0.298515i
\(83\) 49118.1 85075.0i 0.782611 1.35552i −0.147804 0.989017i \(-0.547221\pi\)
0.930416 0.366506i \(-0.119446\pi\)
\(84\) 0 0
\(85\) 7.03776 + 12.1898i 0.000105654 + 0.000182999i
\(86\) −8436.22 + 13401.2i −0.122999 + 0.195388i
\(87\) 0 0
\(88\) −95818.6 71090.4i −1.31899 0.978597i
\(89\) 19178.8i 0.256653i 0.991732 + 0.128326i \(0.0409605\pi\)
−0.991732 + 0.128326i \(0.959040\pi\)
\(90\) 0 0
\(91\) 19529.6i 0.247224i
\(92\) −36725.4 76589.3i −0.452373 0.943406i
\(93\) 0 0
\(94\) −47620.5 29977.7i −0.555872 0.349928i
\(95\) 190.736 + 330.364i 0.00216832 + 0.00375563i
\(96\) 0 0
\(97\) −9697.23 + 16796.1i −0.104645 + 0.181250i −0.913593 0.406630i \(-0.866704\pi\)
0.808948 + 0.587880i \(0.200037\pi\)
\(98\) −163466. + 86219.0i −1.71934 + 0.906855i
\(99\) 0 0
\(100\) 56470.0 82528.6i 0.564700 0.825286i
\(101\) 18242.5 + 10532.3i 0.177943 + 0.102735i 0.586326 0.810075i \(-0.300574\pi\)
−0.408383 + 0.912811i \(0.633907\pi\)
\(102\) 0 0
\(103\) −109139. + 63011.2i −1.01364 + 0.585228i −0.912257 0.409619i \(-0.865662\pi\)
−0.101388 + 0.994847i \(0.532328\pi\)
\(104\) 14583.2 6318.97i 0.132212 0.0572879i
\(105\) 0 0
\(106\) 85552.0 + 3272.97i 0.739546 + 0.0282929i
\(107\) −147922. −1.24903 −0.624516 0.781012i \(-0.714704\pi\)
−0.624516 + 0.781012i \(0.714704\pi\)
\(108\) 0 0
\(109\) 121171. 0.976857 0.488429 0.872604i \(-0.337570\pi\)
0.488429 + 0.872604i \(0.337570\pi\)
\(110\) 615.768 + 23.5575i 0.00485217 + 0.000185630i
\(111\) 0 0
\(112\) 177603. + 142611.i 1.33784 + 1.07425i
\(113\) −102842. + 59376.0i −0.757662 + 0.437436i −0.828456 0.560055i \(-0.810780\pi\)
0.0707938 + 0.997491i \(0.477447\pi\)
\(114\) 0 0
\(115\) 379.922 + 219.348i 0.00267886 + 0.00154664i
\(116\) 40789.4 + 27910.1i 0.281451 + 0.192582i
\(117\) 0 0
\(118\) −172407. + 90934.7i −1.13985 + 0.601208i
\(119\) −9471.77 + 16405.6i −0.0613146 + 0.106200i
\(120\) 0 0
\(121\) −136684. 236744.i −0.848700 1.46999i
\(122\) 212305. + 133648.i 1.29140 + 0.812950i
\(123\) 0 0
\(124\) −40061.9 + 19210.1i −0.233979 + 0.112196i
\(125\) 1032.96i 0.00591301i
\(126\) 0 0
\(127\) 215170.i 1.18378i −0.806018 0.591891i \(-0.798381\pi\)
0.806018 0.591891i \(-0.201619\pi\)
\(128\) 49025.9 178763.i 0.264485 0.964390i
\(129\) 0 0
\(130\) −43.7310 + 69.4680i −0.000226950 + 0.000360518i
\(131\) 123220. + 213424.i 0.627341 + 1.08659i 0.988083 + 0.153921i \(0.0491900\pi\)
−0.360742 + 0.932666i \(0.617477\pi\)
\(132\) 0 0
\(133\) −256701. + 444620.i −1.25834 + 2.17951i
\(134\) −92598.3 175561.i −0.445493 0.844628i
\(135\) 0 0
\(136\) 15315.1 + 1764.63i 0.0710023 + 0.00818098i
\(137\) −182252. 105223.i −0.829606 0.478973i 0.0241120 0.999709i \(-0.492324\pi\)
−0.853718 + 0.520736i \(0.825658\pi\)
\(138\) 0 0
\(139\) 246037. 142050.i 1.08010 0.623596i 0.149177 0.988811i \(-0.452338\pi\)
0.930923 + 0.365214i \(0.119004\pi\)
\(140\) −1172.97 89.8804i −0.00505786 0.000387565i
\(141\) 0 0
\(142\) −1298.03 + 33929.1i −0.00540212 + 0.141205i
\(143\) 57869.0 0.236650
\(144\) 0 0
\(145\) −255.267 −0.00100827
\(146\) −7115.46 + 185991.i −0.0276262 + 0.722119i
\(147\) 0 0
\(148\) −140539. 10769.0i −0.527402 0.0404129i
\(149\) −256622. + 148161.i −0.946953 + 0.546723i −0.892133 0.451773i \(-0.850792\pi\)
−0.0548196 + 0.998496i \(0.517458\pi\)
\(150\) 0 0
\(151\) 381289. + 220137.i 1.36086 + 0.785690i 0.989738 0.142896i \(-0.0456414\pi\)
0.371118 + 0.928586i \(0.378975\pi\)
\(152\) 415066. + 47824.4i 1.45716 + 0.167896i
\(153\) 0 0
\(154\) 386909. + 733555.i 1.31464 + 2.49248i
\(155\) 114.735 198.728i 0.000383591 0.000664399i
\(156\) 0 0
\(157\) 20432.3 + 35389.8i 0.0661558 + 0.114585i 0.897206 0.441612i \(-0.145593\pi\)
−0.831050 + 0.556197i \(0.812260\pi\)
\(158\) −83202.3 + 132170.i −0.265151 + 0.421200i
\(159\) 0 0
\(160\) 312.408 + 904.965i 0.000964767 + 0.00279468i
\(161\) 590420.i 1.79513i
\(162\) 0 0
\(163\) 326446.i 0.962369i −0.876619 0.481185i \(-0.840207\pi\)
0.876619 0.481185i \(-0.159793\pi\)
\(164\) −104818. + 50261.1i −0.304316 + 0.145923i
\(165\) 0 0
\(166\) 470283. + 296049.i 1.32461 + 0.833860i
\(167\) −232137. 402072.i −0.644099 1.11561i −0.984509 0.175335i \(-0.943899\pi\)
0.340410 0.940277i \(1.61057\pi\)
\(168\) 0 0
\(169\) 181792. 314873.i 0.489619 0.848045i
\(170\) −70.4272 + 37.1464i −0.000186904 + 9.85812e-5i
\(171\) 0 0
\(172\) −73928.9 50585.7i −0.190543 0.130379i
\(173\) −356838. 206020.i −0.906474 0.523353i −0.0271793 0.999631i \(-0.508653\pi\)
−0.879295 + 0.476277i \(0.841986\pi\)
\(174\) 0 0
\(175\) −601976. + 347551.i −1.48588 + 0.857874i
\(176\) 422575. 526262.i 1.02831 1.28062i
\(177\) 0 0
\(178\) −108412. 4147.54i −0.256465 0.00981162i
\(179\) −91420.4 −0.213261 −0.106630 0.994299i \(-0.534006\pi\)
−0.106630 + 0.994299i \(0.534006\pi\)
\(180\) 0 0
\(181\) −705467. −1.60059 −0.800295 0.599606i \(-0.795324\pi\)
−0.800295 + 0.599606i \(0.795324\pi\)
\(182\) −110395. 4223.41i −0.247043 0.00945116i
\(183\) 0 0
\(184\) 440880. 191035.i 0.960010 0.415977i
\(185\) 630.455 363.993i 0.00135433 0.000781923i
\(186\) 0 0
\(187\) 48612.0 + 28066.2i 0.101658 + 0.0586920i
\(188\) 179754. 262703.i 0.370923 0.542088i
\(189\) 0 0
\(190\) −1908.70 + 1006.73i −0.00383578 + 0.00202316i
\(191\) −65114.9 + 112782.i −0.129151 + 0.223696i −0.923348 0.383965i \(-0.874558\pi\)
0.794197 + 0.607660i \(0.207892\pi\)
\(192\) 0 0
\(193\) −229197. 396982.i −0.442911 0.767144i 0.554993 0.831855i \(-0.312721\pi\)
−0.997904 + 0.0647106i \(0.979388\pi\)
\(194\) −92846.6 58448.0i −0.177117 0.111498i
\(195\) 0 0
\(196\) −452021. 942672.i −0.840463 1.75275i
\(197\) 484753.i 0.889928i −0.895549 0.444964i \(-0.853217\pi\)
0.895549 0.444964i \(-0.146783\pi\)
\(198\) 0 0
\(199\) 616397.i 1.10339i −0.834047 0.551694i \(-0.813982\pi\)
0.834047 0.551694i \(-0.186018\pi\)
\(200\) 454299. + 337056.i 0.803094 + 0.595837i
\(201\) 0 0
\(202\) −63481.2 + 100842.i −0.109463 + 0.173885i
\(203\) −171776. 297524.i −0.292565 0.506737i
\(204\) 0 0
\(205\) 300.193 519.949i 0.000498903 0.000864125i
\(206\) −332583. 630557.i −0.546049 1.03528i
\(207\) 0 0
\(208\) 32565.7 + 83801.4i 0.0521917 + 0.134305i
\(209\) 1.31747e6 + 760642.i 2.08629 + 1.20452i
\(210\) 0 0
\(211\) −388325. + 224199.i −0.600466 + 0.346679i −0.769225 0.638978i \(-0.779357\pi\)
0.168759 + 0.985657i \(0.446024\pi\)
\(212\) −37002.4 + 482893.i −0.0565445 + 0.737924i
\(213\) 0 0
\(214\) 31989.1 836162.i 0.0477494 1.24812i
\(215\) 462.660 0.000682599
\(216\) 0 0
\(217\) 308834. 0.445220
\(218\) −26204.0 + 684944.i −0.0373444 + 0.976143i
\(219\) 0 0
\(220\) −266.328 + 3475.67i −0.000370988 + 0.00484152i
\(221\) −6475.61 + 3738.70i −0.00891867 + 0.00514920i
\(222\) 0 0
\(223\) 48031.9 + 27731.2i 0.0646796 + 0.0373428i 0.531991 0.846750i \(-0.321444\pi\)
−0.467311 + 0.884093i \(0.654777\pi\)
\(224\) −844546. + 973098.i −1.12461 + 1.29580i
\(225\) 0 0
\(226\) −313395. 594179.i −0.408152 0.773831i
\(227\) 309416. 535925.i 0.398546 0.690302i −0.595001 0.803725i \(-0.702848\pi\)
0.993547 + 0.113423i \(0.0361815\pi\)
\(228\) 0 0
\(229\) 78993.5 + 136821.i 0.0995412 + 0.172410i 0.911495 0.411312i \(-0.134929\pi\)
−0.811954 + 0.583722i \(0.801596\pi\)
\(230\) −1322.07 + 2100.16i −0.00164792 + 0.00261778i
\(231\) 0 0
\(232\) −166589. + 224535.i −0.203201 + 0.273883i
\(233\) 824409.i 0.994840i −0.867510 0.497420i \(-0.834281\pi\)
0.867510 0.497420i \(-0.165719\pi\)
\(234\) 0 0
\(235\) 1644.04i 0.00194197i
\(236\) −476744. 994232.i −0.557193 1.16200i
\(237\) 0 0
\(238\) −90687.8 57089.1i −0.103778 0.0653297i
\(239\) −227607. 394226.i −0.257745 0.446427i 0.707893 0.706320i \(-0.249646\pi\)
−0.965637 + 0.259893i \(0.916313\pi\)
\(240\) 0 0
\(241\) 134036. 232158.i 0.148655 0.257478i −0.782075 0.623184i \(-0.785839\pi\)
0.930731 + 0.365705i \(0.119172\pi\)
\(242\) 1.36780e6 721438.i 1.50136 0.791883i
\(243\) 0 0
\(244\) −801388. + 1.17120e6i −0.861724 + 1.25937i
\(245\) 4676.14 + 2699.77i 0.00497705 + 0.00287350i
\(246\) 0 0
\(247\) −175500. + 101325.i −0.183036 + 0.105676i
\(248\) −99925.7 230613.i −0.103169 0.238098i
\(249\) 0 0
\(250\) −5839.04 223.385i −0.00590869 0.000226049i
\(251\) 1.05745e6 1.05944 0.529719 0.848173i \(-0.322298\pi\)
0.529719 + 0.848173i \(0.322298\pi\)
\(252\) 0 0
\(253\) 1.74950e6 1.71835
\(254\) 1.21629e6 + 46531.9i 1.18292 + 0.0452550i
\(255\) 0 0
\(256\) 999895. + 315788.i 0.953574 + 0.301159i
\(257\) −18796.2 + 10852.0i −0.0177516 + 0.0102489i −0.508850 0.860855i \(-0.669929\pi\)
0.491098 + 0.871104i \(0.336596\pi\)
\(258\) 0 0
\(259\) 848497. + 489880.i 0.785961 + 0.453775i
\(260\) −383.226 262.222i −0.000351578 0.000240567i
\(261\) 0 0
\(262\) −1.23307e6 + 650375.i −1.10977 + 0.585343i
\(263\) −1.03830e6 + 1.79839e6i −0.925622 + 1.60322i −0.135063 + 0.990837i \(0.543124\pi\)
−0.790558 + 0.612387i \(0.790210\pi\)
\(264\) 0 0
\(265\) −1250.69 2166.25i −0.00109404 0.00189493i
\(266\) −2.45780e6 1.54721e6i −2.12982 1.34074i
\(267\) 0 0
\(268\) 1.01242e6 485466.i 0.861041 0.412878i
\(269\) 175156.i 0.147585i −0.997274 0.0737927i \(-0.976490\pi\)
0.997274 0.0737927i \(-0.0235103\pi\)
\(270\) 0 0
\(271\) 926017.i 0.765942i 0.923760 + 0.382971i \(0.125099\pi\)
−0.923760 + 0.382971i \(0.874901\pi\)
\(272\) −13286.9 + 86190.3i −0.0108894 + 0.0706377i
\(273\) 0 0
\(274\) 634212. 1.00747e6i 0.510338 0.810688i
\(275\) 1.02984e6 + 1.78374e6i 0.821181 + 1.42233i
\(276\) 0 0
\(277\) −561144. + 971930.i −0.439415 + 0.761089i −0.997644 0.0685974i \(-0.978148\pi\)
0.558229 + 0.829687i \(0.311481\pi\)
\(278\) 749760. + 1.42150e6i 0.581849 + 1.10315i
\(279\) 0 0
\(280\) 761.731 6611.03i 0.000580640 0.00503934i
\(281\) −1.74330e6 1.00650e6i −1.31707 0.760408i −0.333810 0.942641i \(-0.608334\pi\)
−0.983255 + 0.182233i \(0.941668\pi\)
\(282\) 0 0
\(283\) −28134.7 + 16243.6i −0.0208822 + 0.0120563i −0.510405 0.859934i \(-0.670504\pi\)
0.489523 + 0.871991i \(0.337171\pi\)
\(284\) −191511. 14674.8i −0.140896 0.0107963i
\(285\) 0 0
\(286\) −12514.6 + 327117.i −0.00904692 + 0.236477i
\(287\) 808029. 0.579058
\(288\) 0 0
\(289\) 1.41260e6 0.994892
\(290\) 55.2033 1442.95i 3.85452e−5 0.00100753i
\(291\) 0 0
\(292\) −1.04981e6 80443.4i −0.720535 0.0552120i
\(293\) 1.69871e6 980754.i 1.15598 0.667407i 0.205645 0.978627i \(-0.434071\pi\)
0.950338 + 0.311220i \(0.100737\pi\)
\(294\) 0 0
\(295\) 4931.90 + 2847.43i 0.00329958 + 0.00190502i
\(296\) 91266.5 792098.i 0.0605455 0.525472i
\(297\) 0 0
\(298\) −782015. 1.48265e6i −0.510122 0.967161i
\(299\) −116525. + 201828.i −0.0753776 + 0.130558i
\(300\) 0 0
\(301\) 311335. + 539249.i 0.198067 + 0.343062i
\(302\) −1.32683e6 + 2.10771e6i −0.837140 + 1.32982i
\(303\) 0 0
\(304\) −360099. + 2.33591e6i −0.223480 + 1.44968i
\(305\) 7329.54i 0.00451157i
\(306\) 0 0
\(307\) 2.30255e6i 1.39432i −0.716915 0.697160i \(-0.754447\pi\)
0.716915 0.697160i \(-0.245553\pi\)
\(308\) −4.23025e6 + 2.02845e6i −2.54091 + 1.21839i
\(309\) 0 0
\(310\) 1098.54 + 691.544i 0.000649249 + 0.000408710i
\(311\) −900581. 1.55985e6i −0.527985 0.914498i −0.999468 0.0326220i \(-0.989614\pi\)
0.471482 0.881875i \(1.65628\pi\)
\(312\) 0 0
\(313\) −1.06851e6 + 1.85072e6i −0.616480 + 1.06777i 0.373643 + 0.927573i \(0.378109\pi\)
−0.990123 + 0.140202i \(0.955225\pi\)
\(314\) −204467. + 107845.i −0.117030 + 0.0617269i
\(315\) 0 0
\(316\) −729124. 498902.i −0.410756 0.281059i
\(317\) 2.21433e6 + 1.27844e6i 1.23764 + 0.714551i 0.968611 0.248582i \(-0.0799645\pi\)
0.269027 + 0.963133i \(0.413298\pi\)
\(318\) 0 0
\(319\) −881606. + 508995.i −0.485063 + 0.280051i
\(320\) −5183.07 + 1570.25i −0.00282952 + 0.000857224i
\(321\) 0 0
\(322\) −3.33748e6 127682.i −1.79382 0.0686263i
\(323\) −196569. −0.104836
\(324\) 0 0
\(325\) −274371. −0.144089
\(326\) 1.84530e6 + 70596.1i 0.961666 + 0.0367906i
\(327\) 0 0
\(328\) −261445. 603374.i −0.134182 0.309672i
\(329\) −1.91619e6 + 1.10631e6i −0.975999 + 0.563493i
\(330\) 0 0
\(331\) 1.38965e6 + 802314.i 0.697164 + 0.402508i 0.806290 0.591520i \(-0.201472\pi\)
−0.109126 + 0.994028i \(0.534805\pi\)
\(332\) −1.77518e6 + 2.59436e6i −0.883889 + 1.29177i
\(333\) 0 0
\(334\) 2.32300e6 1.22525e6i 1.13942 0.600979i
\(335\) −2899.52 + 5022.12i −0.00141161 + 0.00244498i
\(336\) 0 0
\(337\) 840067. + 1.45504e6i 0.402939 + 0.697911i 0.994079 0.108658i \(-0.0346554\pi\)
−0.591140 + 0.806569i \(0.701322\pi\)
\(338\) 1.74058e6 + 1.09571e6i 0.828707 + 0.521681i
\(339\) 0 0
\(340\) −194.748 406.138i −9.13639e−5 0.000190536i
\(341\) 915117.i 0.426177i
\(342\) 0 0
\(343\) 3.52851e6i 1.61941i
\(344\) 301934. 406960.i 0.137568 0.185420i
\(345\) 0 0
\(346\) 1.24174e6 1.97255e6i 0.557624 0.885804i
\(347\) 752957. + 1.30416e6i 0.335696 + 0.581443i 0.983618 0.180264i \(-0.0576951\pi\)
−0.647922 + 0.761707i \(0.724362\pi\)
\(348\) 0 0
\(349\) 1.76659e6 3.05983e6i 0.776377 1.34473i −0.157640 0.987497i \(-0.550388\pi\)
0.934017 0.357228i \(-0.116278\pi\)
\(350\) −1.83443e6 3.47796e6i −0.800443 1.51759i
\(351\) 0 0
\(352\) 2.88342e6 + 2.50251e6i 1.24037 + 1.07651i
\(353\) 83593.0 + 48262.4i 0.0357053 + 0.0206145i 0.517746 0.855534i \(-0.326771\pi\)
−0.482041 + 0.876149i \(0.660104\pi\)
\(354\) 0 0
\(355\) 859.115 496.010i 0.000361810 0.000208891i
\(356\) 46889.7 611927.i 0.0196089 0.255902i
\(357\) 0 0
\(358\) 19770.3 516774.i 0.00815278 0.213105i
\(359\) −1.43721e6 −0.588552 −0.294276 0.955720i \(-0.595078\pi\)
−0.294276 + 0.955720i \(0.595078\pi\)
\(360\) 0 0
\(361\) −2.85126e6 −1.15151
\(362\) 152562. 3.98781e6i 0.0611892 1.59942i
\(363\) 0 0
\(364\) 47747.5 623121.i 0.0188885 0.246501i
\(365\) 4709.44 2719.00i 0.00185028 0.00106826i
\(366\) 0 0
\(367\) −2.46407e6 1.42263e6i −0.954968 0.551351i −0.0603472 0.998177i \(-0.519221\pi\)
−0.894621 + 0.446827i \(0.852554\pi\)
\(368\) 984525. + 2.53348e6i 0.378972 + 0.975211i
\(369\) 0 0
\(370\) 1921.21 + 3642.50i 0.000729576 + 0.00138323i
\(371\) 1.68324e6 2.91545e6i 0.634907 1.09969i
\(372\) 0 0
\(373\) −1.92380e6 3.33212e6i −0.715959 1.24008i −0.962589 0.270967i \(-0.912657\pi\)
0.246630 0.969110i \(-0.420677\pi\)
\(374\) −169163. + 268721.i −0.0625354 + 0.0993395i
\(375\) 0 0
\(376\) 1.44611e6 + 1.07291e6i 0.527512 + 0.391375i
\(377\) 135607.i 0.0491391i
\(378\) 0 0
\(379\) 1.26215e6i 0.451351i −0.974202 0.225676i \(-0.927541\pi\)
0.974202 0.225676i \(-0.0724589\pi\)
\(380\) −5278.00 11007.1i −0.00187504 0.00391032i
\(381\) 0 0
\(382\) −623445. 392466.i −0.218595 0.137608i
\(383\) −819424. 1.41928e6i −0.285438 0.494393i 0.687277 0.726395i \(-0.258806\pi\)
−0.972715 + 0.232002i \(0.925472\pi\)
\(384\) 0 0
\(385\) 12115.2 20984.2i 0.00416563 0.00721508i
\(386\) 2.29359e6 1.20974e6i 0.783516 0.413260i
\(387\) 0 0
\(388\) 350469. 512196.i 0.118187 0.172726i
\(389\) −2.12915e6 1.22927e6i −0.713400 0.411881i 0.0989190 0.995095i \(-0.468462\pi\)
−0.812318 + 0.583214i \(0.801795\pi\)
\(390\) 0 0
\(391\) −195771. + 113028.i −0.0647599 + 0.0373891i
\(392\) 5.42641e6 2.35129e6i 1.78360 0.772842i
\(393\) 0 0
\(394\) 2.74017e6 + 104831.i 0.889277 + 0.0340212i
\(395\) 4562.99 0.00147149
\(396\) 0 0
\(397\) 176766. 0.0562890 0.0281445 0.999604i \(-0.491040\pi\)
0.0281445 + 0.999604i \(0.491040\pi\)
\(398\) 3.48432e6 + 133300.i 1.10258 + 0.0421816i
\(399\) 0 0
\(400\) −2.00353e6 + 2.49513e6i −0.626103 + 0.779729i
\(401\) 3.74356e6 2.16134e6i 1.16258 0.671217i 0.210661 0.977559i \(-0.432438\pi\)
0.951921 + 0.306342i \(0.0991051\pi\)
\(402\) 0 0
\(403\) 105571. + 60951.4i 0.0323804 + 0.0186948i
\(404\) −556303. 380649.i −0.169573 0.116030i
\(405\) 0 0
\(406\) 1.71897e6 906658.i 0.517551 0.272979i
\(407\) 1.45158e6 2.51422e6i 0.434366 0.752344i
\(408\) 0 0
\(409\) 205225. + 355461.i 0.0606629 + 0.105071i 0.894762 0.446544i \(-0.147345\pi\)
−0.834099 + 0.551615i \(0.814012\pi\)
\(410\) 2874.21 + 1809.35i 0.000844420 + 0.000531573i
\(411\) 0 0
\(412\) 3.63628e6 1.74364e6i 1.05539 0.506072i
\(413\) 7.66444e6i 2.21108i
\(414\) 0 0
\(415\) 16235.9i 0.00462761i
\(416\) −480748. + 165962.i −0.136202 + 0.0470192i
\(417\) 0 0
\(418\) −4.58461e6 + 7.28280e6i −1.28340 + 2.03872i
\(419\) 1.14156e6 + 1.97723e6i 0.317660 + 0.550203i 0.979999 0.199001i \(-0.0637697\pi\)
−0.662340 + 0.749204i \(0.730436\pi\)
\(420\) 0 0
\(421\) 586612. 1.01604e6i 0.161304 0.279387i −0.774032 0.633146i \(-0.781763\pi\)
0.935337 + 0.353759i \(0.115097\pi\)
\(422\) −1.18336e6 2.24357e6i −0.323471 0.613281i
\(423\) 0 0
\(424\) −2.72166e6 313593.i −0.735223 0.0847133i
\(425\) −230481. 133068.i −0.0618961 0.0357357i
\(426\) 0 0
\(427\) 8.54288e6 4.93223e6i 2.26743 1.30910i
\(428\) 4.71967e6 + 361651.i 1.24538 + 0.0954291i
\(429\) 0 0
\(430\) −100.053 + 2615.29i −2.60952e−5 + 0.000682100i
\(431\) −6.84835e6 −1.77579 −0.887897 0.460042i \(-0.847834\pi\)
−0.887897 + 0.460042i \(0.847834\pi\)
\(432\) 0 0
\(433\) −1.99773e6 −0.512054 −0.256027 0.966670i \(-0.582414\pi\)
−0.256027 + 0.966670i \(0.582414\pi\)
\(434\) −66787.3 + 1.74575e6i −0.0170204 + 0.444895i
\(435\) 0 0
\(436\) −3.86613e6 296247.i −0.974002 0.0746343i
\(437\) −5.30573e6 + 3.06326e6i −1.32905 + 0.767328i
\(438\) 0 0
\(439\) −4.92061e6 2.84091e6i −1.21859 0.703553i −0.253973 0.967211i \(-0.581737\pi\)
−0.964616 + 0.263659i \(0.915071\pi\)
\(440\) −19589.4 2257.12i −0.00482380 0.000555805i
\(441\) 0 0
\(442\) −19733.4 37413.3i −0.00480448 0.00910900i
\(443\) −1.18053e6 + 2.04473e6i −0.285803 + 0.495025i −0.972804 0.231632i \(-0.925594\pi\)
0.687001 + 0.726657i \(0.258927\pi\)
\(444\) 0 0
\(445\) 1584.88 + 2745.09i 0.000379399 + 0.000657139i
\(446\) −167144. + 265514.i −0.0397881 + 0.0632047i
\(447\) 0 0
\(448\) −5.31801e6 4.98442e6i −1.25186 1.17333i
\(449\) 1.40173e6i 0.328132i −0.986449 0.164066i \(-0.947539\pi\)
0.986449 0.164066i \(-0.0524610\pi\)
\(450\) 0 0
\(451\) 2.39430e6i 0.554291i
\(452\) 3.42650e6 1.64304e6i 0.788868 0.378270i
\(453\) 0 0
\(454\) 2.96252e6 + 1.86494e6i 0.674562 + 0.424645i
\(455\) 1613.87 + 2795.31i 0.000365461 + 0.000632997i
\(456\) 0 0
\(457\) 431178. 746822.i 0.0965753 0.167273i −0.813690 0.581300i \(-0.802544\pi\)
0.910265 + 0.414026i \(0.135878\pi\)
\(458\) −790492. + 416940.i −0.176090 + 0.0928773i
\(459\) 0 0
\(460\) −11585.7 7927.49i −0.00255286 0.00174679i
\(461\) −3.31136e6 1.91182e6i −0.725696 0.418981i 0.0911497 0.995837i \(-0.470946\pi\)
−0.816845 + 0.576857i \(0.804279\pi\)
\(462\) 0 0
\(463\) −1.52485e6 + 880372.i −0.330578 + 0.190860i −0.656098 0.754676i \(-0.727794\pi\)
0.325519 + 0.945535i \(0.394461\pi\)
\(464\) −1.23321e6 990237.i −0.265914 0.213523i
\(465\) 0 0
\(466\) 4.66016e6 + 178284.i 0.994113 + 0.0380319i
\(467\) 3.33201e6 0.706991 0.353496 0.935436i \(-0.384993\pi\)
0.353496 + 0.935436i \(0.384993\pi\)
\(468\) 0 0
\(469\) −7.80465e6 −1.63841
\(470\) −9293.29 355.534i −0.00194055 7.42399e-5i
\(471\) 0 0
\(472\) 5.72321e6 2.47989e6i 1.18246 0.512363i
\(473\) 1.59787e6 922530.i 0.328389 0.189595i
\(474\) 0 0
\(475\) −6.24644e6 3.60639e6i −1.27028 0.733395i
\(476\) 342320. 500287.i 0.0692493 0.101205i
\(477\) 0 0
\(478\) 2.27767e6 1.20134e6i 0.455954 0.240490i
\(479\) −287756. + 498407.i −0.0573040 + 0.0992535i −0.893254 0.449552i \(-0.851584\pi\)
0.835950 + 0.548805i \(0.184917\pi\)
\(480\) 0 0
\(481\) 193366. + 334919.i 0.0381080 + 0.0660050i
\(482\) 1.28334e6 + 807876.i 0.251607 + 0.158390i
\(483\) 0 0
\(484\) 3.78229e6 + 7.88782e6i 0.733908 + 1.53054i
\(485\) 3205.41i 0.000618770i
\(486\) 0 0
\(487\) 8.10529e6i 1.54863i 0.632803 + 0.774313i \(0.281904\pi\)
−0.632803 + 0.774313i \(0.718096\pi\)
\(488\) −6.44713e6 4.78330e6i −1.22551 0.909239i
\(489\) 0 0
\(490\) −16272.3 + 25849.0i −0.00306167 + 0.00486356i
\(491\) −747070. 1.29396e6i −0.139848 0.242225i 0.787591 0.616199i \(-0.211328\pi\)
−0.927439 + 0.373974i \(0.877995\pi\)
\(492\) 0 0
\(493\) 65768.5 113914.i 0.0121871 0.0211087i
\(494\) −534810. 1.01397e6i −0.0986012 0.186942i
\(495\) 0 0
\(496\) 1.32520e6 514980.i 0.241868 0.0939910i
\(497\) 1.15624e6 + 667555.i 0.209970 + 0.121226i
\(498\) 0 0
\(499\) 2.62531e6 1.51572e6i 0.471985 0.272501i −0.245085 0.969502i \(-0.578816\pi\)
0.717070 + 0.697001i \(0.245483\pi\)
\(500\) 2525.46 32958.1i 0.000451768 0.00589573i
\(501\) 0 0
\(502\) −228681. + 5.97746e6i −0.0405014 + 1.05866i
\(503\) −7.87121e6 −1.38714 −0.693572 0.720388i \(-0.743964\pi\)
−0.693572 + 0.720388i \(0.743964\pi\)
\(504\) 0 0
\(505\) 3481.44 0.000607478
\(506\) −378340. + 9.88941e6i −0.0656911 + 1.71709i
\(507\) 0 0
\(508\) −526064. + 6.86531e6i −0.0904439 + 1.18032i
\(509\) −5.38888e6 + 3.11127e6i −0.921942 + 0.532284i −0.884254 0.467006i \(-0.845333\pi\)
−0.0376882 + 0.999290i \(0.511999\pi\)
\(510\) 0 0
\(511\) 6.33821e6 + 3.65936e6i 1.07378 + 0.619945i
\(512\) −2.00130e6 + 5.58383e6i −0.337393 + 0.941364i
\(513\) 0 0
\(514\) −57278.4 108596.i −0.00956275 0.0181304i
\(515\) −10414.1 + 18037.8i −0.00173024 + 0.00299686i
\(516\) 0 0
\(517\) 3.27816e6 + 5.67795e6i 0.539392 + 0.934254i
\(518\) −2.95265e6 + 4.69038e6i −0.483490 + 0.768039i
\(519\) 0 0
\(520\) 1565.14 2109.56i 0.000253831 0.000342124i
\(521\) 636052.i 0.102659i 0.998682 + 0.0513296i \(0.0163459\pi\)
−0.998682 + 0.0513296i \(0.983654\pi\)
\(522\) 0 0
\(523\) 5.87088e6i 0.938531i 0.883057 + 0.469266i \(0.155481\pi\)
−0.883057 + 0.469266i \(0.844519\pi\)
\(524\) −3.40973e6 7.11085e6i −0.542489 1.13134i
\(525\) 0 0
\(526\) −9.94124e6 6.25813e6i −1.56667 0.986235i
\(527\) 59122.2 + 102403.i 0.00927309 + 0.0160615i
\(528\) 0 0
\(529\) −304621. + 527619.i −0.0473283 + 0.0819749i
\(530\) 12515.7 6601.31i 0.00193537 0.00102080i
\(531\) 0 0
\(532\) 9.27748e6 1.35586e7i 1.42119 2.07700i
\(533\) 276215. + 159473.i 0.0421142 + 0.0243147i
\(534\) 0 0
\(535\) −21172.4 + 12223.9i −0.00319805 + 0.00184639i
\(536\) 2.52526e6 + 5.82791e6i 0.379659 + 0.876196i
\(537\) 0 0
\(538\) 990106. + 37878.6i 0.147478 + 0.00564207i
\(539\) 2.15330e7 3.19252
\(540\) 0 0
\(541\) 2.16059e6 0.317380 0.158690 0.987328i \(-0.449273\pi\)
0.158690 + 0.987328i \(0.449273\pi\)
\(542\) −5.23451e6 200257.i −0.765382 0.0292813i
\(543\) 0 0
\(544\) −484336. 93746.5i −0.0701697 0.0135818i
\(545\) 17343.4 10013.2i 0.00250117 0.00144405i
\(546\) 0 0
\(547\) 6.31053e6 + 3.64339e6i 0.901774 + 0.520639i 0.877775 0.479073i \(-0.159027\pi\)
0.0239984 + 0.999712i \(0.492360\pi\)
\(548\) 5.55777e6 + 3.80289e6i 0.790586 + 0.540957i
\(549\) 0 0
\(550\) −1.03057e7 + 5.43566e6i −1.45268 + 0.766206i
\(551\) 1.78244e6 3.08728e6i 0.250113 0.433209i
\(552\) 0 0
\(553\) 3.07055e6 + 5.31834e6i 0.426976 + 0.739543i
\(554\) −5.37270e6 3.38218e6i −0.743734 0.468190i
\(555\) 0 0
\(556\) −8.19748e6 + 3.93077e6i −1.12459 + 0.539251i
\(557\) 296984.i 0.0405598i −0.999794 0.0202799i \(-0.993544\pi\)
0.999794 0.0202799i \(-0.00645573\pi\)
\(558\) 0 0
\(559\) 245781.i 0.0332674i
\(560\) 37205.6 + 5735.53i 0.00501346 + 0.000772865i
\(561\) 0 0
\(562\) 6.06644e6 9.63674e6i 0.810202 1.28703i
\(563\) −345248. 597988.i −0.0459051 0.0795099i 0.842160 0.539228i \(-0.181284\pi\)
−0.888065 + 0.459718i \(0.847951\pi\)
\(564\) 0 0
\(565\) −9813.33 + 16997.2i −0.00129329 + 0.00224004i
\(566\) −85736.1 162550.i −0.0112492 0.0213278i
\(567\) 0 0
\(568\) 124368. 1.07938e6i 0.0161748 0.140380i
\(569\) 3.83851e6 + 2.21616e6i 0.497029 + 0.286960i 0.727486 0.686123i \(-0.240689\pi\)
−0.230457 + 0.973083i \(0.574022\pi\)
\(570\) 0 0
\(571\) 4.13165e6 2.38541e6i 0.530314 0.306177i −0.210831 0.977523i \(-0.567617\pi\)
0.741144 + 0.671346i \(0.234283\pi\)
\(572\) −1.84639e6 141483.i −0.235958 0.0180806i
\(573\) 0 0
\(574\) −174742. + 4.56756e6i −0.0221369 + 0.578635i
\(575\) −8.29478e6 −1.04625
\(576\) 0 0
\(577\) −2.33515e6 −0.291995 −0.145998 0.989285i \(-0.546639\pi\)
−0.145998 + 0.989285i \(0.546639\pi\)
\(578\) −305485. + 7.98505e6i −0.0380339 + 0.994164i
\(579\) 0 0
\(580\) 8144.68 + 624.097i 0.00100532 + 7.70340e-5i
\(581\) 1.89236e7 1.09256e7i 2.32575 1.34278i
\(582\) 0 0
\(583\) −8.63888e6 4.98766e6i −1.05266 0.607751i
\(584\) 681753. 5.91690e6i 0.0827171 0.717897i
\(585\) 0 0
\(586\) 5.17657e6 + 9.81445e6i 0.622727 + 1.18065i
\(587\) −3.03042e6 + 5.24884e6i −0.363001 + 0.628736i −0.988453 0.151526i \(-0.951581\pi\)
0.625452 + 0.780262i \(0.284914\pi\)
\(588\) 0 0
\(589\) 1.60232e6 + 2.77529e6i 0.190309 + 0.329625i
\(590\) −17162.3 + 27262.9i −0.00202976 + 0.00322434i
\(591\) 0 0
\(592\) 4.45777e6 + 687200.i 0.522773 + 0.0805896i
\(593\) 1.50413e7i 1.75650i −0.478204 0.878249i \(-0.658712\pi\)
0.478204 0.878249i \(-0.341288\pi\)
\(594\) 0 0
\(595\) 3130.88i 0.000362555i
\(596\) 8.55014e6 4.09988e6i 0.985956 0.472776i
\(597\) 0 0
\(598\) −1.11568e6 702331.i −0.127581 0.0803136i
\(599\) 5.82159e6 + 1.00833e7i 0.662941 + 1.14825i 0.979839 + 0.199788i \(0.0640253\pi\)
−0.316898 + 0.948460i \(0.602641\pi\)
\(600\) 0 0
\(601\) 5.34600e6 9.25955e6i 0.603730 1.04569i −0.388520 0.921440i \(-0.627014\pi\)
0.992251 0.124252i \(-0.0396530\pi\)
\(602\) −3.11555e6 + 1.64328e6i −0.350383 + 0.184807i
\(603\) 0 0
\(604\) −1.16274e7 7.95601e6i −1.29685 0.887366i
\(605\) −39127.6 22590.4i −0.00434606 0.00250920i
\(606\) 0 0
\(607\) −1.36860e7 + 7.90159e6i −1.50766 + 0.870448i −0.507700 + 0.861534i \(0.669504\pi\)
−0.999960 + 0.00891441i \(0.997162\pi\)
\(608\) −1.31264e7 2.54069e6i −1.44008 0.278736i
\(609\) 0 0
\(610\) 41431.9 + 1585.06i 0.00450827 + 0.000172473i
\(611\) −873369. −0.0946444
\(612\) 0 0
\(613\) 1.38482e7 1.48848 0.744240 0.667912i \(-0.232812\pi\)
0.744240 + 0.667912i \(0.232812\pi\)
\(614\) 1.30157e7 + 497941.i 1.39330 + 0.0533037i
\(615\) 0 0
\(616\) −1.05514e7 2.43511e7i −1.12037 2.58563i
\(617\) −9.84163e6 + 5.68207e6i −1.04077 + 0.600888i −0.920051 0.391799i \(-0.871853\pi\)
−0.120718 + 0.992687i \(0.538520\pi\)
\(618\) 0 0
\(619\) −5.57020e6 3.21595e6i −0.584311 0.337352i 0.178534 0.983934i \(-0.442865\pi\)
−0.762845 + 0.646582i \(0.776198\pi\)
\(620\) −4146.67 + 6060.18i −0.000433232 + 0.000633150i
\(621\) 0 0
\(622\) 9.01216e6 4.75340e6i 0.934013 0.492639i
\(623\) −2.13301e6 + 3.69448e6i −0.220177 + 0.381359i
\(624\) 0 0
\(625\) −4.88268e6 8.45706e6i −0.499987 0.866003i
\(626\) −1.02305e7 6.44024e6i −1.04343 0.656850i
\(627\) 0 0
\(628\) −565398. 1.17912e6i −0.0572078 0.119305i
\(629\) 375125.i 0.0378050i
\(630\) 0 0
\(631\) 189565.i 0.0189533i 0.999955 + 0.00947664i \(0.00301655\pi\)
−0.999955 + 0.00947664i \(0.996983\pi\)
\(632\) 2.97783e6 4.01364e6i 0.296556 0.399711i
\(633\) 0 0
\(634\) −7.70554e6 + 1.22405e7i −0.761342 + 1.20942i
\(635\) −17781.0 30797.6i −0.00174994 0.00303098i
\(636\) 0 0
\(637\) −1.43421e6 + 2.48412e6i −0.140044 + 0.242563i
\(638\) −2.68655e6 5.09354e6i −0.261303 0.495414i
\(639\) 0 0
\(640\) −7755.31 29638.0i −0.000748427 0.00286022i
\(641\) 1.05418e6 + 608632.i 0.101338 + 0.0585073i 0.549812 0.835288i \(-0.314699\pi\)
−0.448475 + 0.893796i \(0.648033\pi\)
\(642\) 0 0
\(643\) 1.05398e7 6.08518e6i 1.00532 0.580424i 0.0955052 0.995429i \(-0.469553\pi\)
0.909819 + 0.415005i \(0.136220\pi\)
\(644\) 1.44350e6 1.88382e7i 0.137152 1.78988i
\(645\) 0 0
\(646\) 42509.4 1.11115e6i 0.00400777 0.104759i
\(647\) −3.77606e6 −0.354632 −0.177316 0.984154i \(-0.556741\pi\)
−0.177316 + 0.984154i \(0.556741\pi\)
\(648\) 0 0
\(649\) 2.27108e7 2.11651
\(650\) 59334.5 1.55094e6i 0.00550838 0.143983i
\(651\) 0 0
\(652\) −798119. + 1.04157e7i −0.0735273 + 0.959556i
\(653\) 2.34130e6 1.35175e6i 0.214869 0.124055i −0.388703 0.921363i \(-0.627077\pi\)
0.603572 + 0.797308i \(0.293744\pi\)
\(654\) 0 0
\(655\) 35273.5 + 20365.1i 0.00321251 + 0.00185474i
\(656\) 3.46724e6 1.34739e6i 0.314575 0.122246i
\(657\) 0 0
\(658\) −5.83930e6 1.10709e7i −0.525770 0.996828i
\(659\) −2.57880e6 + 4.46661e6i −0.231315 + 0.400649i −0.958195 0.286115i \(-0.907636\pi\)
0.726880 + 0.686764i \(0.240969\pi\)
\(660\) 0 0
\(661\) −2.13265e6 3.69386e6i −0.189853 0.328834i 0.755348 0.655324i \(-0.227468\pi\)
−0.945201 + 0.326489i \(0.894134\pi\)
\(662\) −4.83578e6 + 7.68179e6i −0.428866 + 0.681267i
\(663\) 0 0
\(664\) −1.42813e7 1.05957e7i −1.25703 0.932626i
\(665\) 84852.4i 0.00744063i
\(666\) 0 0
\(667\) 4.09966e6i 0.356807i
\(668\) 6.42364e6 + 1.33963e7i 0.556981 + 1.16156i
\(669\) 0 0
\(670\) −27761.6 17476.3i −0.00238923 0.00150405i
\(671\) −1.46149e7 2.53137e7i −1.25311 2.17045i
\(672\) 0 0
\(673\) −6.22631e6 + 1.07843e7i −0.529899 + 0.917811i 0.469493 + 0.882936i \(0.344437\pi\)
−0.999392 + 0.0348752i \(0.988897\pi\)
\(674\) −8.40659e6 + 4.43400e6i −0.712804 + 0.375964i
\(675\) 0 0
\(676\) −6.57017e6 + 9.60203e6i −0.552981 + 0.808158i
\(677\) 1.63455e7 + 9.43705e6i 1.37065 + 0.791343i 0.991009 0.133793i \(-0.0427156\pi\)
0.379637 + 0.925136i \(0.376049\pi\)
\(678\) 0 0
\(679\) −3.73603e6 + 2.15700e6i −0.310983 + 0.179546i
\(680\) 2337.90 1013.02i 0.000193889 8.40131e-5i
\(681\) 0 0
\(682\) 5.17290e6 + 197900.i 0.425866 + 0.0162924i
\(683\) 1.32651e7 1.08807 0.544036 0.839062i \(-0.316896\pi\)
0.544036 + 0.839062i \(0.316896\pi\)
\(684\) 0 0
\(685\) −34781.5 −0.00283219
\(686\) −1.99457e7 763064.i −1.61822 0.0619086i
\(687\) 0 0
\(688\) 2.23513e6 + 1.79476e6i 0.180025 + 0.144556i
\(689\) 1.15079e6 664407.i 0.0923521 0.0533195i
\(690\) 0 0
\(691\) −4.37907e6 2.52826e6i −0.348889 0.201431i 0.315307 0.948990i \(-0.397893\pi\)
−0.664196 + 0.747559i \(0.731226\pi\)
\(692\) 1.08817e7 + 7.44581e6i 0.863839 + 0.591080i
\(693\) 0 0
\(694\) −7.53488e6 + 3.97422e6i −0.593851 + 0.313223i
\(695\) 23477.2 40663.7i 0.00184367 0.00319334i
\(696\) 0 0
\(697\) 154687. + 267926.i 0.0120607 + 0.0208897i
\(698\) 1.69143e7 + 1.06478e7i 1.31406 + 0.827218i
\(699\) 0 0
\(700\) 2.00566e7 9.61737e6i 1.54708 0.741841i
\(701\) 1.64236e7i 1.26233i −0.775649 0.631165i \(-0.782577\pi\)
0.775649 0.631165i \(-0.217423\pi\)
\(702\) 0 0
\(703\) 1.01666e7i 0.775863i
\(704\) −1.47695e7 + 1.57580e7i −1.12314 + 1.19831i
\(705\) 0 0
\(706\) −290891. + 462090.i −0.0219644 + 0.0348911i
\(707\) 2.34275e6 + 4.05776e6i 0.176269 + 0.305308i
\(708\) 0 0
\(709\) 1.63475e6 2.83147e6i 0.122134 0.211542i −0.798475 0.602028i \(-0.794360\pi\)
0.920609 + 0.390486i \(0.127693\pi\)
\(710\) 2618.02 + 4963.60i 0.000194907 + 0.000369531i
\(711\) 0 0
\(712\) 3.44891e6 + 397388.i 0.254966 + 0.0293775i
\(713\) 3.19162e6 + 1.84268e6i 0.235119 + 0.135746i
\(714\) 0 0
\(715\) 8282.89 4782.13i 0.000605922 0.000349829i
\(716\) 2.91690e6 + 223512.i 0.212637 + 0.0162936i
\(717\) 0 0
\(718\) 310807. 8.12416e6i 0.0224998 0.588122i
\(719\) 1.65702e7 1.19538 0.597689 0.801728i \(-0.296086\pi\)
0.597689 + 0.801728i \(0.296086\pi\)
\(720\) 0 0
\(721\) −2.80318e7 −2.00822
\(722\) 616605. 1.61174e7i 0.0440214 1.15067i
\(723\) 0 0
\(724\) 2.25090e7 + 1.72478e6i 1.59591 + 0.122289i
\(725\) 4.17990e6 2.41327e6i 0.295339 0.170514i
\(726\) 0 0
\(727\) 1.27235e7 + 7.34592e6i 0.892834 + 0.515478i 0.874868 0.484361i \(-0.160948\pi\)
0.0179654 + 0.999839i \(0.494281\pi\)
\(728\) 3.51200e6 + 404658.i 0.245599 + 0.0282982i
\(729\) 0 0
\(730\) 14351.3 + 27209.2i 0.000996744 + 0.00188977i
\(731\) −119202. + 206465.i −0.00825071 + 0.0142907i
\(732\) 0 0
\(733\) −4.45862e6 7.72256e6i −0.306507 0.530886i 0.671089 0.741377i \(-0.265827\pi\)
−0.977596 + 0.210491i \(0.932494\pi\)
\(734\) 8.57462e6 1.36211e7i 0.587455 0.933192i
\(735\) 0 0
\(736\) −1.45340e7 + 5.01736e6i −0.988986 + 0.341414i
\(737\) 2.31263e7i 1.56833i
\(738\) 0 0
\(739\) 1.80178e7i 1.21364i −0.794840 0.606820i \(-0.792445\pi\)
0.794840 0.606820i \(-0.207555\pi\)
\(740\) −21005.5 + 10072.4i −0.00141011 + 0.000676163i
\(741\) 0 0
\(742\) 1.61162e7 + 1.01453e7i 1.07462 + 0.676483i
\(743\) −747641. 1.29495e6i −0.0496845 0.0860561i 0.840114 0.542411i \(-0.182488\pi\)
−0.889798 + 0.456354i \(0.849155\pi\)
\(744\) 0 0
\(745\) −24487.2 + 42413.1i −0.00161640 + 0.00279968i
\(746\) 1.92516e7 1.01541e7i 1.26654 0.668028i
\(747\) 0 0
\(748\) −1.48242e6 1.01434e6i −0.0968762 0.0662873i
\(749\) −2.84948e7 1.64515e7i −1.85593 1.07152i
\(750\) 0 0
\(751\) −1.22754e7 + 7.08720e6i −0.794210 + 0.458537i −0.841443 0.540347i \(-0.818293\pi\)
0.0472327 + 0.998884i \(0.484960\pi\)
\(752\) −6.37758e6 + 7.94244e6i −0.411255 + 0.512164i
\(753\) 0 0
\(754\) 766546. + 29325.9i 0.0491032 + 0.00187855i
\(755\) 72766.1 0.00464582
\(756\) 0 0
\(757\) −2.06134e7 −1.30740 −0.653701 0.756753i \(-0.726784\pi\)
−0.653701 + 0.756753i \(0.726784\pi\)
\(758\) 7.13461e6 + 272950.i 0.451021 + 0.0172548i
\(759\) 0 0
\(760\) 63361.2 27454.7i 0.00397914 0.00172418i
\(761\) −2.19743e7 + 1.26869e7i −1.37548 + 0.794134i −0.991612 0.129254i \(-0.958742\pi\)
−0.383869 + 0.923388i \(0.625408\pi\)
\(762\) 0 0
\(763\) 2.33416e7 + 1.34763e7i 1.45151 + 0.838028i
\(764\) 2.35332e6 3.43928e6i 0.145864 0.213174i
\(765\) 0 0
\(766\) 8.20002e6 4.32504e6i 0.504944 0.266329i
\(767\) −1.51265e6 + 2.61999e6i −0.0928434 + 0.160810i
\(768\) 0 0
\(769\) 7.30670e6 + 1.26556e7i 0.445559 + 0.771732i 0.998091 0.0617604i \(-0.0196715\pi\)
−0.552532 + 0.833492i \(0.686338\pi\)
\(770\) 115998. + 73022.1i 0.00705056 + 0.00443841i
\(771\) 0 0
\(772\) 6.34231e6 + 1.32266e7i 0.383005 + 0.798742i
\(773\) 5.98384e6i 0.360190i 0.983649 + 0.180095i \(0.0576405\pi\)
−0.983649 + 0.180095i \(0.942360\pi\)
\(774\) 0 0