Properties

Label 69.6.c.b.68.17
Level $69$
Weight $6$
Character 69.68
Analytic conductor $11.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,6,Mod(68,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.68");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.0664835671\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 68.17
Character \(\chi\) \(=\) 69.68
Dual form 69.6.c.b.68.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.27619i q^{2} +(11.5059 - 10.5173i) q^{3} +30.3713 q^{4} -80.0597 q^{5} +(13.4221 + 14.6838i) q^{6} -196.848i q^{7} +79.5978i q^{8} +(21.7727 - 242.023i) q^{9} +O(q^{10})\) \(q+1.27619i q^{2} +(11.5059 - 10.5173i) q^{3} +30.3713 q^{4} -80.0597 q^{5} +(13.4221 + 14.6838i) q^{6} -196.848i q^{7} +79.5978i q^{8} +(21.7727 - 242.023i) q^{9} -102.171i q^{10} +20.8886 q^{11} +(349.450 - 319.425i) q^{12} -791.678 q^{13} +251.216 q^{14} +(-921.160 + 842.012i) q^{15} +870.301 q^{16} +174.605 q^{17} +(308.867 + 27.7861i) q^{18} -892.972i q^{19} -2431.52 q^{20} +(-2070.32 - 2264.92i) q^{21} +26.6578i q^{22} +(2039.46 - 1508.96i) q^{23} +(837.154 + 915.846i) q^{24} +3284.55 q^{25} -1010.33i q^{26} +(-2294.91 - 3013.68i) q^{27} -5978.55i q^{28} -5427.01i q^{29} +(-1074.57 - 1175.58i) q^{30} +3748.89 q^{31} +3657.80i q^{32} +(240.343 - 219.692i) q^{33} +222.829i q^{34} +15759.6i q^{35} +(661.265 - 7350.55i) q^{36} +10793.1i q^{37} +1139.60 q^{38} +(-9108.99 + 8326.32i) q^{39} -6372.57i q^{40} -5102.57i q^{41} +(2890.48 - 2642.12i) q^{42} +10175.5i q^{43} +634.414 q^{44} +(-1743.11 + 19376.2i) q^{45} +(1925.72 + 2602.74i) q^{46} -2207.39i q^{47} +(10013.6 - 9153.22i) q^{48} -21942.3 q^{49} +4191.71i q^{50} +(2008.99 - 1836.37i) q^{51} -24044.3 q^{52} +38439.7 q^{53} +(3846.04 - 2928.75i) q^{54} -1672.33 q^{55} +15668.7 q^{56} +(-9391.65 - 10274.5i) q^{57} +6925.91 q^{58} +49618.2i q^{59} +(-27976.9 + 25573.0i) q^{60} -28860.1i q^{61} +4784.31i q^{62} +(-47641.8 - 4285.92i) q^{63} +23181.6 q^{64} +63381.5 q^{65} +(280.369 + 306.723i) q^{66} +61124.2i q^{67} +5302.99 q^{68} +(7595.69 - 38811.6i) q^{69} -20112.3 q^{70} +11772.5i q^{71} +(19264.5 + 1733.06i) q^{72} +48746.9 q^{73} -13774.0 q^{74} +(37791.8 - 34544.6i) q^{75} -27120.7i q^{76} -4111.89i q^{77} +(-10626.0 - 11624.8i) q^{78} -65855.0i q^{79} -69676.0 q^{80} +(-58100.9 - 10539.0i) q^{81} +6511.86 q^{82} +53578.7 q^{83} +(-62878.2 - 68788.8i) q^{84} -13978.8 q^{85} -12985.9 q^{86} +(-57077.5 - 62442.8i) q^{87} +1662.69i q^{88} -106893. q^{89} +(-24727.8 - 2224.55i) q^{90} +155841. i q^{91} +(61941.1 - 45829.1i) q^{92} +(43134.5 - 39428.3i) q^{93} +2817.05 q^{94} +71491.0i q^{95} +(38470.2 + 42086.4i) q^{96} -59613.7i q^{97} -28002.6i q^{98} +(454.800 - 5055.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 408 q^{4} - 528 q^{6} - 444 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 408 q^{4} - 528 q^{6} - 444 q^{9} - 2484 q^{12} + 520 q^{13} + 4936 q^{16} + 7188 q^{18} + 18660 q^{24} + 36032 q^{25} - 22032 q^{27} + 6544 q^{31} - 33912 q^{36} - 63912 q^{39} + 54328 q^{46} + 88284 q^{48} - 207664 q^{49} + 46296 q^{52} - 38628 q^{54} - 139296 q^{55} - 184144 q^{58} + 486584 q^{64} - 113580 q^{69} + 37176 q^{70} - 15504 q^{72} - 93896 q^{73} + 249840 q^{75} + 368028 q^{78} - 339372 q^{81} - 23512 q^{82} + 259584 q^{85} + 509928 q^{87} + 82740 q^{93} - 562000 q^{94} + 1404 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.27619i 0.225601i 0.993618 + 0.112800i \(0.0359821\pi\)
−0.993618 + 0.112800i \(0.964018\pi\)
\(3\) 11.5059 10.5173i 0.738106 0.674685i
\(4\) 30.3713 0.949104
\(5\) −80.0597 −1.43215 −0.716075 0.698023i \(-0.754063\pi\)
−0.716075 + 0.698023i \(0.754063\pi\)
\(6\) 13.4221 + 14.6838i 0.152210 + 0.166517i
\(7\) 196.848i 1.51840i −0.650856 0.759201i \(-0.725590\pi\)
0.650856 0.759201i \(-0.274410\pi\)
\(8\) 79.5978i 0.439720i
\(9\) 21.7727 242.023i 0.0895995 0.995978i
\(10\) 102.171i 0.323095i
\(11\) 20.8886 0.0520508 0.0260254 0.999661i \(-0.491715\pi\)
0.0260254 + 0.999661i \(0.491715\pi\)
\(12\) 349.450 319.425i 0.700539 0.640347i
\(13\) −791.678 −1.29924 −0.649621 0.760258i \(-0.725073\pi\)
−0.649621 + 0.760258i \(0.725073\pi\)
\(14\) 251.216 0.342553
\(15\) −921.160 + 842.012i −1.05708 + 0.966251i
\(16\) 870.301 0.849903
\(17\) 174.605 0.146533 0.0732663 0.997312i \(-0.476658\pi\)
0.0732663 + 0.997312i \(0.476658\pi\)
\(18\) 308.867 + 27.7861i 0.224694 + 0.0202137i
\(19\) 892.972i 0.567484i −0.958901 0.283742i \(-0.908424\pi\)
0.958901 0.283742i \(-0.0915759\pi\)
\(20\) −2431.52 −1.35926
\(21\) −2070.32 2264.92i −1.02444 1.12074i
\(22\) 26.6578i 0.0117427i
\(23\) 2039.46 1508.96i 0.803887 0.594781i
\(24\) 837.154 + 915.846i 0.296672 + 0.324560i
\(25\) 3284.55 1.05106
\(26\) 1010.33i 0.293110i
\(27\) −2294.91 3013.68i −0.605838 0.795588i
\(28\) 5978.55i 1.44112i
\(29\) 5427.01i 1.19830i −0.800637 0.599150i \(-0.795505\pi\)
0.800637 0.599150i \(-0.204495\pi\)
\(30\) −1074.57 1175.58i −0.217987 0.238478i
\(31\) 3748.89 0.700647 0.350323 0.936629i \(-0.386072\pi\)
0.350323 + 0.936629i \(0.386072\pi\)
\(32\) 3657.80i 0.631459i
\(33\) 240.343 219.692i 0.0384190 0.0351179i
\(34\) 222.829i 0.0330579i
\(35\) 15759.6i 2.17458i
\(36\) 661.265 7350.55i 0.0850393 0.945287i
\(37\) 10793.1i 1.29611i 0.761596 + 0.648053i \(0.224416\pi\)
−0.761596 + 0.648053i \(0.775584\pi\)
\(38\) 1139.60 0.128025
\(39\) −9108.99 + 8326.32i −0.958978 + 0.876580i
\(40\) 6372.57i 0.629745i
\(41\) 5102.57i 0.474056i −0.971503 0.237028i \(-0.923827\pi\)
0.971503 0.237028i \(-0.0761733\pi\)
\(42\) 2890.48 2642.12i 0.252840 0.231116i
\(43\) 10175.5i 0.839240i 0.907700 + 0.419620i \(0.137837\pi\)
−0.907700 + 0.419620i \(0.862163\pi\)
\(44\) 634.414 0.0494016
\(45\) −1743.11 + 19376.2i −0.128320 + 1.42639i
\(46\) 1925.72 + 2602.74i 0.134183 + 0.181358i
\(47\) 2207.39i 0.145759i −0.997341 0.0728794i \(-0.976781\pi\)
0.997341 0.0728794i \(-0.0232188\pi\)
\(48\) 10013.6 9153.22i 0.627318 0.573417i
\(49\) −21942.3 −1.30555
\(50\) 4191.71i 0.237119i
\(51\) 2008.99 1836.37i 0.108157 0.0988634i
\(52\) −24044.3 −1.23312
\(53\) 38439.7 1.87971 0.939854 0.341576i \(-0.110961\pi\)
0.939854 + 0.341576i \(0.110961\pi\)
\(54\) 3846.04 2928.75i 0.179485 0.136678i
\(55\) −1672.33 −0.0745446
\(56\) 15668.7 0.667672
\(57\) −9391.65 10274.5i −0.382873 0.418863i
\(58\) 6925.91 0.270338
\(59\) 49618.2i 1.85571i 0.372937 + 0.927856i \(0.378351\pi\)
−0.372937 + 0.927856i \(0.621649\pi\)
\(60\) −27976.9 + 25573.0i −1.00328 + 0.917073i
\(61\) 28860.1i 0.993053i −0.868021 0.496527i \(-0.834608\pi\)
0.868021 0.496527i \(-0.165392\pi\)
\(62\) 4784.31i 0.158067i
\(63\) −47641.8 4285.92i −1.51230 0.136048i
\(64\) 23181.6 0.707445
\(65\) 63381.5 1.86071
\(66\) 280.369 + 306.723i 0.00792263 + 0.00866736i
\(67\) 61124.2i 1.66351i 0.555140 + 0.831757i \(0.312665\pi\)
−0.555140 + 0.831757i \(0.687335\pi\)
\(68\) 5302.99 0.139075
\(69\) 7595.69 38811.6i 0.192063 0.981383i
\(70\) −20112.3 −0.490588
\(71\) 11772.5i 0.277154i 0.990352 + 0.138577i \(0.0442529\pi\)
−0.990352 + 0.138577i \(0.955747\pi\)
\(72\) 19264.5 + 1733.06i 0.437951 + 0.0393987i
\(73\) 48746.9 1.07063 0.535316 0.844652i \(-0.320193\pi\)
0.535316 + 0.844652i \(0.320193\pi\)
\(74\) −13774.0 −0.292403
\(75\) 37791.8 34544.6i 0.775790 0.709132i
\(76\) 27120.7i 0.538602i
\(77\) 4111.89i 0.0790341i
\(78\) −10626.0 11624.8i −0.197757 0.216346i
\(79\) 65855.0i 1.18719i −0.804763 0.593596i \(-0.797708\pi\)
0.804763 0.593596i \(-0.202292\pi\)
\(80\) −69676.0 −1.21719
\(81\) −58100.9 10539.0i −0.983944 0.178478i
\(82\) 6511.86 0.106947
\(83\) 53578.7 0.853683 0.426842 0.904326i \(-0.359626\pi\)
0.426842 + 0.904326i \(0.359626\pi\)
\(84\) −62878.2 68788.8i −0.972304 1.06370i
\(85\) −13978.8 −0.209857
\(86\) −12985.9 −0.189333
\(87\) −57077.5 62442.8i −0.808476 0.884472i
\(88\) 1662.69i 0.0228878i
\(89\) −106893. −1.43045 −0.715227 0.698892i \(-0.753677\pi\)
−0.715227 + 0.698892i \(0.753677\pi\)
\(90\) −24727.8 2224.55i −0.321795 0.0289491i
\(91\) 155841.i 1.97277i
\(92\) 61941.1 45829.1i 0.762973 0.564510i
\(93\) 43134.5 39428.3i 0.517151 0.472716i
\(94\) 2817.05 0.0328833
\(95\) 71491.0i 0.812723i
\(96\) 38470.2 + 42086.4i 0.426036 + 0.466083i
\(97\) 59613.7i 0.643304i −0.946858 0.321652i \(-0.895762\pi\)
0.946858 0.321652i \(-0.104238\pi\)
\(98\) 28002.6i 0.294533i
\(99\) 454.800 5055.51i 0.00466372 0.0518414i
\(100\) 99756.1 0.997561
\(101\) 8155.58i 0.0795521i −0.999209 0.0397760i \(-0.987336\pi\)
0.999209 0.0397760i \(-0.0126644\pi\)
\(102\) 2343.57 + 2563.86i 0.0223037 + 0.0244002i
\(103\) 54139.3i 0.502828i −0.967880 0.251414i \(-0.919104\pi\)
0.967880 0.251414i \(-0.0808956\pi\)
\(104\) 63015.8i 0.571303i
\(105\) 165749. + 181329.i 1.46716 + 1.60507i
\(106\) 49056.4i 0.424064i
\(107\) −60053.1 −0.507079 −0.253540 0.967325i \(-0.581595\pi\)
−0.253540 + 0.967325i \(0.581595\pi\)
\(108\) −69699.5 91529.6i −0.575003 0.755096i
\(109\) 152525.i 1.22963i −0.788670 0.614816i \(-0.789230\pi\)
0.788670 0.614816i \(-0.210770\pi\)
\(110\) 2134.22i 0.0168173i
\(111\) 113514. + 124184.i 0.874463 + 0.956662i
\(112\) 171317.i 1.29049i
\(113\) −25828.9 −0.190287 −0.0951436 0.995464i \(-0.530331\pi\)
−0.0951436 + 0.995464i \(0.530331\pi\)
\(114\) 13112.2 11985.6i 0.0944959 0.0863766i
\(115\) −163278. + 120807.i −1.15129 + 0.851817i
\(116\) 164826.i 1.13731i
\(117\) −17237.0 + 191604.i −0.116412 + 1.29402i
\(118\) −63322.3 −0.418651
\(119\) 34370.7i 0.222496i
\(120\) −67022.3 73322.3i −0.424880 0.464818i
\(121\) −160615. −0.997291
\(122\) 36831.0 0.224034
\(123\) −53665.3 58709.8i −0.319838 0.349903i
\(124\) 113859. 0.664987
\(125\) −12773.4 −0.0731192
\(126\) 5469.65 60800.1i 0.0306926 0.341175i
\(127\) 234394. 1.28955 0.644775 0.764373i \(-0.276951\pi\)
0.644775 + 0.764373i \(0.276951\pi\)
\(128\) 146634.i 0.791059i
\(129\) 107019. + 117079.i 0.566223 + 0.619447i
\(130\) 80886.9i 0.419778i
\(131\) 50125.1i 0.255198i −0.991826 0.127599i \(-0.959273\pi\)
0.991826 0.127599i \(-0.0407270\pi\)
\(132\) 7299.52 6672.33i 0.0364636 0.0333305i
\(133\) −175780. −0.861669
\(134\) −78006.3 −0.375290
\(135\) 183730. + 241275.i 0.867651 + 1.13940i
\(136\) 13898.2i 0.0644333i
\(137\) 346120. 1.57553 0.787763 0.615979i \(-0.211239\pi\)
0.787763 + 0.615979i \(0.211239\pi\)
\(138\) 49531.0 + 9693.56i 0.221401 + 0.0433297i
\(139\) 5881.35 0.0258191 0.0129095 0.999917i \(-0.495891\pi\)
0.0129095 + 0.999917i \(0.495891\pi\)
\(140\) 478641.i 2.06390i
\(141\) −23215.8 25398.1i −0.0983413 0.107585i
\(142\) −15023.9 −0.0625262
\(143\) −16537.0 −0.0676266
\(144\) 18948.8 210632.i 0.0761509 0.846485i
\(145\) 434485.i 1.71615i
\(146\) 62210.5i 0.241536i
\(147\) −252467. + 230774.i −0.963631 + 0.880833i
\(148\) 327800.i 1.23014i
\(149\) −153793. −0.567505 −0.283753 0.958898i \(-0.591579\pi\)
−0.283753 + 0.958898i \(0.591579\pi\)
\(150\) 44085.5 + 48229.6i 0.159981 + 0.175019i
\(151\) −90252.7 −0.322120 −0.161060 0.986945i \(-0.551491\pi\)
−0.161060 + 0.986945i \(0.551491\pi\)
\(152\) 71078.6 0.249534
\(153\) 3801.62 42258.4i 0.0131293 0.145943i
\(154\) 5247.56 0.0178302
\(155\) −300135. −1.00343
\(156\) −276652. + 252881.i −0.910170 + 0.831966i
\(157\) 259521.i 0.840280i −0.907459 0.420140i \(-0.861981\pi\)
0.907459 0.420140i \(-0.138019\pi\)
\(158\) 84043.6 0.267832
\(159\) 442285. 404282.i 1.38742 1.26821i
\(160\) 292842.i 0.904344i
\(161\) −297036. 401464.i −0.903118 1.22062i
\(162\) 13449.7 74147.9i 0.0402649 0.221979i
\(163\) 223631. 0.659271 0.329635 0.944108i \(-0.393074\pi\)
0.329635 + 0.944108i \(0.393074\pi\)
\(164\) 154972.i 0.449928i
\(165\) −19241.7 + 17588.4i −0.0550218 + 0.0502941i
\(166\) 68376.7i 0.192592i
\(167\) 635080.i 1.76213i −0.472998 0.881064i \(-0.656828\pi\)
0.472998 0.881064i \(-0.343172\pi\)
\(168\) 180283. 164793.i 0.492812 0.450468i
\(169\) 255461. 0.688032
\(170\) 17839.7i 0.0473439i
\(171\) −216119. 19442.4i −0.565202 0.0508463i
\(172\) 309044.i 0.796526i
\(173\) 273947.i 0.695907i 0.937512 + 0.347953i \(0.113123\pi\)
−0.937512 + 0.347953i \(0.886877\pi\)
\(174\) 79689.0 72841.9i 0.199538 0.182393i
\(175\) 646558.i 1.59593i
\(176\) 18179.3 0.0442381
\(177\) 521849. + 570903.i 1.25202 + 1.36971i
\(178\) 136416.i 0.322712i
\(179\) 100929.i 0.235442i −0.993047 0.117721i \(-0.962441\pi\)
0.993047 0.117721i \(-0.0375589\pi\)
\(180\) −52940.7 + 588483.i −0.121789 + 1.35379i
\(181\) 347500.i 0.788421i −0.919020 0.394211i \(-0.871018\pi\)
0.919020 0.394211i \(-0.128982\pi\)
\(182\) −198883. −0.445060
\(183\) −303530. 332062.i −0.669999 0.732978i
\(184\) 120110. + 162336.i 0.261537 + 0.353485i
\(185\) 864089.i 1.85622i
\(186\) 50318.0 + 55047.9i 0.106645 + 0.116670i
\(187\) 3647.25 0.00762714
\(188\) 67041.4i 0.138340i
\(189\) −593239. + 451750.i −1.20802 + 0.919906i
\(190\) −91236.2 −0.183351
\(191\) −869385. −1.72436 −0.862182 0.506599i \(-0.830903\pi\)
−0.862182 + 0.506599i \(0.830903\pi\)
\(192\) 266725. 243808.i 0.522169 0.477303i
\(193\) 202279. 0.390893 0.195447 0.980714i \(-0.437384\pi\)
0.195447 + 0.980714i \(0.437384\pi\)
\(194\) 76078.5 0.145130
\(195\) 729263. 666602.i 1.37340 1.25539i
\(196\) −666418. −1.23910
\(197\) 812892.i 1.49234i 0.665757 + 0.746169i \(0.268109\pi\)
−0.665757 + 0.746169i \(0.731891\pi\)
\(198\) 6451.80 + 580.413i 0.0116955 + 0.00105214i
\(199\) 40521.5i 0.0725358i 0.999342 + 0.0362679i \(0.0115470\pi\)
−0.999342 + 0.0362679i \(0.988453\pi\)
\(200\) 261443.i 0.462170i
\(201\) 642862. + 703291.i 1.12235 + 1.22785i
\(202\) 10408.1 0.0179470
\(203\) −1.06830e6 −1.81950
\(204\) 61015.8 55773.1i 0.102652 0.0938317i
\(205\) 408510.i 0.678919i
\(206\) 69092.1 0.113438
\(207\) −320797. 526449.i −0.520361 0.853946i
\(208\) −688998. −1.10423
\(209\) 18652.9i 0.0295380i
\(210\) −231411. + 211527.i −0.362105 + 0.330992i
\(211\) 716481. 1.10789 0.553947 0.832552i \(-0.313121\pi\)
0.553947 + 0.832552i \(0.313121\pi\)
\(212\) 1.16747e6 1.78404
\(213\) 123815. + 135453.i 0.186992 + 0.204569i
\(214\) 76639.2i 0.114398i
\(215\) 814650.i 1.20192i
\(216\) 239883. 182670.i 0.349836 0.266399i
\(217\) 737964.i 1.06386i
\(218\) 194651. 0.277406
\(219\) 560879. 512686.i 0.790239 0.722340i
\(220\) −50791.0 −0.0707506
\(221\) −138231. −0.190381
\(222\) −158483. + 144865.i −0.215824 + 0.197280i
\(223\) −145527. −0.195966 −0.0979831 0.995188i \(-0.531239\pi\)
−0.0979831 + 0.995188i \(0.531239\pi\)
\(224\) 720032. 0.958809
\(225\) 71513.4 794935.i 0.0941740 1.04683i
\(226\) 32962.6i 0.0429290i
\(227\) −544805. −0.701740 −0.350870 0.936424i \(-0.614114\pi\)
−0.350870 + 0.936424i \(0.614114\pi\)
\(228\) −285237. 312049.i −0.363387 0.397545i
\(229\) 1734.50i 0.00218567i 0.999999 + 0.00109284i \(0.000347861\pi\)
−0.999999 + 0.00109284i \(0.999652\pi\)
\(230\) −154172. 208374.i −0.192171 0.259732i
\(231\) −43246.0 47311.1i −0.0533231 0.0583355i
\(232\) 431978. 0.526917
\(233\) 309502.i 0.373485i 0.982409 + 0.186742i \(0.0597930\pi\)
−0.982409 + 0.186742i \(0.940207\pi\)
\(234\) −244524. 21997.7i −0.291932 0.0262625i
\(235\) 176723.i 0.208749i
\(236\) 1.50697e6i 1.76126i
\(237\) −692617. 757723.i −0.800981 0.876273i
\(238\) 43863.6 0.0501952
\(239\) 1.15098e6i 1.30339i 0.758483 + 0.651693i \(0.225941\pi\)
−0.758483 + 0.651693i \(0.774059\pi\)
\(240\) −801687. + 732803.i −0.898414 + 0.821220i
\(241\) 1.55779e6i 1.72769i 0.503756 + 0.863846i \(0.331951\pi\)
−0.503756 + 0.863846i \(0.668049\pi\)
\(242\) 204975.i 0.224990i
\(243\) −779346. + 489804.i −0.846671 + 0.532117i
\(244\) 876518.i 0.942511i
\(245\) 1.75670e6 1.86974
\(246\) 74925.0 68487.2i 0.0789385 0.0721559i
\(247\) 706946.i 0.737300i
\(248\) 298404.i 0.308088i
\(249\) 616472. 563503.i 0.630108 0.575968i
\(250\) 16301.3i 0.0164958i
\(251\) 22290.6 0.0223325 0.0111663 0.999938i \(-0.496446\pi\)
0.0111663 + 0.999938i \(0.496446\pi\)
\(252\) −1.44694e6 130169.i −1.43533 0.129124i
\(253\) 42601.4 31520.0i 0.0418430 0.0309588i
\(254\) 299132.i 0.290924i
\(255\) −160839. + 147019.i −0.154896 + 0.141587i
\(256\) 554677. 0.528982
\(257\) 1.38634e6i 1.30929i −0.755935 0.654647i \(-0.772817\pi\)
0.755935 0.654647i \(-0.227183\pi\)
\(258\) −149415. + 136577.i −0.139748 + 0.127740i
\(259\) 2.12460e6 1.96801
\(260\) 1.92498e6 1.76601
\(261\) −1.31346e6 118161.i −1.19348 0.107367i
\(262\) 63969.2 0.0575729
\(263\) 1.66301e6 1.48254 0.741269 0.671208i \(-0.234224\pi\)
0.741269 + 0.671208i \(0.234224\pi\)
\(264\) 17487.0 + 19130.7i 0.0154420 + 0.0168936i
\(265\) −3.07747e6 −2.69203
\(266\) 224329.i 0.194393i
\(267\) −1.22990e6 + 1.12422e6i −1.05583 + 0.965106i
\(268\) 1.85642e6i 1.57885i
\(269\) 1.60222e6i 1.35002i 0.737809 + 0.675010i \(0.235861\pi\)
−0.737809 + 0.675010i \(0.764139\pi\)
\(270\) −307913. + 234474.i −0.257050 + 0.195743i
\(271\) −255594. −0.211411 −0.105705 0.994397i \(-0.533710\pi\)
−0.105705 + 0.994397i \(0.533710\pi\)
\(272\) 151959. 0.124539
\(273\) 1.63902e6 + 1.79309e6i 1.33100 + 1.45612i
\(274\) 441716.i 0.355440i
\(275\) 68609.6 0.0547083
\(276\) 230691. 1.17876e6i 0.182288 0.931434i
\(277\) −922483. −0.722369 −0.361184 0.932494i \(-0.617627\pi\)
−0.361184 + 0.932494i \(0.617627\pi\)
\(278\) 7505.74i 0.00582480i
\(279\) 81623.5 907317.i 0.0627776 0.697828i
\(280\) −1.25443e6 −0.956207
\(281\) 992232. 0.749631 0.374815 0.927100i \(-0.377706\pi\)
0.374815 + 0.927100i \(0.377706\pi\)
\(282\) 32412.8 29627.8i 0.0242714 0.0221859i
\(283\) 292415.i 0.217037i −0.994094 0.108518i \(-0.965389\pi\)
0.994094 0.108518i \(-0.0346106\pi\)
\(284\) 357545.i 0.263048i
\(285\) 751893. + 822570.i 0.548332 + 0.599875i
\(286\) 21104.4i 0.0152566i
\(287\) −1.00443e6 −0.719807
\(288\) 885270. + 79640.1i 0.628919 + 0.0565784i
\(289\) −1.38937e6 −0.978528
\(290\) −554486. −0.387164
\(291\) −626975. 685910.i −0.434028 0.474827i
\(292\) 1.48051e6 1.01614
\(293\) −150873. −0.102670 −0.0513349 0.998681i \(-0.516348\pi\)
−0.0513349 + 0.998681i \(0.516348\pi\)
\(294\) −294512. 322196.i −0.198717 0.217396i
\(295\) 3.97241e6i 2.65766i
\(296\) −859104. −0.569923
\(297\) −47937.4 62951.6i −0.0315343 0.0414110i
\(298\) 196269.i 0.128030i
\(299\) −1.61459e6 + 1.19461e6i −1.04444 + 0.772766i
\(300\) 1.14779e6 1.04917e6i 0.736305 0.673040i
\(301\) 2.00304e6 1.27430
\(302\) 115180.i 0.0726706i
\(303\) −85774.7 93837.5i −0.0536726 0.0587178i
\(304\) 777154.i 0.482306i
\(305\) 2.31053e6i 1.42220i
\(306\) 53929.8 + 4851.59i 0.0329249 + 0.00296197i
\(307\) 1.91204e6 1.15785 0.578924 0.815382i \(-0.303473\pi\)
0.578924 + 0.815382i \(0.303473\pi\)
\(308\) 124883.i 0.0750116i
\(309\) −569399. 622923.i −0.339251 0.371140i
\(310\) 383030.i 0.226375i
\(311\) 1.82521e6i 1.07007i −0.844829 0.535036i \(-0.820298\pi\)
0.844829 0.535036i \(-0.179702\pi\)
\(312\) −662757. 725056.i −0.385450 0.421682i
\(313\) 2.85121e6i 1.64501i 0.568759 + 0.822504i \(0.307424\pi\)
−0.568759 + 0.822504i \(0.692576\pi\)
\(314\) 331199. 0.189568
\(315\) 3.81419e6 + 343129.i 2.16584 + 0.194841i
\(316\) 2.00010e6i 1.12677i
\(317\) 2.10359e6i 1.17575i −0.808953 0.587873i \(-0.799965\pi\)
0.808953 0.587873i \(-0.200035\pi\)
\(318\) 515942. + 564440.i 0.286110 + 0.313004i
\(319\) 113363.i 0.0623725i
\(320\) −1.85591e6 −1.01317
\(321\) −690966. + 631596.i −0.374278 + 0.342119i
\(322\) 512345. 379075.i 0.275374 0.203744i
\(323\) 155917.i 0.0831550i
\(324\) −1.76460e6 320082.i −0.933865 0.169394i
\(325\) −2.60031e6 −1.36558
\(326\) 285397.i 0.148732i
\(327\) −1.60415e6 1.75494e6i −0.829615 0.907598i
\(328\) 406153. 0.208452
\(329\) −434522. −0.221320
\(330\) −22446.2 24556.2i −0.0113464 0.0124130i
\(331\) 1.56186e6 0.783559 0.391779 0.920059i \(-0.371860\pi\)
0.391779 + 0.920059i \(0.371860\pi\)
\(332\) 1.62726e6 0.810234
\(333\) 2.61216e6 + 234994.i 1.29089 + 0.116130i
\(334\) 810484. 0.397538
\(335\) 4.89359e6i 2.38240i
\(336\) −1.80180e6 1.97116e6i −0.870678 0.952521i
\(337\) 1.97846e6i 0.948970i −0.880264 0.474485i \(-0.842634\pi\)
0.880264 0.474485i \(-0.157366\pi\)
\(338\) 326018.i 0.155221i
\(339\) −297185. + 271650.i −0.140452 + 0.128384i
\(340\) −424555. −0.199176
\(341\) 78309.1 0.0364692
\(342\) 24812.2 275810.i 0.0114710 0.127510i
\(343\) 1.01088e6i 0.463943i
\(344\) −809950. −0.369030
\(345\) −608109. + 3.10724e6i −0.275064 + 1.40549i
\(346\) −349609. −0.156997
\(347\) 1.37659e6i 0.613734i 0.951752 + 0.306867i \(0.0992806\pi\)
−0.951752 + 0.306867i \(0.900719\pi\)
\(348\) −1.73352e6 1.89647e6i −0.767328 0.839456i
\(349\) −1.69269e6 −0.743897 −0.371948 0.928253i \(-0.621310\pi\)
−0.371948 + 0.928253i \(0.621310\pi\)
\(350\) 825133. 0.360042
\(351\) 1.81683e6 + 2.38587e6i 0.787130 + 1.03366i
\(352\) 76406.3i 0.0328679i
\(353\) 2.61540e6i 1.11712i 0.829463 + 0.558561i \(0.188647\pi\)
−0.829463 + 0.558561i \(0.811353\pi\)
\(354\) −728582. + 665980.i −0.309008 + 0.282457i
\(355\) 942499.i 0.396927i
\(356\) −3.24648e6 −1.35765
\(357\) −361487. 395467.i −0.150114 0.164225i
\(358\) 128805. 0.0531159
\(359\) 3.58025e6 1.46615 0.733073 0.680150i \(-0.238085\pi\)
0.733073 + 0.680150i \(0.238085\pi\)
\(360\) −1.54231e6 138748.i −0.627212 0.0564248i
\(361\) 1.67870e6 0.677962
\(362\) 443476. 0.177869
\(363\) −1.84802e6 + 1.68923e6i −0.736106 + 0.672857i
\(364\) 4.73309e6i 1.87237i
\(365\) −3.90266e6 −1.53331
\(366\) 423774. 387362.i 0.165361 0.151152i
\(367\) 3.14970e6i 1.22068i 0.792138 + 0.610342i \(0.208968\pi\)
−0.792138 + 0.610342i \(0.791032\pi\)
\(368\) 1.77494e6 1.31325e6i 0.683226 0.505507i
\(369\) −1.23494e6 111097.i −0.472149 0.0424752i
\(370\) 1.10274e6 0.418765
\(371\) 7.56680e6i 2.85415i
\(372\) 1.31005e6 1.19749e6i 0.490830 0.448657i
\(373\) 2.01867e6i 0.751266i 0.926769 + 0.375633i \(0.122575\pi\)
−0.926769 + 0.375633i \(0.877425\pi\)
\(374\) 4654.59i 0.00172069i
\(375\) −146970. + 134342.i −0.0539697 + 0.0493325i
\(376\) 175703. 0.0640930
\(377\) 4.29645e6i 1.55688i
\(378\) −576519. 757087.i −0.207532 0.272531i
\(379\) 1.69715e6i 0.606908i −0.952846 0.303454i \(-0.901860\pi\)
0.952846 0.303454i \(-0.0981399\pi\)
\(380\) 2.17128e6i 0.771359i
\(381\) 2.69693e6 2.46520e6i 0.951824 0.870040i
\(382\) 1.10950e6i 0.389018i
\(383\) −1.88013e6 −0.654924 −0.327462 0.944864i \(-0.606193\pi\)
−0.327462 + 0.944864i \(0.606193\pi\)
\(384\) 1.54219e6 + 1.68716e6i 0.533716 + 0.583885i
\(385\) 329196.i 0.113189i
\(386\) 258147.i 0.0881859i
\(387\) 2.46271e6 + 221549.i 0.835864 + 0.0751954i
\(388\) 1.81055e6i 0.610563i
\(389\) 1.23969e6 0.415373 0.207687 0.978195i \(-0.433407\pi\)
0.207687 + 0.978195i \(0.433407\pi\)
\(390\) 850712. + 930679.i 0.283218 + 0.309841i
\(391\) 356100. 263472.i 0.117796 0.0871549i
\(392\) 1.74656e6i 0.574075i
\(393\) −527181. 576736.i −0.172178 0.188363i
\(394\) −1.03741e6 −0.336673
\(395\) 5.27233e6i 1.70024i
\(396\) 13812.9 153543.i 0.00442636 0.0492029i
\(397\) 556498. 0.177210 0.0886049 0.996067i \(-0.471759\pi\)
0.0886049 + 0.996067i \(0.471759\pi\)
\(398\) −51713.2 −0.0163641
\(399\) −2.02251e6 + 1.84873e6i −0.636003 + 0.581356i
\(400\) 2.85854e6 0.893295
\(401\) −2.64380e6 −0.821047 −0.410523 0.911850i \(-0.634654\pi\)
−0.410523 + 0.911850i \(0.634654\pi\)
\(402\) −897534. + 820415.i −0.277004 + 0.253203i
\(403\) −2.96792e6 −0.910310
\(404\) 247696.i 0.0755032i
\(405\) 4.65154e6 + 843746.i 1.40916 + 0.255608i
\(406\) 1.36335e6i 0.410482i
\(407\) 225452.i 0.0674633i
\(408\) 146171. + 159911.i 0.0434722 + 0.0475586i
\(409\) −3.94099e6 −1.16492 −0.582461 0.812859i \(-0.697910\pi\)
−0.582461 + 0.812859i \(0.697910\pi\)
\(410\) −521337. −0.153165
\(411\) 3.98243e6 3.64025e6i 1.16290 1.06298i
\(412\) 1.64428e6i 0.477236i
\(413\) 9.76726e6 2.81772
\(414\) 671850. 409399.i 0.192651 0.117394i
\(415\) −4.28949e6 −1.22260
\(416\) 2.89580e6i 0.820418i
\(417\) 67670.4 61856.0i 0.0190572 0.0174197i
\(418\) 23804.7 0.00666380
\(419\) −2.63743e6 −0.733917 −0.366958 0.930237i \(-0.619601\pi\)
−0.366958 + 0.930237i \(0.619601\pi\)
\(420\) 5.03401e6 + 5.50721e6i 1.39249 + 1.52338i
\(421\) 599700.i 0.164903i 0.996595 + 0.0824515i \(0.0262750\pi\)
−0.996595 + 0.0824515i \(0.973725\pi\)
\(422\) 914367.i 0.249942i
\(423\) −534239. 48060.8i −0.145172 0.0130599i
\(424\) 3.05972e6i 0.826545i
\(425\) 573499. 0.154014
\(426\) −172864. + 158011.i −0.0461510 + 0.0421855i
\(427\) −5.68106e6 −1.50786
\(428\) −1.82389e6 −0.481271
\(429\) −190274. + 173925.i −0.0499156 + 0.0456267i
\(430\) 1.03965e6 0.271154
\(431\) −6.87699e6 −1.78322 −0.891610 0.452804i \(-0.850424\pi\)
−0.891610 + 0.452804i \(0.850424\pi\)
\(432\) −1.99726e6 2.62281e6i −0.514903 0.676173i
\(433\) 6.73591e6i 1.72654i 0.504743 + 0.863270i \(0.331587\pi\)
−0.504743 + 0.863270i \(0.668413\pi\)
\(434\) 941784. 0.240009
\(435\) 4.56961e6 + 4.99915e6i 1.15786 + 1.26670i
\(436\) 4.63239e6i 1.16705i
\(437\) −1.34746e6 1.82118e6i −0.337529 0.456193i
\(438\) 654286. + 715789.i 0.162961 + 0.178279i
\(439\) 1.75564e6 0.434784 0.217392 0.976084i \(-0.430245\pi\)
0.217392 + 0.976084i \(0.430245\pi\)
\(440\) 133114.i 0.0327787i
\(441\) −477743. + 5.31054e6i −0.116976 + 1.30030i
\(442\) 176409.i 0.0429503i
\(443\) 7.53505e6i 1.82422i 0.409946 + 0.912110i \(0.365547\pi\)
−0.409946 + 0.912110i \(0.634453\pi\)
\(444\) 3.44757e6 + 3.77164e6i 0.829957 + 0.907972i
\(445\) 8.55781e6 2.04863
\(446\) 185720.i 0.0442102i
\(447\) −1.76953e6 + 1.61748e6i −0.418879 + 0.382887i
\(448\) 4.56326e6i 1.07419i
\(449\) 5.86864e6i 1.37379i −0.726755 0.686897i \(-0.758972\pi\)
0.726755 0.686897i \(-0.241028\pi\)
\(450\) 1.01449e6 + 91264.8i 0.236165 + 0.0212458i
\(451\) 106585.i 0.0246750i
\(452\) −784458. −0.180602
\(453\) −1.03844e6 + 949215.i −0.237759 + 0.217330i
\(454\) 695275.i 0.158313i
\(455\) 1.24765e7i 2.82531i
\(456\) 817825. 747555.i 0.184182 0.168357i
\(457\) 5.34684e6i 1.19759i 0.800904 + 0.598793i \(0.204353\pi\)
−0.800904 + 0.598793i \(0.795647\pi\)
\(458\) −2213.55 −0.000493090
\(459\) −400703. 526204.i −0.0887750 0.116580i
\(460\) −4.95898e6 + 3.66906e6i −1.09269 + 0.808463i
\(461\) 5.80691e6i 1.27260i 0.771441 + 0.636301i \(0.219536\pi\)
−0.771441 + 0.636301i \(0.780464\pi\)
\(462\) 60378.0 55190.1i 0.0131605 0.0120297i
\(463\) −4.53602e6 −0.983383 −0.491691 0.870769i \(-0.663621\pi\)
−0.491691 + 0.870769i \(0.663621\pi\)
\(464\) 4.72313e6i 1.01844i
\(465\) −3.45333e6 + 3.15661e6i −0.740638 + 0.677000i
\(466\) −394983. −0.0842586
\(467\) −2.16503e6 −0.459379 −0.229689 0.973264i \(-0.573771\pi\)
−0.229689 + 0.973264i \(0.573771\pi\)
\(468\) −523509. + 5.81927e6i −0.110487 + 1.22816i
\(469\) 1.20322e7 2.52588
\(470\) −225532. −0.0470939
\(471\) −2.72947e6 2.98603e6i −0.566925 0.620215i
\(472\) −3.94950e6 −0.815994
\(473\) 212552.i 0.0436831i
\(474\) 967000. 883912.i 0.197688 0.180702i
\(475\) 2.93301e6i 0.596457i
\(476\) 1.04389e6i 0.211171i
\(477\) 836935. 9.30328e6i 0.168421 1.87215i
\(478\) −1.46887e6 −0.294045
\(479\) −4.63191e6 −0.922403 −0.461202 0.887295i \(-0.652582\pi\)
−0.461202 + 0.887295i \(0.652582\pi\)
\(480\) −3.07991e6 3.36942e6i −0.610148 0.667501i
\(481\) 8.54463e6i 1.68396i
\(482\) −1.98804e6 −0.389769
\(483\) −7.64000e6 1.49520e6i −1.49013 0.291630i
\(484\) −4.87808e6 −0.946533
\(485\) 4.77265e6i 0.921309i
\(486\) −625084. 994595.i −0.120046 0.191010i
\(487\) 9.50630e6 1.81631 0.908153 0.418638i \(-0.137492\pi\)
0.908153 + 0.418638i \(0.137492\pi\)
\(488\) 2.29720e6 0.436665
\(489\) 2.57309e6 2.35200e6i 0.486611 0.444800i
\(490\) 2.24188e6i 0.421815i
\(491\) 4.09756e6i 0.767047i −0.923531 0.383523i \(-0.874711\pi\)
0.923531 0.383523i \(-0.125289\pi\)
\(492\) −1.62989e6 1.78309e6i −0.303560 0.332095i
\(493\) 947583.i 0.175590i
\(494\) −902199. −0.166336
\(495\) −36411.2 + 404742.i −0.00667916 + 0.0742447i
\(496\) 3.26267e6 0.595482
\(497\) 2.31739e6 0.420832
\(498\) 719138. + 786737.i 0.129939 + 0.142153i
\(499\) −1443.25 −0.000259472 −0.000129736 1.00000i \(-0.500041\pi\)
−0.000129736 1.00000i \(0.500041\pi\)
\(500\) −387945. −0.0693978
\(501\) −6.67933e6 7.30718e6i −1.18888 1.30064i
\(502\) 28447.1i 0.00503824i
\(503\) 5.18638e6 0.913996 0.456998 0.889468i \(-0.348925\pi\)
0.456998 + 0.889468i \(0.348925\pi\)
\(504\) 341150. 3.79218e6i 0.0598231 0.664986i
\(505\) 652933.i 0.113931i
\(506\) 40225.5 + 54367.6i 0.00698435 + 0.00943982i
\(507\) 2.93932e6 2.68677e6i 0.507840 0.464205i
\(508\) 7.11887e6 1.22392
\(509\) 4.48149e6i 0.766705i −0.923602 0.383353i \(-0.874769\pi\)
0.923602 0.383353i \(-0.125231\pi\)
\(510\) −187625. 205262.i −0.0319422 0.0349448i
\(511\) 9.59576e6i 1.62565i
\(512\) 5.40015e6i 0.910398i
\(513\) −2.69113e6 + 2.04929e6i −0.451484 + 0.343803i
\(514\) 1.76924e6 0.295378
\(515\) 4.33437e6i 0.720125i
\(516\) 3.25031e6 + 3.55584e6i 0.537404 + 0.587920i
\(517\) 46109.3i 0.00758686i
\(518\) 2.71139e6i 0.443985i
\(519\) 2.88118e6 + 3.15201e6i 0.469518 + 0.513653i
\(520\) 5.04503e6i 0.818192i
\(521\) −1.55720e6 −0.251333 −0.125667 0.992073i \(-0.540107\pi\)
−0.125667 + 0.992073i \(0.540107\pi\)
\(522\) 150796. 1.67623e6i 0.0242221 0.269250i
\(523\) 5.42090e6i 0.866597i 0.901251 + 0.433298i \(0.142650\pi\)
−0.901251 + 0.433298i \(0.857350\pi\)
\(524\) 1.52237e6i 0.242209i
\(525\) −6.80005e6 7.43925e6i −1.07675 1.17796i
\(526\) 2.12232e6i 0.334462i
\(527\) 654576. 0.102668
\(528\) 209170. 191198.i 0.0326524 0.0298468i
\(529\) 1.88244e6 6.15491e6i 0.292470 0.956275i
\(530\) 3.92744e6i 0.607324i
\(531\) 1.20087e7 + 1.08032e6i 1.84825 + 0.166271i
\(532\) −5.33868e6 −0.817814
\(533\) 4.03959e6i 0.615913i
\(534\) −1.43473e6 1.56959e6i −0.217729 0.238195i
\(535\) 4.80783e6 0.726214
\(536\) −4.86535e6 −0.731480
\(537\) −1.06150e6 1.16128e6i −0.158849 0.173781i
\(538\) −2.04473e6 −0.304566
\(539\) −458344. −0.0679547
\(540\) 5.58012e6 + 7.32783e6i 0.823491 + 1.08141i
\(541\) 5.88262e6 0.864127 0.432064 0.901843i \(-0.357786\pi\)
0.432064 + 0.901843i \(0.357786\pi\)
\(542\) 326187.i 0.0476945i
\(543\) −3.65476e6 3.99831e6i −0.531936 0.581938i
\(544\) 638670.i 0.0925293i
\(545\) 1.22111e7i 1.76102i
\(546\) −2.28833e6 + 2.09171e6i −0.328501 + 0.300275i
\(547\) −8.94337e6 −1.27801 −0.639003 0.769204i \(-0.720653\pi\)
−0.639003 + 0.769204i \(0.720653\pi\)
\(548\) 1.05121e7 1.49534
\(549\) −6.98479e6 628361.i −0.989059 0.0889771i
\(550\) 87559.0i 0.0123422i
\(551\) −4.84617e6 −0.680017
\(552\) 3.08931e6 + 604600.i 0.431533 + 0.0844541i
\(553\) −1.29635e7 −1.80264
\(554\) 1.17726e6i 0.162967i
\(555\) −9.08788e6 9.94214e6i −1.25236 1.37008i
\(556\) 178625. 0.0245050
\(557\) −76523.7 −0.0104510 −0.00522550 0.999986i \(-0.501663\pi\)
−0.00522550 + 0.999986i \(0.501663\pi\)
\(558\) 1.15791e6 + 104167.i 0.157431 + 0.0141627i
\(559\) 8.05575e6i 1.09038i
\(560\) 1.37156e7i 1.84818i
\(561\) 41965.0 38359.3i 0.00562963 0.00514592i
\(562\) 1.26628e6i 0.169117i
\(563\) 7.73965e6 1.02908 0.514542 0.857465i \(-0.327962\pi\)
0.514542 + 0.857465i \(0.327962\pi\)
\(564\) −705095. 771374.i −0.0933361 0.102110i
\(565\) 2.06785e6 0.272520
\(566\) 373177. 0.0489637
\(567\) −2.07458e6 + 1.14371e7i −0.271002 + 1.49402i
\(568\) −937062. −0.121870
\(569\) 1.52774e7 1.97819 0.989096 0.147271i \(-0.0470490\pi\)
0.989096 + 0.147271i \(0.0470490\pi\)
\(570\) −1.04976e6 + 959559.i −0.135332 + 0.123704i
\(571\) 1.36736e6i 0.175506i −0.996142 0.0877532i \(-0.972031\pi\)
0.996142 0.0877532i \(-0.0279687\pi\)
\(572\) −502252. −0.0641847
\(573\) −1.00031e7 + 9.14359e6i −1.27276 + 1.16340i
\(574\) 1.28185e6i 0.162389i
\(575\) 6.69870e6 4.95624e6i 0.844930 0.625148i
\(576\) 504725. 5.61046e6i 0.0633867 0.704600i
\(577\) −7.52623e6 −0.941105 −0.470552 0.882372i \(-0.655945\pi\)
−0.470552 + 0.882372i \(0.655945\pi\)
\(578\) 1.77310e6i 0.220757i
\(579\) 2.32741e6 2.12743e6i 0.288520 0.263730i
\(580\) 1.31959e7i 1.62880i
\(581\) 1.05469e7i 1.29624i
\(582\) 875353. 800140.i 0.107121 0.0979171i
\(583\) 802951. 0.0978403
\(584\) 3.88015e6i 0.470778i
\(585\) 1.37998e6 1.53398e7i 0.166719 1.85323i
\(586\) 192543.i 0.0231624i
\(587\) 620332.i 0.0743069i 0.999310 + 0.0371534i \(0.0118290\pi\)
−0.999310 + 0.0371534i \(0.988171\pi\)
\(588\) −7.66775e6 + 7.00892e6i −0.914587 + 0.836003i
\(589\) 3.34766e6i 0.397606i
\(590\) 5.06956e6 0.599571
\(591\) 8.54943e6 + 9.35307e6i 1.00686 + 1.10150i
\(592\) 9.39321e6i 1.10156i
\(593\) 4.96024e6i 0.579250i −0.957140 0.289625i \(-0.906469\pi\)
0.957140 0.289625i \(-0.0935307\pi\)
\(594\) 80338.3 61177.4i 0.00934236 0.00711418i
\(595\) 2.75171e6i 0.318647i
\(596\) −4.67089e6 −0.538622
\(597\) 426177. + 466237.i 0.0489388 + 0.0535391i
\(598\) −1.52455e6 2.06053e6i −0.174337 0.235628i
\(599\) 2.30566e6i 0.262560i −0.991345 0.131280i \(-0.958091\pi\)
0.991345 0.131280i \(-0.0419087\pi\)
\(600\) 2.74967e6 + 3.00814e6i 0.311819 + 0.341130i
\(601\) −3.65731e6 −0.413025 −0.206512 0.978444i \(-0.566211\pi\)
−0.206512 + 0.978444i \(0.566211\pi\)
\(602\) 2.55626e6i 0.287484i
\(603\) 1.47934e7 + 1.33084e6i 1.65682 + 0.149050i
\(604\) −2.74110e6 −0.305726
\(605\) 1.28588e7 1.42827
\(606\) 119755. 109465.i 0.0132468 0.0121086i
\(607\) 5.25634e6 0.579044 0.289522 0.957171i \(-0.406504\pi\)
0.289522 + 0.957171i \(0.406504\pi\)
\(608\) 3.26631e6 0.358343
\(609\) −1.22918e7 + 1.12356e7i −1.34299 + 1.22759i
\(610\) −2.94867e6 −0.320850
\(611\) 1.74754e6i 0.189376i
\(612\) 115460. 1.28344e6i 0.0124610 0.138515i
\(613\) 3.67092e6i 0.394570i 0.980346 + 0.197285i \(0.0632124\pi\)
−0.980346 + 0.197285i \(0.936788\pi\)
\(614\) 2.44013e6i 0.261212i
\(615\) 4.29642e6 + 4.70029e6i 0.458057 + 0.501114i
\(616\) 327297. 0.0347528
\(617\) −1.73511e6 −0.183490 −0.0917451 0.995783i \(-0.529245\pi\)
−0.0917451 + 0.995783i \(0.529245\pi\)
\(618\) 794969. 726663.i 0.0837296 0.0765353i
\(619\) 7.42838e6i 0.779233i 0.920977 + 0.389617i \(0.127393\pi\)
−0.920977 + 0.389617i \(0.872607\pi\)
\(620\) −9.11551e6 −0.952361
\(621\) −9.22790e6 2.68336e6i −0.960226 0.279222i
\(622\) 2.32932e6 0.241409
\(623\) 2.10417e7i 2.17200i
\(624\) −7.92756e6 + 7.24640e6i −0.815038 + 0.745008i
\(625\) −9.24158e6 −0.946338
\(626\) −3.63869e6 −0.371115
\(627\) −196178. 214619.i −0.0199289 0.0218022i
\(628\) 7.88201e6i 0.797513i
\(629\) 1.88452e6i 0.189922i
\(630\) −437899. + 4.86763e6i −0.0439564 + 0.488615i
\(631\) 9.24226e6i 0.924070i 0.886862 + 0.462035i \(0.152880\pi\)
−0.886862 + 0.462035i \(0.847120\pi\)
\(632\) 5.24191e6 0.522032
\(633\) 8.24378e6 7.53545e6i 0.817743 0.747480i
\(634\) 2.68459e6 0.265249
\(635\) −1.87655e7 −1.84683
\(636\) 1.34328e7 1.22786e7i 1.31681 1.20366i
\(637\) 1.73713e7 1.69622
\(638\) 144672. 0.0140713
\(639\) 2.84920e6 + 256318.i 0.276039 + 0.0248329i
\(640\) 1.17394e7i 1.13292i
\(641\) 8.97691e6 0.862942 0.431471 0.902127i \(-0.357995\pi\)
0.431471 + 0.902127i \(0.357995\pi\)
\(642\) −806038. 881805.i −0.0771823 0.0844374i
\(643\) 5.63467e6i 0.537453i 0.963216 + 0.268727i \(0.0866029\pi\)
−0.963216 + 0.268727i \(0.913397\pi\)
\(644\) −9.02138e6 1.21930e7i −0.857153 1.15850i
\(645\) −8.56792e6 9.37330e6i −0.810916 0.887142i
\(646\) 198980. 0.0187598
\(647\) 1.01191e7i 0.950349i 0.879892 + 0.475174i \(0.157615\pi\)
−0.879892 + 0.475174i \(0.842385\pi\)
\(648\) 838878. 4.62470e6i 0.0784804 0.432660i
\(649\) 1.03645e6i 0.0965913i
\(650\) 3.31849e6i 0.308075i
\(651\) −7.76139e6 8.49096e6i −0.717773 0.785244i
\(652\) 6.79198e6 0.625717
\(653\) 4.41505e6i 0.405184i 0.979263 + 0.202592i \(0.0649365\pi\)
−0.979263 + 0.202592i \(0.935063\pi\)
\(654\) 2.23964e6 2.04721e6i 0.204755 0.187162i
\(655\) 4.01300e6i 0.365482i
\(656\) 4.44077e6i 0.402901i
\(657\) 1.06135e6 1.17979e7i 0.0959281 1.06633i
\(658\) 554533.i 0.0499301i
\(659\) 7.07020e6 0.634188 0.317094 0.948394i \(-0.397293\pi\)
0.317094 + 0.948394i \(0.397293\pi\)
\(660\) −584397. + 534184.i −0.0522214 + 0.0477344i
\(661\) 1.36132e6i 0.121187i −0.998163 0.0605937i \(-0.980701\pi\)
0.998163 0.0605937i \(-0.0192994\pi\)
\(662\) 1.99323e6i 0.176772i
\(663\) −1.59048e6 + 1.45382e6i −0.140522 + 0.128448i
\(664\) 4.26474e6i 0.375381i
\(665\) 1.40729e7 1.23404
\(666\) −299897. + 3.33362e6i −0.0261991 + 0.291226i
\(667\) −8.18913e6 1.10682e7i −0.712727 0.963299i
\(668\) 1.92882e7i 1.67244i
\(669\) −1.67442e6 + 1.53055e6i −0.144644 + 0.132216i
\(670\) 6.24515e6 0.537472
\(671\) 602846.i 0.0516892i
\(672\) 8.28464e6 7.57280e6i 0.707702 0.646894i
\(673\) 1.60775e7 1.36830 0.684148 0.729344i \(-0.260174\pi\)
0.684148 + 0.729344i \(0.260174\pi\)
\(674\) 2.52489e6 0.214089
\(675\) −7.53774e6 9.89859e6i −0.636769 0.836207i
\(676\) 7.75870e6 0.653014
\(677\) −9.18709e6 −0.770382 −0.385191 0.922837i \(-0.625865\pi\)
−0.385191 + 0.922837i \(0.625865\pi\)
\(678\) −346678. 379265.i −0.0289636 0.0316861i
\(679\) −1.17349e7 −0.976795
\(680\) 1.11268e6i 0.0922782i
\(681\) −6.26848e6 + 5.72988e6i −0.517958 + 0.473454i
\(682\) 99937.4i 0.00822749i
\(683\) 3.89239e6i 0.319275i 0.987176 + 0.159637i \(0.0510325\pi\)
−0.987176 + 0.159637i \(0.948967\pi\)
\(684\) −6.56383e6 590491.i −0.536435 0.0482584i
\(685\) −2.77103e7 −2.25639
\(686\) −1.29008e6 −0.104666
\(687\) 18242.3 + 19957.0i 0.00147464 + 0.00161326i
\(688\) 8.85577e6i 0.713272i
\(689\) −3.04319e7 −2.44220
\(690\) −3.96543e6 776063.i −0.317079 0.0620547i
\(691\) 1.11648e7 0.889518 0.444759 0.895650i \(-0.353289\pi\)
0.444759 + 0.895650i \(0.353289\pi\)
\(692\) 8.32013e6i 0.660488i
\(693\) −995169. 89526.8i −0.0787162 0.00708141i
\(694\) −1.75679e6 −0.138459
\(695\) −470859. −0.0369768
\(696\) 4.97031e6 4.54324e6i 0.388920 0.355503i
\(697\) 890934.i 0.0694646i
\(698\) 2.16019e6i 0.167824i
\(699\) 3.25512e6 + 3.56110e6i 0.251985 + 0.275671i
\(700\) 1.96368e7i 1.51470i
\(701\) 4.27810e6 0.328818 0.164409 0.986392i \(-0.447428\pi\)
0.164409 + 0.986392i \(0.447428\pi\)
\(702\) −3.04483e6 + 2.31862e6i −0.233195 + 0.177577i
\(703\) 9.63790e6 0.735519
\(704\) 484230. 0.0368231
\(705\) 1.85865e6 + 2.03336e6i 0.140840 + 0.154078i
\(706\) −3.33775e6 −0.252024
\(707\) −1.60541e6 −0.120792
\(708\) 1.58493e7 + 1.73391e7i 1.18830 + 1.30000i
\(709\) 4.55553e6i 0.340348i −0.985414 0.170174i \(-0.945567\pi\)
0.985414 0.170174i \(-0.0544330\pi\)
\(710\) 1.20281e6 0.0895470
\(711\) −1.59384e7 1.43384e6i −1.18242 0.106372i
\(712\) 8.50844e6i 0.628999i
\(713\) 7.64571e6 5.65692e6i 0.563241 0.416732i
\(714\) 504692. 461327.i 0.0370494 0.0338660i
\(715\) 1.32395e6 0.0968515
\(716\) 3.06535e6i 0.223459i
\(717\) 1.21052e7 + 1.32431e7i 0.879375 + 0.962036i
\(718\) 4.56909e6i 0.330764i
\(719\) 1.76274e6i 0.127164i 0.997977 + 0.0635821i \(0.0202525\pi\)
−0.997977 + 0.0635821i \(0.979748\pi\)
\(720\) −1.51703e6 + 1.68632e7i −0.109060 + 1.21229i
\(721\) −1.06572e7 −0.763495
\(722\) 2.14234e6i 0.152949i
\(723\) 1.63838e7 + 1.79238e7i 1.16565 + 1.27522i
\(724\) 1.05540e7i 0.748294i
\(725\) 1.78253e7i 1.25948i
\(726\) −2.15579e6 2.35843e6i −0.151797 0.166066i
\(727\) 222075.i 0.0155834i 0.999970 + 0.00779172i \(0.00248021\pi\)
−0.999970 + 0.00779172i \(0.997520\pi\)
\(728\) −1.24046e7 −0.867468
\(729\) −3.81568e6 + 1.38323e7i −0.265921 + 0.963995i
\(730\) 4.98055e6i 0.345915i
\(731\) 1.77670e6i 0.122976i
\(732\) −9.21861e6 1.00852e7i −0.635898 0.695673i
\(733\) 3.03919e6i 0.208929i −0.994529 0.104464i \(-0.966687\pi\)
0.994529 0.104464i \(-0.0333128\pi\)
\(734\) −4.01962e6 −0.275388
\(735\) 2.02124e7 1.84757e7i 1.38007 1.26149i
\(736\) 5.51946e6 + 7.45993e6i 0.375580 + 0.507622i
\(737\) 1.27680e6i 0.0865872i
\(738\) 141781. 1.57602e6i 0.00958244 0.106517i
\(739\) 1.00967e7 0.680096 0.340048 0.940408i \(-0.389557\pi\)
0.340048 + 0.940408i \(0.389557\pi\)
\(740\) 2.62435e7i 1.76174i
\(741\) 7.43517e6 + 8.13407e6i 0.497445 + 0.544205i
\(742\) 9.65669e6 0.643900
\(743\) −5.27625e6 −0.350633 −0.175317 0.984512i \(-0.556095\pi\)
−0.175317 + 0.984512i \(0.556095\pi\)
\(744\) 3.13840e6 + 3.43341e6i 0.207863 + 0.227402i
\(745\) 1.23126e7 0.812753
\(746\) −2.57621e6 −0.169486
\(747\) 1.16655e6 1.29673e7i 0.0764896 0.850250i
\(748\) 110772. 0.00723895
\(749\) 1.18214e7i 0.769950i
\(750\) −171446. 187562.i −0.0111295 0.0121756i
\(751\) 8.55220e6i 0.553322i 0.960968 + 0.276661i \(0.0892279\pi\)
−0.960968 + 0.276661i \(0.910772\pi\)
\(752\) 1.92109e6i 0.123881i
\(753\) 256474. 234437.i 0.0164838 0.0150674i
\(754\) −5.48309e6 −0.351234
\(755\) 7.22560e6 0.461325
\(756\) −1.80175e7 + 1.37202e7i −1.14654 + 0.873086i
\(757\) 2.04752e7i 1.29864i −0.760516 0.649320i \(-0.775054\pi\)
0.760516 0.649320i \(-0.224946\pi\)
\(758\) 2.16589e6 0.136919
\(759\) 158663. 810718.i 0.00999705 0.0510817i
\(760\) −5.69053e6 −0.357370
\(761\) 1.69707e6i 0.106228i −0.998588 0.0531140i \(-0.983085\pi\)
0.998588 0.0531140i \(-0.0169147\pi\)
\(762\) 3.14607e6 + 3.44179e6i 0.196282 + 0.214732i
\(763\) −3.00243e7 −1.86708
\(764\) −2.64044e7 −1.63660
\(765\) −304356. + 3.38319e6i −0.0188031 + 0.209013i
\(766\) 2.39941e6i 0.147751i
\(767\) 3.92816e7i 2.41102i
\(768\) 6.38208e6 5.83371e6i 0.390444 0.356896i
\(769\) 8.50809e6i 0.518819i 0.965767 + 0.259410i \(0.0835280\pi\)
−0.965767 + 0.259410i \(0.916472\pi\)
\(770\) −420117. −0.0255355
\(771\) −1.45806e7 1.59511e7i −0.883361 0.966397i
\(772\) 6.14349e6 0.370998
\(773\) 1.74244e7 1.04884 0.524420 0.851460i \(-0.324282\pi\)
0.524420 + 0.851460i \(0.324282\pi\)
\(774\) −282738. + 3.14289e6i −0.0169642 + 0.188572i
\(775\) 1.23134e7 0.736418
\(776\) 4.74512e6 0.282874
\(777\) 2.44455e7 2.23450e7i 1.45260 1.32779i
\(778\) 1.58208e6i 0.0937087i
\(779\) −4.55645e6 −0.269019
\(780\) 2.21487e7 2.02456e7i 1.30350 1.19150i
\(781\) 245910.i 0.0144261i
\(782\) 336240. + 454451.i 0.0196622 + 0.0265748i
\(783\) −1.63553e7 + 1.24545e7i −0.953354 + 0.725976i
\(784\) −1.90964e7 −1.10959
\(785\) 2.07772e7i 1.20341i
\(786\) 736025. 672784.i 0.0424949 0.0388436i
\(787\) 2.50321e7i 1.44066i −0.693634 0.720328i \(-0.743991\pi\)
0.693634 0.720328i \(-0.256009\pi\)
\(788\) 2.46886e7i 1.41638i
\(789\) 1.91345e7 1.74904e7i 1.09427 1.00025i
\(790\) −6.72850e6 −0.383575
\(791\) 5.08438e6i 0.288933i
\(792\) 402407. + 36201.1i 0.0227957 + 0.00205073i
\(793\) 2.28479e7i 1.29022i
\(794\) 710199.i 0.0399787i
\(795\) −3.54091e7 + 3.23667e7i −1.98700 + 1.81627i
\(796\) 1.23069e6i 0.0688440i
\(797\) −2.04001e7 −1.13759 −0.568797 0.822478i \(-0.692591\pi\)
−0.568797 + 0.822478i \(0.692591\pi\)
\(798\) −2.35934e6 2.58111e6i −0.131154 0.143483i
\(799\) 385422.i 0.0213584i
\(800\) 1.20142e7i 0.663698i
\(801\) −2.32734e6 + 2.58705e7i −0.128168 + 1.42470i
\(802\) 3.37400e6i 0.185229i
\(803\) 1.01825e6 0.0557272
\(804\) 1.95246e7 + 2.13599e7i 1.06523 + 1.16536i
\(805\) 2.37806e7 + 3.21411e7i 1.29340 + 1.74812i
\(806\) 3.78763e6i 0.205367i
\(807\) 1.68510e7 + 1.84350e7i 0.910839 + 0.996457i
\(808\) 649166. 0.0349806
\(809\) 1.70605e7i 0.916475i −0.888830 0.458238i \(-0.848481\pi\)
0.888830 0.458238i \(-0.151519\pi\)
\(810\) −1.07678e6 + 5.93626e6i −0.0576654 + 0.317907i
\(811\) −2.15503e7 −1.15054 −0.575269 0.817964i \(-0.695103\pi\)
−0.575269 + 0.817964i \(0.695103\pi\)
\(812\) −3.24457e7 −1.72690
\(813\) −2.94084e6 + 2.68816e6i −0.156043 + 0.142636i
\(814\) −287720. −0.0152198
\(815\) −1.79039e7 −0.944175
\(816\) 1.74843e6 1.59820e6i 0.0919226 0.0840243i
\(817\) 9.08646e6 0.476255
\(818\) 5.02946e6i 0.262808i
\(819\) 3.77170e7 + 3.39307e6i 1.96484 + 0.176760i
\(820\) 1.24070e7i 0.644365i
\(821\) 1.63166e7i 0.844834i 0.906402 + 0.422417i \(0.138818\pi\)
−0.906402 + 0.422417i \(0.861182\pi\)
\(822\) 4.64566e6 + 5.08235e6i 0.239810 + 0.262352i
\(823\) 1.20206e7 0.618624 0.309312 0.950961i \(-0.399901\pi\)
0.309312 + 0.950961i \(0.399901\pi\)
\(824\) 4.30937e6 0.221103
\(825\) 789417. 721588.i 0.0403805 0.0369109i
\(826\) 1.24649e7i 0.635680i
\(827\) 2.90002e7 1.47447 0.737236 0.675635i \(-0.236131\pi\)
0.737236 + 0.675635i \(0.236131\pi\)
\(828\) −9.74304e6 1.59890e7i −0.493877 0.810484i
\(829\) 4.57153e6 0.231034 0.115517 0.993306i \(-0.463148\pi\)
0.115517 + 0.993306i \(0.463148\pi\)
\(830\) 5.47421e6i 0.275820i
\(831\) −1.06140e7 + 9.70203e6i −0.533184 + 0.487371i
\(832\) −1.83523e7 −0.919143
\(833\) −3.83124e6 −0.191305
\(834\) 78940.1 + 86360.5i 0.00392991 + 0.00429932i
\(835\) 5.08443e7i 2.52363i
\(836\) 566514.i 0.0280346i
\(837\) −8.60338e6 1.12980e7i −0.424478 0.557426i
\(838\) 3.36587e6i 0.165572i
\(839\) 1.67247e7 0.820263 0.410132 0.912026i \(-0.365483\pi\)
0.410132 + 0.912026i \(0.365483\pi\)
\(840\) −1.44334e7 + 1.31932e7i −0.705781 + 0.645139i
\(841\) −8.94131e6 −0.435924
\(842\) −765332. −0.0372023
\(843\) 1.14165e7 1.04356e7i 0.553306 0.505765i
\(844\) 2.17605e7 1.05151
\(845\) −2.04522e7 −0.985365
\(846\) 61334.8 681791.i 0.00294633 0.0327511i
\(847\) 3.16168e7i 1.51429i
\(848\) 3.34541e7 1.59757
\(849\) −3.07541e6 3.36450e6i −0.146431 0.160196i
\(850\) 731894.i 0.0347457i
\(851\) 1.62863e7 + 2.20120e7i 0.770899 + 1.04192i
\(852\) 3.76041e6 + 4.11389e6i 0.177475 + 0.194157i
\(853\) −1.92985e7 −0.908137 −0.454068 0.890967i \(-0.650028\pi\)
−0.454068 + 0.890967i \(0.650028\pi\)
\(854\) 7.25012e6i 0.340174i
\(855\) 1.73024e7 + 1.55655e6i 0.809454 + 0.0728196i
\(856\) 4.78009e6i 0.222973i
\(857\) 1.36216e7i 0.633545i −0.948502 0.316772i \(-0.897401\pi\)
0.948502 0.316772i \(-0.102599\pi\)
\(858\) −221962. 242826.i −0.0102934 0.0112610i
\(859\) 2.08230e7 0.962854 0.481427 0.876486i \(-0.340119\pi\)
0.481427 + 0.876486i \(0.340119\pi\)
\(860\) 2.47420e7i 1.14075i
\(861\) −1.15569e7 + 1.05639e7i −0.531294 + 0.485643i
\(862\) 8.77635e6i 0.402296i
\(863\) 3.02999e7i 1.38489i 0.721473 + 0.692443i \(0.243465\pi\)
−0.721473 + 0.692443i \(0.756535\pi\)
\(864\) 1.10235e7 8.39432e6i 0.502381 0.382562i
\(865\) 2.19321e7i 0.996643i
\(866\) −8.59631e6 −0.389509
\(867\) −1.59860e7 + 1.46124e7i −0.722257 + 0.660199i
\(868\) 2.24130e7i 1.00972i
\(869\) 1.37562e6i 0.0617943i
\(870\) −6.37987e6 + 5.83170e6i −0.285768 + 0.261214i
\(871\) 4.83907e7i 2.16131i
\(872\) 1.21407e7 0.540694
\(873\) −1.44279e7 1.29795e6i −0.640717 0.0576398i
\(874\) 2.32417e6 1.71961e6i 0.102918 0.0761469i
\(875\) 2.51442e6i 0.111024i
\(876\) 1.70346e7 1.55710e7i 0.750020 0.685576i
\(877\) 6.18389e6 0.271496 0.135748 0.990743i \(-0.456656\pi\)
0.135748 + 0.990743i \(0.456656\pi\)
\(878\) 2.24053e6i 0.0980876i
\(879\) −1.73593e6 + 1.58678e6i −0.0757811 + 0.0692698i
\(880\) −1.45543e6 −0.0633557
\(881\) 2.91955e7 1.26729 0.633645 0.773624i \(-0.281558\pi\)
0.633645 + 0.773624i \(0.281558\pi\)
\(882\) −6.77727e6 609692.i −0.293348 0.0263900i
\(883\) −3.67569e7 −1.58649 −0.793244 0.608905i \(-0.791609\pi\)
−0.793244 + 0.608905i \(0.791609\pi\)
\(884\) −4.19826e6 −0.180692
\(885\) −4.17791e7 4.57063e7i −1.79308 1.96163i
\(886\) −9.61617e6 −0.411546
\(887\) 3.76607e7i 1.60724i −0.595145 0.803618i \(-0.702906\pi\)
0.595145 0.803618i \(-0.297094\pi\)
\(888\) −9.88478e6 + 9.03545e6i −0.420663 + 0.384519i
\(889\) 4.61402e7i 1.95806i
\(890\) 1.09214e7i 0.462172i
\(891\) −1.21365e6 220144.i −0.0512151 0.00928993i
\(892\) −4.41985e6 −0.185992
\(893\) −1.97114e6 −0.0827158
\(894\) −2.06422e6 2.25826e6i −0.0863798 0.0944995i
\(895\) 8.08035e6i 0.337188i
\(896\) 2.88646e7 1.20115
\(897\) −6.01335e6 + 3.07263e7i −0.249537 + 1.27505i
\(898\) 7.48951e6 0.309929
\(899\) 2.03453e7i 0.839585i
\(900\) 2.17196e6 2.41432e7i 0.0893810 0.993549i
\(901\) 6.71177e6 0.275439
\(902\) 136024. 0.00556670
\(903\) 2.30468e7 2.10666e7i 0.940571 0.859754i
\(904\) 2.05592e6i 0.0836731i
\(905\) 2.78207e7i 1.12914i
\(906\) −1.21138e6 1.32525e6i −0.0490298 0.0536386i
\(907\) 1.30537e7i 0.526885i 0.964675 + 0.263443i \(0.0848579\pi\)
−0.964675 + 0.263443i \(0.915142\pi\)
\(908\) −1.65464e7 −0.666024
\(909\) −1.97384e6 177569.i −0.0792321 0.00712783i
\(910\) 1.59225e7 0.637393
\(911\) −2.20067e7 −0.878534 −0.439267 0.898357i \(-0.644762\pi\)
−0.439267 + 0.898357i \(0.644762\pi\)
\(912\) −8.17356e6 8.94188e6i −0.325405 0.355993i
\(913\) 1.11918e6 0.0444349
\(914\) −6.82359e6 −0.270176
\(915\) 2.43005e7 + 2.65847e7i 0.959539 + 1.04974i
\(916\) 52679.1i 0.00207443i
\(917\) −9.86705e6 −0.387493
\(918\) 671538. 511374.i 0.0263005 0.0200277i
\(919\) 6.53274e6i 0.255156i 0.991829 + 0.127578i \(0.0407204\pi\)
−0.991829 + 0.127578i \(0.959280\pi\)
\(920\) −9.61594e6 1.29966e7i −0.374561 0.506244i
\(921\) 2.19998e7 2.01095e7i 0.854614 0.781183i
\(922\) −7.41073e6 −0.287100
\(923\) 9.32000e6i 0.360091i
\(924\) −1.31344e6 1.43690e6i −0.0506092 0.0553664i
\(925\) 3.54503e7i 1.36228i
\(926\) 5.78883e6i 0.221852i
\(927\) −1.31029e7 1.17876e6i −0.500806 0.0450531i
\(928\) 1.98509e7 0.756677
\(929\) 1.39556e7i 0.530529i 0.964176 + 0.265265i \(0.0854593\pi\)
−0.964176 + 0.265265i \(0.914541\pi\)
\(930\) −4.02844e6 4.40712e6i −0.152732 0.167089i
\(931\) 1.95939e7i 0.740877i
\(932\) 9.39998e6i 0.354476i
\(933\) −1.91963e7 2.10008e7i −0.721962 0.789826i
\(934\) 2.76299e6i 0.103636i
\(935\) −291998. −0.0109232
\(936\) −1.52513e7 1.37202e6i −0.569005 0.0511884i
\(937\) 4.24419e7i 1.57923i −0.613602 0.789615i \(-0.710280\pi\)
0.613602 0.789615i \(-0.289720\pi\)
\(938\) 1.53554e7i 0.569842i
\(939\) 2.99870e7 + 3.28058e7i 1.10986 + 1.21419i
\(940\) 5.36731e6i 0.198124i
\(941\) 3.11592e6 0.114713 0.0573565 0.998354i \(-0.481733\pi\)
0.0573565 + 0.998354i \(0.481733\pi\)
\(942\) 3.81075e6 3.48332e6i 0.139921 0.127899i
\(943\) −7.69956e6 1.04065e7i −0.281960 0.381087i
\(944\) 4.31827e7i 1.57718i
\(945\) 4.74945e7 3.61669e7i 1.73007 1.31744i
\(946\) −271258. −0.00985495
\(947\) 1.39901e7i 0.506929i 0.967345 + 0.253464i \(0.0815701\pi\)
−0.967345 + 0.253464i \(0.918430\pi\)
\(948\) −2.10357e7 2.30131e7i −0.760215 0.831675i
\(949\) −3.85919e7 −1.39101
\(950\) 3.74308e6 0.134561
\(951\) −2.21241e7 2.42038e7i −0.793259 0.867825i
\(952\) 2.73583e6 0.0978357
\(953\) 7.04777e6 0.251373 0.125687 0.992070i \(-0.459887\pi\)
0.125687 + 0.992070i \(0.459887\pi\)
\(954\) 1.18728e7 + 1.06809e6i 0.422358 + 0.0379959i
\(955\) 6.96027e7 2.46955
\(956\) 3.49568e7i 1.23705i
\(957\) −1.19227e6 1.30434e6i −0.0420818 0.0460375i
\(958\) 5.91120e6i 0.208095i
\(959\) 6.81332e7i 2.39228i
\(960\) −2.13539e7 + 1.95191e7i −0.747825 + 0.683570i
\(961\) −1.45749e7 −0.509094
\(962\) 1.09046e7 0.379902
\(963\) −1.30752e6 + 1.45342e7i −0.0454340 + 0.505040i
\(964\) 4.73122e7i 1.63976i
\(965\) −1.61944e7 −0.559818
\(966\) 1.90816e6 9.75010e6i 0.0657919 0.336176i
\(967\) −2.59611e7 −0.892804 −0.446402 0.894832i \(-0.647295\pi\)
−0.446402 + 0.894832i \(0.647295\pi\)
\(968\) 1.27846e7i 0.438528i
\(969\) −1.63983e6 1.79397e6i −0.0561034 0.0613771i
\(970\) −6.09082e6 −0.207848
\(971\) −5.77704e6 −0.196633 −0.0983167 0.995155i \(-0.531346\pi\)
−0.0983167 + 0.995155i \(0.531346\pi\)
\(972\) −2.36698e7 + 1.48760e7i −0.803579 + 0.505034i
\(973\) 1.15774e6i 0.0392037i
\(974\) 1.21319e7i 0.409760i
\(975\) −2.99189e7 + 2.73482e7i −1.00794 + 0.921334i
\(976\) 2.51169e7i 0.843999i
\(977\) −7.49681e6 −0.251270 −0.125635 0.992077i \(-0.540097\pi\)
−0.125635 + 0.992077i \(0.540097\pi\)
\(978\) 3.00160e6 + 3.28375e6i 0.100347 + 0.109780i
\(979\) −2.23284e6 −0.0744562
\(980\) 5.33532e7 1.77458
\(981\) −3.69145e7 3.32088e6i −1.22469 0.110174i
\(982\) 5.22928e6 0.173046
\(983\) −2.54694e7 −0.840688 −0.420344 0.907365i \(-0.638091\pi\)
−0.420344 + 0.907365i \(0.638091\pi\)
\(984\) 4.67317e6 4.27164e6i 0.153859 0.140639i
\(985\) 6.50798e7i 2.13725i
\(986\) 1.20930e6 0.0396133
\(987\) −4.99957e6 + 4.57000e6i −0.163358 + 0.149322i
\(988\) 2.14709e7i 0.699774i
\(989\) 1.53544e7 + 2.07526e7i 0.499164 + 0.674654i
\(990\) −516529. 46467.6i −0.0167497 0.00150682i
\(991\) −4.73562e7 −1.53177 −0.765884 0.642979i \(-0.777698\pi\)
−0.765884 + 0.642979i \(0.777698\pi\)
\(992\) 1.37127e7i 0.442429i
\(993\) 1.79706e7 1.64265e7i 0.578349 0.528656i
\(994\) 2.95744e6i 0.0949400i
\(995\) 3.24413e6i 0.103882i
\(996\) 1.87231e7 1.71143e7i 0.598038 0.546653i
\(997\) −2.11118e7 −0.672648 −0.336324 0.941746i \(-0.609184\pi\)
−0.336324 + 0.941746i \(0.609184\pi\)
\(998\) 1841.87i 5.85372e-5i
\(999\) 3.25269e7 2.47691e7i 1.03117 0.785229i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 69.6.c.b.68.17 yes 32
3.2 odd 2 inner 69.6.c.b.68.16 yes 32
23.22 odd 2 inner 69.6.c.b.68.18 yes 32
69.68 even 2 inner 69.6.c.b.68.15 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.c.b.68.15 32 69.68 even 2 inner
69.6.c.b.68.16 yes 32 3.2 odd 2 inner
69.6.c.b.68.17 yes 32 1.1 even 1 trivial
69.6.c.b.68.18 yes 32 23.22 odd 2 inner