Properties

Label 98.5.d.c.19.3
Level $98$
Weight $5$
Character 98.19
Analytic conductor $10.130$
Analytic rank $0$
Dimension $8$
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] = [98,5,Mod(19,98)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(98, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("98.19");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 98.d (of order \(6\), degree \(2\), not 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: \(10.1302563822\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.3
Root \(-0.662827 + 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 98.19
Dual form 98.5.d.c.31.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.41421 - 2.44949i) q^{2} +(-13.8528 + 7.99789i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-24.1168 - 13.9239i) q^{5} +45.2429i q^{6} -22.6274 q^{8} +(87.4325 - 151.438i) q^{9} +O(q^{10})\) \(q+(1.41421 - 2.44949i) q^{2} +(-13.8528 + 7.99789i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-24.1168 - 13.9239i) q^{5} +45.2429i q^{6} -22.6274 q^{8} +(87.4325 - 151.438i) q^{9} +(-68.2127 + 39.3826i) q^{10} +(69.8320 + 120.953i) q^{11} +(110.822 + 63.9831i) q^{12} +101.931i q^{13} +445.446 q^{15} +(-32.0000 + 55.4256i) q^{16} +(470.154 - 271.443i) q^{17} +(-247.296 - 428.330i) q^{18} +(121.203 + 69.9767i) q^{19} +222.782i q^{20} +395.029 q^{22} +(-114.823 + 198.880i) q^{23} +(313.452 - 180.972i) q^{24} +(75.2473 + 130.332i) q^{25} +(249.678 + 144.152i) q^{26} +1501.44i q^{27} -383.113 q^{29} +(629.955 - 1091.11i) q^{30} +(344.238 - 198.746i) q^{31} +(90.5097 + 156.767i) q^{32} +(-1934.73 - 1117.02i) q^{33} -1535.52i q^{34} -1398.92 q^{36} +(449.456 - 778.480i) q^{37} +(342.814 - 197.924i) q^{38} +(-815.230 - 1412.02i) q^{39} +(545.701 + 315.061i) q^{40} +657.862i q^{41} +1155.70 q^{43} +(558.656 - 967.621i) q^{44} +(-4217.19 + 2434.79i) q^{45} +(324.770 + 562.517i) q^{46} +(1121.08 + 647.253i) q^{47} -1023.73i q^{48} +425.663 q^{50} +(-4341.95 + 7520.48i) q^{51} +(706.196 - 407.722i) q^{52} +(2584.22 + 4476.00i) q^{53} +(3677.77 + 2123.36i) q^{54} -3889.32i q^{55} -2238.66 q^{57} +(-541.803 + 938.431i) q^{58} +(3598.54 - 2077.62i) q^{59} +(-1781.78 - 3086.14i) q^{60} +(-1593.56 - 920.043i) q^{61} -1124.28i q^{62} +512.000 q^{64} +(1419.27 - 2458.24i) q^{65} +(-5472.25 + 3159.40i) q^{66} +(3157.79 + 5469.45i) q^{67} +(-3761.23 - 2171.55i) q^{68} -3673.38i q^{69} +1263.28 q^{71} +(-1978.37 + 3426.64i) q^{72} +(-3460.15 + 1997.72i) q^{73} +(-1271.25 - 2201.87i) q^{74} +(-2084.76 - 1203.64i) q^{75} -1119.63i q^{76} -4611.63 q^{78} +(5307.13 - 9192.22i) q^{79} +(1543.48 - 891.126i) q^{80} +(-4926.35 - 8532.69i) q^{81} +(1611.43 + 930.357i) q^{82} +5750.31i q^{83} -15118.2 q^{85} +(1634.41 - 2830.88i) q^{86} +(5307.17 - 3064.09i) q^{87} +(-1580.12 - 2736.84i) q^{88} +(-3626.09 - 2093.52i) q^{89} +13773.3i q^{90} +1837.17 q^{92} +(-3179.10 + 5506.36i) q^{93} +(3170.88 - 1830.71i) q^{94} +(-1948.69 - 3375.23i) q^{95} +(-2507.62 - 1447.77i) q^{96} -3814.28i q^{97} +24422.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 32 q^{4} + 196 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 32 q^{4} + 196 q^{9} - 24 q^{11} + 1776 q^{15} - 256 q^{16} - 1424 q^{18} + 3296 q^{22} - 104 q^{23} - 948 q^{25} - 2816 q^{29} + 2528 q^{30} - 3136 q^{36} + 3392 q^{37} - 2200 q^{39} - 4048 q^{43} - 192 q^{44} + 2304 q^{46} + 8768 q^{50} - 18936 q^{51} + 16680 q^{53} - 12128 q^{57} - 352 q^{58} - 7104 q^{60} + 4096 q^{64} + 6048 q^{65} + 20816 q^{67} - 3968 q^{71} - 11392 q^{72} - 576 q^{74} - 24448 q^{78} + 29616 q^{79} - 30852 q^{81} - 59376 q^{85} + 18800 q^{86} - 13184 q^{88} + 1664 q^{92} - 18192 q^{93} - 7240 q^{95} + 144320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 2.44949i 0.353553 0.612372i
\(3\) −13.8528 + 7.99789i −1.53919 + 0.888654i −0.540309 + 0.841467i \(0.681693\pi\)
−0.998886 + 0.0471876i \(0.984974\pi\)
\(4\) −4.00000 6.92820i −0.250000 0.433013i
\(5\) −24.1168 13.9239i −0.964673 0.556954i −0.0670647 0.997749i \(-0.521363\pi\)
−0.897608 + 0.440795i \(0.854697\pi\)
\(6\) 45.2429i 1.25675i
\(7\) 0 0
\(8\) −22.6274 −0.353553
\(9\) 87.4325 151.438i 1.07941 1.86960i
\(10\) −68.2127 + 39.3826i −0.682127 + 0.393826i
\(11\) 69.8320 + 120.953i 0.577124 + 0.999608i 0.995807 + 0.0914757i \(0.0291584\pi\)
−0.418683 + 0.908132i \(0.637508\pi\)
\(12\) 110.822 + 63.9831i 0.769597 + 0.444327i
\(13\) 101.931i 0.603140i 0.953444 + 0.301570i \(0.0975106\pi\)
−0.953444 + 0.301570i \(0.902489\pi\)
\(14\) 0 0
\(15\) 445.446 1.97976
\(16\) −32.0000 + 55.4256i −0.125000 + 0.216506i
\(17\) 470.154 271.443i 1.62683 0.939251i 0.641799 0.766873i \(-0.278188\pi\)
0.985031 0.172377i \(-0.0551448\pi\)
\(18\) −247.296 428.330i −0.763261 1.32201i
\(19\) 121.203 + 69.9767i 0.335743 + 0.193841i 0.658388 0.752679i \(-0.271239\pi\)
−0.322645 + 0.946520i \(0.604572\pi\)
\(20\) 222.782i 0.556954i
\(21\) 0 0
\(22\) 395.029 0.816177
\(23\) −114.823 + 198.880i −0.217057 + 0.375954i −0.953907 0.300102i \(-0.902979\pi\)
0.736850 + 0.676057i \(0.236313\pi\)
\(24\) 313.452 180.972i 0.544188 0.314187i
\(25\) 75.2473 + 130.332i 0.120396 + 0.208531i
\(26\) 249.678 + 144.152i 0.369346 + 0.213242i
\(27\) 1501.44i 2.05959i
\(28\) 0 0
\(29\) −383.113 −0.455544 −0.227772 0.973714i \(-0.573144\pi\)
−0.227772 + 0.973714i \(0.573144\pi\)
\(30\) 629.955 1091.11i 0.699950 1.21235i
\(31\) 344.238 198.746i 0.358208 0.206812i −0.310086 0.950708i \(-0.600358\pi\)
0.668294 + 0.743897i \(0.267025\pi\)
\(32\) 90.5097 + 156.767i 0.0883883 + 0.153093i
\(33\) −1934.73 1117.02i −1.77661 1.02573i
\(34\) 1535.52i 1.32830i
\(35\) 0 0
\(36\) −1398.92 −1.07941
\(37\) 449.456 778.480i 0.328310 0.568649i −0.653867 0.756610i \(-0.726854\pi\)
0.982177 + 0.187961i \(0.0601877\pi\)
\(38\) 342.814 197.924i 0.237406 0.137066i
\(39\) −815.230 1412.02i −0.535983 0.928349i
\(40\) 545.701 + 315.061i 0.341063 + 0.196913i
\(41\) 657.862i 0.391352i 0.980669 + 0.195676i \(0.0626900\pi\)
−0.980669 + 0.195676i \(0.937310\pi\)
\(42\) 0 0
\(43\) 1155.70 0.625041 0.312521 0.949911i \(-0.398827\pi\)
0.312521 + 0.949911i \(0.398827\pi\)
\(44\) 558.656 967.621i 0.288562 0.499804i
\(45\) −4217.19 + 2434.79i −2.08256 + 1.20237i
\(46\) 324.770 + 562.517i 0.153483 + 0.265840i
\(47\) 1121.08 + 647.253i 0.507504 + 0.293007i 0.731807 0.681512i \(-0.238677\pi\)
−0.224303 + 0.974519i \(0.572011\pi\)
\(48\) 1023.73i 0.444327i
\(49\) 0 0
\(50\) 425.663 0.170265
\(51\) −4341.95 + 7520.48i −1.66934 + 2.89138i
\(52\) 706.196 407.722i 0.261167 0.150785i
\(53\) 2584.22 + 4476.00i 0.919978 + 1.59345i 0.799445 + 0.600739i \(0.205127\pi\)
0.120532 + 0.992709i \(0.461540\pi\)
\(54\) 3677.77 + 2123.36i 1.26124 + 0.728176i
\(55\) 3889.32i 1.28573i
\(56\) 0 0
\(57\) −2238.66 −0.689031
\(58\) −541.803 + 938.431i −0.161059 + 0.278963i
\(59\) 3598.54 2077.62i 1.03377 0.596846i 0.115706 0.993284i \(-0.463087\pi\)
0.918062 + 0.396438i \(0.129754\pi\)
\(60\) −1781.78 3086.14i −0.494940 0.857261i
\(61\) −1593.56 920.043i −0.428262 0.247257i 0.270344 0.962764i \(-0.412862\pi\)
−0.698606 + 0.715507i \(0.746196\pi\)
\(62\) 1124.28i 0.292476i
\(63\) 0 0
\(64\) 512.000 0.125000
\(65\) 1419.27 2458.24i 0.335921 0.581832i
\(66\) −5472.25 + 3159.40i −1.25625 + 0.725299i
\(67\) 3157.79 + 5469.45i 0.703450 + 1.21841i 0.967248 + 0.253833i \(0.0816913\pi\)
−0.263798 + 0.964578i \(0.584975\pi\)
\(68\) −3761.23 2171.55i −0.813415 0.469625i
\(69\) 3673.38i 0.771556i
\(70\) 0 0
\(71\) 1263.28 0.250601 0.125301 0.992119i \(-0.460010\pi\)
0.125301 + 0.992119i \(0.460010\pi\)
\(72\) −1978.37 + 3426.64i −0.381630 + 0.661003i
\(73\) −3460.15 + 1997.72i −0.649305 + 0.374877i −0.788190 0.615432i \(-0.788982\pi\)
0.138885 + 0.990309i \(0.455648\pi\)
\(74\) −1271.25 2201.87i −0.232150 0.402096i
\(75\) −2084.76 1203.64i −0.370625 0.213980i
\(76\) 1119.63i 0.193841i
\(77\) 0 0
\(78\) −4611.63 −0.757994
\(79\) 5307.13 9192.22i 0.850366 1.47288i −0.0305129 0.999534i \(-0.509714\pi\)
0.880879 0.473342i \(-0.156953\pi\)
\(80\) 1543.48 891.126i 0.241168 0.139239i
\(81\) −4926.35 8532.69i −0.750854 1.30052i
\(82\) 1611.43 + 930.357i 0.239653 + 0.138364i
\(83\) 5750.31i 0.834709i 0.908744 + 0.417355i \(0.137043\pi\)
−0.908744 + 0.417355i \(0.862957\pi\)
\(84\) 0 0
\(85\) −15118.2 −2.09248
\(86\) 1634.41 2830.88i 0.220985 0.382758i
\(87\) 5307.17 3064.09i 0.701171 0.404821i
\(88\) −1580.12 2736.84i −0.204044 0.353415i
\(89\) −3626.09 2093.52i −0.457782 0.264301i 0.253329 0.967380i \(-0.418474\pi\)
−0.711111 + 0.703080i \(0.751808\pi\)
\(90\) 13773.3i 1.70040i
\(91\) 0 0
\(92\) 1837.17 0.217057
\(93\) −3179.10 + 5506.36i −0.367568 + 0.636647i
\(94\) 3170.88 1830.71i 0.358859 0.207188i
\(95\) −1948.69 3375.23i −0.215921 0.373987i
\(96\) −2507.62 1447.77i −0.272094 0.157093i
\(97\) 3814.28i 0.405386i −0.979242 0.202693i \(-0.935031\pi\)
0.979242 0.202693i \(-0.0649694\pi\)
\(98\) 0 0
\(99\) 24422.3 2.49182
\(100\) 601.978 1042.66i 0.0601978 0.104266i
\(101\) 4265.53 2462.71i 0.418149 0.241418i −0.276136 0.961118i \(-0.589054\pi\)
0.694285 + 0.719700i \(0.255721\pi\)
\(102\) 12280.9 + 21271.1i 1.18040 + 2.04451i
\(103\) 16361.5 + 9446.32i 1.54223 + 0.890407i 0.998698 + 0.0510180i \(0.0162466\pi\)
0.543532 + 0.839389i \(0.317087\pi\)
\(104\) 2306.43i 0.213242i
\(105\) 0 0
\(106\) 14618.5 1.30104
\(107\) 4239.70 7343.37i 0.370311 0.641398i −0.619302 0.785153i \(-0.712584\pi\)
0.989613 + 0.143755i \(0.0459176\pi\)
\(108\) 10402.3 6005.78i 0.891830 0.514899i
\(109\) −5838.98 10113.4i −0.491455 0.851225i 0.508496 0.861064i \(-0.330202\pi\)
−0.999952 + 0.00983867i \(0.996868\pi\)
\(110\) −9526.85 5500.33i −0.787343 0.454573i
\(111\) 14378.8i 1.16702i
\(112\) 0 0
\(113\) 19683.8 1.54153 0.770763 0.637121i \(-0.219875\pi\)
0.770763 + 0.637121i \(0.219875\pi\)
\(114\) −3165.95 + 5483.58i −0.243609 + 0.421944i
\(115\) 5538.35 3197.57i 0.418779 0.241782i
\(116\) 1532.45 + 2654.28i 0.113886 + 0.197256i
\(117\) 15436.1 + 8912.05i 1.12763 + 0.651037i
\(118\) 11752.8i 0.844067i
\(119\) 0 0
\(120\) −10079.3 −0.699950
\(121\) −2432.52 + 4213.24i −0.166144 + 0.287770i
\(122\) −4507.27 + 2602.27i −0.302827 + 0.174837i
\(123\) −5261.51 9113.20i −0.347776 0.602366i
\(124\) −2753.90 1589.97i −0.179104 0.103406i
\(125\) 13213.9i 0.845689i
\(126\) 0 0
\(127\) −27965.5 −1.73386 −0.866931 0.498428i \(-0.833911\pi\)
−0.866931 + 0.498428i \(0.833911\pi\)
\(128\) 724.077 1254.14i 0.0441942 0.0765466i
\(129\) −16009.6 + 9243.17i −0.962060 + 0.555446i
\(130\) −4014.29 6952.96i −0.237532 0.411418i
\(131\) −1013.02 584.866i −0.0590302 0.0340811i 0.470194 0.882563i \(-0.344184\pi\)
−0.529225 + 0.848482i \(0.677517\pi\)
\(132\) 17872.3i 1.02573i
\(133\) 0 0
\(134\) 17863.1 0.994828
\(135\) 20905.9 36210.1i 1.14710 1.98683i
\(136\) −10638.4 + 6142.06i −0.575171 + 0.332075i
\(137\) 10442.3 + 18086.6i 0.556359 + 0.963641i 0.997796 + 0.0663495i \(0.0211352\pi\)
−0.441438 + 0.897292i \(0.645531\pi\)
\(138\) −8997.90 5194.94i −0.472480 0.272786i
\(139\) 3499.87i 0.181143i −0.995890 0.0905716i \(-0.971131\pi\)
0.995890 0.0905716i \(-0.0288694\pi\)
\(140\) 0 0
\(141\) −20706.6 −1.04153
\(142\) 1786.55 3094.40i 0.0886010 0.153461i
\(143\) −12328.8 + 7118.02i −0.602903 + 0.348086i
\(144\) 5595.68 + 9692.00i 0.269853 + 0.467400i
\(145\) 9239.46 + 5334.40i 0.439451 + 0.253717i
\(146\) 11300.8i 0.530156i
\(147\) 0 0
\(148\) −7191.29 −0.328310
\(149\) −14766.9 + 25577.0i −0.665146 + 1.15207i 0.314100 + 0.949390i \(0.398297\pi\)
−0.979246 + 0.202677i \(0.935036\pi\)
\(150\) −5896.60 + 3404.40i −0.262071 + 0.151307i
\(151\) −12890.4 22326.8i −0.565344 0.979204i −0.997018 0.0771741i \(-0.975410\pi\)
0.431674 0.902030i \(-0.357923\pi\)
\(152\) −2742.51 1583.39i −0.118703 0.0685332i
\(153\) 94931.9i 4.05536i
\(154\) 0 0
\(155\) −11069.2 −0.460738
\(156\) −6521.84 + 11296.2i −0.267991 + 0.464175i
\(157\) 22195.7 12814.7i 0.900470 0.519887i 0.0231177 0.999733i \(-0.492641\pi\)
0.877353 + 0.479846i \(0.159307\pi\)
\(158\) −15010.8 25999.5i −0.601299 1.04148i
\(159\) −71597.0 41336.6i −2.83205 1.63508i
\(160\) 5040.97i 0.196913i
\(161\) 0 0
\(162\) −27867.7 −1.06187
\(163\) 3091.39 5354.45i 0.116353 0.201530i −0.801967 0.597369i \(-0.796213\pi\)
0.918320 + 0.395839i \(0.129546\pi\)
\(164\) 4557.80 2631.45i 0.169460 0.0978379i
\(165\) 31106.4 + 53877.8i 1.14257 + 1.97898i
\(166\) 14085.3 + 8132.17i 0.511153 + 0.295114i
\(167\) 39270.9i 1.40811i 0.710144 + 0.704056i \(0.248630\pi\)
−0.710144 + 0.704056i \(0.751370\pi\)
\(168\) 0 0
\(169\) 18171.2 0.636223
\(170\) −21380.3 + 37031.8i −0.739803 + 1.28138i
\(171\) 21194.2 12236.5i 0.724811 0.418470i
\(172\) −4622.80 8006.93i −0.156260 0.270651i
\(173\) 28497.3 + 16452.9i 0.952165 + 0.549732i 0.893753 0.448560i \(-0.148063\pi\)
0.0584119 + 0.998293i \(0.481396\pi\)
\(174\) 17333.1i 0.572504i
\(175\) 0 0
\(176\) −8938.50 −0.288562
\(177\) −33233.2 + 57561.5i −1.06078 + 1.83732i
\(178\) −10256.1 + 5921.38i −0.323701 + 0.186889i
\(179\) 2383.94 + 4129.11i 0.0744029 + 0.128870i 0.900826 0.434179i \(-0.142962\pi\)
−0.826424 + 0.563049i \(0.809628\pi\)
\(180\) 33737.5 + 19478.4i 1.04128 + 0.601184i
\(181\) 35195.4i 1.07431i −0.843484 0.537154i \(-0.819499\pi\)
0.843484 0.537154i \(-0.180501\pi\)
\(182\) 0 0
\(183\) 29433.6 0.878904
\(184\) 2598.16 4500.14i 0.0767414 0.132920i
\(185\) −21678.9 + 12516.3i −0.633423 + 0.365707i
\(186\) 8991.84 + 15574.3i 0.259910 + 0.450177i
\(187\) 65663.6 + 37910.9i 1.87776 + 1.08413i
\(188\) 10356.1i 0.293007i
\(189\) 0 0
\(190\) −11023.5 −0.305359
\(191\) −11657.5 + 20191.4i −0.319551 + 0.553478i −0.980394 0.197046i \(-0.936865\pi\)
0.660844 + 0.750524i \(0.270199\pi\)
\(192\) −7092.61 + 4094.92i −0.192399 + 0.111082i
\(193\) −29591.9 51254.6i −0.794434 1.37600i −0.923198 0.384325i \(-0.874434\pi\)
0.128764 0.991675i \(-0.458899\pi\)
\(194\) −9343.04 5394.21i −0.248247 0.143326i
\(195\) 45404.5i 1.19407i
\(196\) 0 0
\(197\) −60902.2 −1.56928 −0.784640 0.619952i \(-0.787152\pi\)
−0.784640 + 0.619952i \(0.787152\pi\)
\(198\) 34538.4 59822.3i 0.880992 1.52592i
\(199\) −34742.1 + 20058.4i −0.877304 + 0.506512i −0.869769 0.493460i \(-0.835732\pi\)
−0.00753551 + 0.999972i \(0.502399\pi\)
\(200\) −1702.65 2949.08i −0.0425663 0.0737270i
\(201\) −87488.1 50511.3i −2.16549 1.25025i
\(202\) 13931.2i 0.341417i
\(203\) 0 0
\(204\) 69471.2 1.66934
\(205\) 9159.97 15865.5i 0.217965 0.377526i
\(206\) 46277.3 26718.2i 1.09052 0.629613i
\(207\) 20078.6 + 34777.1i 0.468589 + 0.811621i
\(208\) −5649.57 3261.78i −0.130584 0.0753924i
\(209\) 19546.4i 0.447482i
\(210\) 0 0
\(211\) 21929.0 0.492554 0.246277 0.969200i \(-0.420793\pi\)
0.246277 + 0.969200i \(0.420793\pi\)
\(212\) 20673.7 35808.0i 0.459989 0.796724i
\(213\) −17499.9 + 10103.6i −0.385724 + 0.222698i
\(214\) −11991.7 20770.2i −0.261850 0.453537i
\(215\) −27871.8 16091.8i −0.602960 0.348119i
\(216\) 33973.8i 0.728176i
\(217\) 0 0
\(218\) −33030.3 −0.695023
\(219\) 31955.1 55347.8i 0.666272 1.15402i
\(220\) −26946.0 + 15557.3i −0.556736 + 0.321432i
\(221\) 27668.4 + 47923.0i 0.566499 + 0.981205i
\(222\) 35220.7 + 20334.7i 0.714648 + 0.412602i
\(223\) 64358.0i 1.29418i 0.762416 + 0.647088i \(0.224013\pi\)
−0.762416 + 0.647088i \(0.775987\pi\)
\(224\) 0 0
\(225\) 26316.2 0.519827
\(226\) 27837.0 48215.2i 0.545012 0.943989i
\(227\) −37910.1 + 21887.4i −0.735704 + 0.424759i −0.820505 0.571639i \(-0.806308\pi\)
0.0848015 + 0.996398i \(0.472974\pi\)
\(228\) 8954.65 + 15509.9i 0.172258 + 0.298359i
\(229\) 24687.3 + 14253.2i 0.470763 + 0.271795i 0.716559 0.697526i \(-0.245716\pi\)
−0.245796 + 0.969322i \(0.579049\pi\)
\(230\) 18088.2i 0.341931i
\(231\) 0 0
\(232\) 8668.85 0.161059
\(233\) 1097.45 1900.83i 0.0202149 0.0350132i −0.855741 0.517404i \(-0.826898\pi\)
0.875956 + 0.482391i \(0.160232\pi\)
\(234\) 43659.9 25207.1i 0.797354 0.460353i
\(235\) −18024.5 31219.4i −0.326383 0.565313i
\(236\) −28788.3 16621.0i −0.516884 0.298423i
\(237\) 169783.i 3.02273i
\(238\) 0 0
\(239\) 80942.6 1.41704 0.708519 0.705692i \(-0.249364\pi\)
0.708519 + 0.705692i \(0.249364\pi\)
\(240\) −14254.3 + 24689.1i −0.247470 + 0.428630i
\(241\) 37253.5 21508.3i 0.641406 0.370316i −0.143750 0.989614i \(-0.545916\pi\)
0.785156 + 0.619298i \(0.212583\pi\)
\(242\) 6880.19 + 11916.8i 0.117482 + 0.203484i
\(243\) 31163.7 + 17992.4i 0.527760 + 0.304702i
\(244\) 14720.7i 0.247257i
\(245\) 0 0
\(246\) −29763.6 −0.491830
\(247\) −7132.76 + 12354.3i −0.116913 + 0.202500i
\(248\) −7789.22 + 4497.11i −0.126646 + 0.0731189i
\(249\) −45990.4 79657.6i −0.741768 1.28478i
\(250\) 32367.3 + 18687.3i 0.517877 + 0.298996i
\(251\) 31568.5i 0.501080i −0.968106 0.250540i \(-0.919392\pi\)
0.968106 0.250540i \(-0.0806082\pi\)
\(252\) 0 0
\(253\) −32073.4 −0.501076
\(254\) −39549.1 + 68501.1i −0.613013 + 1.06177i
\(255\) 209428. 120913.i 3.22073 1.85949i
\(256\) −2048.00 3547.24i −0.0312500 0.0541266i
\(257\) −58981.4 34052.9i −0.892995 0.515571i −0.0180739 0.999837i \(-0.505753\pi\)
−0.874921 + 0.484266i \(0.839087\pi\)
\(258\) 52287.3i 0.785519i
\(259\) 0 0
\(260\) −22708.3 −0.335921
\(261\) −33496.5 + 58017.6i −0.491721 + 0.851685i
\(262\) −2865.25 + 1654.25i −0.0417406 + 0.0240990i
\(263\) 4173.78 + 7229.20i 0.0603418 + 0.104515i 0.894618 0.446831i \(-0.147448\pi\)
−0.834276 + 0.551346i \(0.814114\pi\)
\(264\) 43778.0 + 25275.2i 0.628127 + 0.362649i
\(265\) 143929.i 2.04954i
\(266\) 0 0
\(267\) 66975.1 0.939488
\(268\) 25262.3 43755.6i 0.351725 0.609205i
\(269\) −79605.9 + 45960.5i −1.10012 + 0.635156i −0.936253 0.351326i \(-0.885731\pi\)
−0.163869 + 0.986482i \(0.552397\pi\)
\(270\) −59130.8 102417.i −0.811122 1.40490i
\(271\) −4446.49 2567.18i −0.0605450 0.0349557i 0.469422 0.882974i \(-0.344462\pi\)
−0.529967 + 0.848018i \(0.677796\pi\)
\(272\) 34744.8i 0.469625i
\(273\) 0 0
\(274\) 59070.5 0.786810
\(275\) −10509.3 + 18202.7i −0.138966 + 0.240697i
\(276\) −25449.9 + 14693.5i −0.334094 + 0.192889i
\(277\) 33127.1 + 57377.8i 0.431741 + 0.747798i 0.997023 0.0770996i \(-0.0245660\pi\)
−0.565282 + 0.824898i \(0.691233\pi\)
\(278\) −8572.89 4949.56i −0.110927 0.0640438i
\(279\) 69507.4i 0.892941i
\(280\) 0 0
\(281\) 38156.4 0.483230 0.241615 0.970372i \(-0.422323\pi\)
0.241615 + 0.970372i \(0.422323\pi\)
\(282\) −29283.6 + 50720.7i −0.368236 + 0.637804i
\(283\) 95464.8 55116.6i 1.19198 0.688192i 0.233228 0.972422i \(-0.425071\pi\)
0.958756 + 0.284230i \(0.0917379\pi\)
\(284\) −5053.13 8752.27i −0.0626504 0.108514i
\(285\) 53989.4 + 31170.8i 0.664690 + 0.383759i
\(286\) 40265.6i 0.492268i
\(287\) 0 0
\(288\) 31653.9 0.381630
\(289\) 105603. 182909.i 1.26438 2.18998i
\(290\) 26133.1 15088.0i 0.310739 0.179405i
\(291\) 30506.2 + 52838.3i 0.360248 + 0.623968i
\(292\) 27681.2 + 15981.7i 0.324653 + 0.187438i
\(293\) 79011.7i 0.920357i −0.887826 0.460179i \(-0.847785\pi\)
0.887826 0.460179i \(-0.152215\pi\)
\(294\) 0 0
\(295\) −115714. −1.32966
\(296\) −10170.0 + 17615.0i −0.116075 + 0.201048i
\(297\) −181604. + 104849.i −2.05879 + 1.18864i
\(298\) 41767.1 + 72342.8i 0.470329 + 0.814634i
\(299\) −20271.9 11704.0i −0.226753 0.130916i
\(300\) 19258.2i 0.213980i
\(301\) 0 0
\(302\) −72919.1 −0.799517
\(303\) −39392.9 + 68230.6i −0.429075 + 0.743179i
\(304\) −7757.00 + 4478.51i −0.0839357 + 0.0484603i
\(305\) 25621.1 + 44377.0i 0.275421 + 0.477044i
\(306\) −232535. 134254.i −2.48339 1.43379i
\(307\) 2801.57i 0.0297252i 0.999890 + 0.0148626i \(0.00473109\pi\)
−0.999890 + 0.0148626i \(0.995269\pi\)
\(308\) 0 0
\(309\) −302203. −3.16506
\(310\) −15654.3 + 27114.0i −0.162896 + 0.282143i
\(311\) −17891.5 + 10329.7i −0.184981 + 0.106799i −0.589631 0.807673i \(-0.700727\pi\)
0.404650 + 0.914472i \(0.367393\pi\)
\(312\) 18446.5 + 31950.3i 0.189498 + 0.328221i
\(313\) −32368.6 18688.0i −0.330397 0.190755i 0.325620 0.945501i \(-0.394427\pi\)
−0.656017 + 0.754746i \(0.727760\pi\)
\(314\) 72490.8i 0.735231i
\(315\) 0 0
\(316\) −84914.1 −0.850366
\(317\) 53333.0 92375.5i 0.530735 0.919259i −0.468622 0.883399i \(-0.655249\pi\)
0.999357 0.0358607i \(-0.0114173\pi\)
\(318\) −202507. + 116917.i −2.00256 + 1.15618i
\(319\) −26753.5 46338.5i −0.262905 0.455366i
\(320\) −12347.8 7129.01i −0.120584 0.0696193i
\(321\) 135634.i 1.31632i
\(322\) 0 0
\(323\) 75978.8 0.728262
\(324\) −39410.8 + 68261.5i −0.375427 + 0.650259i
\(325\) −13284.8 + 7670.00i −0.125773 + 0.0726154i
\(326\) −8743.77 15144.7i −0.0822742 0.142503i
\(327\) 161772. + 93399.0i 1.51289 + 0.873468i
\(328\) 14885.7i 0.138364i
\(329\) 0 0
\(330\) 175964. 1.61583
\(331\) −54181.4 + 93844.9i −0.494532 + 0.856554i −0.999980 0.00630282i \(-0.997994\pi\)
0.505448 + 0.862857i \(0.331327\pi\)
\(332\) 39839.3 23001.2i 0.361440 0.208677i
\(333\) −78594.1 136129.i −0.708764 1.22761i
\(334\) 96193.6 + 55537.4i 0.862289 + 0.497843i
\(335\) 175874.i 1.56716i
\(336\) 0 0
\(337\) 186946. 1.64610 0.823050 0.567968i \(-0.192270\pi\)
0.823050 + 0.567968i \(0.192270\pi\)
\(338\) 25697.9 44510.1i 0.224939 0.389605i
\(339\) −272674. + 157429.i −2.37271 + 1.36988i
\(340\) 60472.6 + 104742.i 0.523119 + 0.906069i
\(341\) 48077.7 + 27757.7i 0.413461 + 0.238712i
\(342\) 69219.9i 0.591805i
\(343\) 0 0
\(344\) −26150.5 −0.220985
\(345\) −51147.6 + 88590.2i −0.429721 + 0.744299i
\(346\) 80602.6 46536.0i 0.673282 0.388720i
\(347\) 31613.7 + 54756.5i 0.262552 + 0.454754i 0.966919 0.255082i \(-0.0821024\pi\)
−0.704367 + 0.709836i \(0.748769\pi\)
\(348\) −42457.3 24512.7i −0.350586 0.202411i
\(349\) 93605.0i 0.768508i −0.923227 0.384254i \(-0.874459\pi\)
0.923227 0.384254i \(-0.125541\pi\)
\(350\) 0 0
\(351\) −153043. −1.24222
\(352\) −12640.9 + 21894.8i −0.102022 + 0.176707i
\(353\) 124059. 71625.3i 0.995583 0.574800i 0.0886445 0.996063i \(-0.471746\pi\)
0.906938 + 0.421263i \(0.138413\pi\)
\(354\) 93997.5 + 162809.i 0.750084 + 1.29918i
\(355\) −30466.3 17589.7i −0.241748 0.139573i
\(356\) 33496.4i 0.264301i
\(357\) 0 0
\(358\) 13485.6 0.105222
\(359\) −51169.9 + 88628.9i −0.397032 + 0.687680i −0.993358 0.115062i \(-0.963293\pi\)
0.596326 + 0.802742i \(0.296627\pi\)
\(360\) 95424.1 55093.1i 0.736297 0.425101i
\(361\) −55367.0 95898.5i −0.424851 0.735864i
\(362\) −86210.8 49773.9i −0.657877 0.379826i
\(363\) 77820.0i 0.590579i
\(364\) 0 0
\(365\) 111264. 0.835156
\(366\) 41625.4 72097.3i 0.310739 0.538216i
\(367\) 13307.7 7683.22i 0.0988034 0.0570442i −0.449784 0.893137i \(-0.648499\pi\)
0.548588 + 0.836093i \(0.315166\pi\)
\(368\) −7348.70 12728.3i −0.0542644 0.0939886i
\(369\) 99625.0 + 57518.5i 0.731671 + 0.422430i
\(370\) 70803.0i 0.517187i
\(371\) 0 0
\(372\) 50865.5 0.367568
\(373\) −48745.4 + 84429.5i −0.350361 + 0.606843i −0.986313 0.164886i \(-0.947275\pi\)
0.635951 + 0.771729i \(0.280608\pi\)
\(374\) 185725. 107228.i 1.32778 0.766594i
\(375\) −105683. 183049.i −0.751525 1.30168i
\(376\) −25367.1 14645.7i −0.179430 0.103594i
\(377\) 39050.9i 0.274757i
\(378\) 0 0
\(379\) −66090.7 −0.460110 −0.230055 0.973178i \(-0.573891\pi\)
−0.230055 + 0.973178i \(0.573891\pi\)
\(380\) −15589.5 + 27001.8i −0.107961 + 0.186993i
\(381\) 387399. 223665.i 2.66875 1.54080i
\(382\) 32972.5 + 57110.0i 0.225956 + 0.391368i
\(383\) 180913. + 104450.i 1.23331 + 0.712053i 0.967719 0.252032i \(-0.0810990\pi\)
0.265593 + 0.964085i \(0.414432\pi\)
\(384\) 23164.4i 0.157093i
\(385\) 0 0
\(386\) −167397. −1.12350
\(387\) 101046. 175017.i 0.674678 1.16858i
\(388\) −26426.1 + 15257.1i −0.175537 + 0.101347i
\(389\) 71999.6 + 124707.i 0.475807 + 0.824122i 0.999616 0.0277137i \(-0.00882267\pi\)
−0.523809 + 0.851836i \(0.675489\pi\)
\(390\) 111218. + 64211.7i 0.731216 + 0.422168i
\(391\) 124672.i 0.815485i
\(392\) 0 0
\(393\) 18710.8 0.121145
\(394\) −86128.7 + 149179.i −0.554824 + 0.960984i
\(395\) −255982. + 147791.i −1.64065 + 0.947229i
\(396\) −97689.4 169203.i −0.622955 1.07899i
\(397\) −246451. 142289.i −1.56369 0.902796i −0.996879 0.0789466i \(-0.974844\pi\)
−0.566809 0.823849i \(-0.691822\pi\)
\(398\) 113467.i 0.716316i
\(399\) 0 0
\(400\) −9631.65 −0.0601978
\(401\) 53923.0 93397.4i 0.335340 0.580826i −0.648210 0.761462i \(-0.724482\pi\)
0.983550 + 0.180636i \(0.0578155\pi\)
\(402\) −247454. + 142867.i −1.53123 + 0.884059i
\(403\) 20258.3 + 35088.4i 0.124736 + 0.216050i
\(404\) −34124.3 19701.7i −0.209074 0.120709i
\(405\) 274375.i 1.67276i
\(406\) 0 0
\(407\) 125546. 0.757901
\(408\) 98247.1 170169.i 0.590200 1.02226i
\(409\) 73553.4 42466.1i 0.439700 0.253861i −0.263771 0.964585i \(-0.584966\pi\)
0.703470 + 0.710725i \(0.251633\pi\)
\(410\) −25908.3 44874.5i −0.154124 0.266951i
\(411\) −289309. 167033.i −1.71269 0.988821i
\(412\) 151141.i 0.890407i
\(413\) 0 0
\(414\) 113582. 0.662686
\(415\) 80066.5 138679.i 0.464895 0.805221i
\(416\) −15979.4 + 9225.70i −0.0923365 + 0.0533105i
\(417\) 27991.6 + 48482.8i 0.160974 + 0.278815i
\(418\) 47878.8 + 27642.8i 0.274025 + 0.158209i
\(419\) 331905.i 1.89054i 0.326292 + 0.945269i \(0.394201\pi\)
−0.326292 + 0.945269i \(0.605799\pi\)
\(420\) 0 0
\(421\) 101490. 0.572609 0.286304 0.958139i \(-0.407573\pi\)
0.286304 + 0.958139i \(0.407573\pi\)
\(422\) 31012.3 53714.8i 0.174144 0.301626i
\(423\) 196037. 113182.i 1.09561 0.632552i
\(424\) −58474.2 101280.i −0.325261 0.563369i
\(425\) 70755.6 + 40850.7i 0.391726 + 0.226163i
\(426\) 57154.5i 0.314943i
\(427\) 0 0
\(428\) −67835.1 −0.370311
\(429\) 113858. 197208.i 0.618657 1.07155i
\(430\) −78833.4 + 45514.5i −0.426357 + 0.246157i
\(431\) −114899. 199011.i −0.618530 1.07133i −0.989754 0.142782i \(-0.954395\pi\)
0.371224 0.928543i \(-0.378938\pi\)
\(432\) −83218.5 48046.2i −0.445915 0.257449i
\(433\) 114264.i 0.609442i 0.952442 + 0.304721i \(0.0985632\pi\)
−0.952442 + 0.304721i \(0.901437\pi\)
\(434\) 0 0
\(435\) −170656. −0.901868
\(436\) −46711.8 + 80907.3i −0.245728 + 0.425613i
\(437\) −27833.9 + 16069.9i −0.145751 + 0.0841493i
\(438\) −90382.6 156547.i −0.471125 0.816013i
\(439\) −305134. 176169.i −1.58330 0.914116i −0.994374 0.105926i \(-0.966219\pi\)
−0.588921 0.808190i \(-0.700447\pi\)
\(440\) 88005.3i 0.454573i
\(441\) 0 0
\(442\) 156516. 0.801151
\(443\) 98158.2 170015.i 0.500172 0.866323i −0.499828 0.866125i \(-0.666604\pi\)
1.00000 0.000198349i \(-6.31363e-5\pi\)
\(444\) 99619.2 57515.2i 0.505332 0.291754i
\(445\) 58299.9 + 100978.i 0.294407 + 0.509927i
\(446\) 157644. + 91016.0i 0.792517 + 0.457560i
\(447\) 472416.i 2.36434i
\(448\) 0 0
\(449\) 77520.3 0.384523 0.192262 0.981344i \(-0.438418\pi\)
0.192262 + 0.981344i \(0.438418\pi\)
\(450\) 37216.8 64461.3i 0.183786 0.318328i
\(451\) −79570.1 + 45939.8i −0.391198 + 0.225858i
\(452\) −78735.0 136373.i −0.385382 0.667501i
\(453\) 357135. + 206192.i 1.74035 + 1.00479i
\(454\) 123814.i 0.600699i
\(455\) 0 0
\(456\) 50655.2 0.243609
\(457\) −94936.1 + 164434.i −0.454568 + 0.787335i −0.998663 0.0516882i \(-0.983540\pi\)
0.544095 + 0.839024i \(0.316873\pi\)
\(458\) 69826.2 40314.2i 0.332880 0.192188i
\(459\) 407557. + 705910.i 1.93447 + 3.35061i
\(460\) −44306.8 25580.5i −0.209389 0.120891i
\(461\) 52599.9i 0.247505i 0.992313 + 0.123752i \(0.0394928\pi\)
−0.992313 + 0.123752i \(0.960507\pi\)
\(462\) 0 0
\(463\) −244268. −1.13947 −0.569736 0.821828i \(-0.692955\pi\)
−0.569736 + 0.821828i \(0.692955\pi\)
\(464\) 12259.6 21234.3i 0.0569430 0.0986282i
\(465\) 153339. 88530.5i 0.709166 0.409437i
\(466\) −3104.05 5376.36i −0.0142941 0.0247581i
\(467\) 257742. + 148807.i 1.18182 + 0.682324i 0.956435 0.291946i \(-0.0943028\pi\)
0.225385 + 0.974270i \(0.427636\pi\)
\(468\) 142593.i 0.651037i
\(469\) 0 0
\(470\) −101962. −0.461576
\(471\) −204981. + 355037.i −0.924000 + 1.60041i
\(472\) −81425.7 + 47011.2i −0.365492 + 0.211017i
\(473\) 80704.9 + 139785.i 0.360726 + 0.624796i
\(474\) 415883. + 240110.i 1.85103 + 1.06869i
\(475\) 21062.2i 0.0933505i
\(476\) 0 0
\(477\) 903778. 3.97215
\(478\) 114470. 198268.i 0.500998 0.867755i
\(479\) −40591.3 + 23435.4i −0.176914 + 0.102141i −0.585842 0.810425i \(-0.699236\pi\)
0.408928 + 0.912567i \(0.365903\pi\)
\(480\) 40317.1 + 69831.3i 0.174988 + 0.303087i
\(481\) 79351.0 + 45813.3i 0.342975 + 0.198016i
\(482\) 121669.i 0.523706i
\(483\) 0 0
\(484\) 38920.3 0.166144
\(485\) −53109.5 + 91988.3i −0.225782 + 0.391065i
\(486\) 88144.3 50890.1i 0.373183 0.215457i
\(487\) −53591.9 92824.0i −0.225965 0.391383i 0.730643 0.682759i \(-0.239220\pi\)
−0.956609 + 0.291376i \(0.905887\pi\)
\(488\) 36058.2 + 20818.2i 0.151413 + 0.0874185i
\(489\) 98898.4i 0.413592i
\(490\) 0 0
\(491\) −116367. −0.482687 −0.241344 0.970440i \(-0.577588\pi\)
−0.241344 + 0.970440i \(0.577588\pi\)
\(492\) −42092.1 + 72905.6i −0.173888 + 0.301183i
\(493\) −180122. + 103993.i −0.741093 + 0.427870i
\(494\) 20174.5 + 34943.3i 0.0826702 + 0.143189i
\(495\) −588989. 340053.i −2.40379 1.38783i
\(496\) 25439.5i 0.103406i
\(497\) 0 0
\(498\) −260161. −1.04902
\(499\) −221454. + 383569.i −0.889369 + 1.54043i −0.0487464 + 0.998811i \(0.515523\pi\)
−0.840623 + 0.541621i \(0.817811\pi\)
\(500\) 91548.5 52855.5i 0.366194 0.211422i
\(501\) −314084. 544009.i −1.25133 2.16736i
\(502\) −77326.8 44644.7i −0.306848 0.177159i
\(503\) 68955.1i 0.272540i 0.990672 + 0.136270i \(0.0435115\pi\)
−0.990672 + 0.136270i \(0.956489\pi\)
\(504\) 0 0
\(505\) −137161. −0.537835
\(506\) −45358.6 + 78563.4i −0.177157 + 0.306845i
\(507\) −251721. + 145331.i −0.979271 + 0.565382i
\(508\) 111862. + 193750.i 0.433466 + 0.750784i
\(509\) −80344.2 46386.8i −0.310112 0.179044i 0.336864 0.941553i \(-0.390634\pi\)
−0.646977 + 0.762510i \(0.723967\pi\)
\(510\) 683989.i 2.62972i
\(511\) 0 0
\(512\) −11585.2 −0.0441942
\(513\) −105066. + 181980.i −0.399234 + 0.691494i
\(514\) −166825. + 96316.2i −0.631443 + 0.364564i
\(515\) −263058. 455631.i −0.991831 1.71790i
\(516\) 128077. + 73945.4i 0.481030 + 0.277723i
\(517\) 180796.i 0.676406i
\(518\) 0 0
\(519\) −526355. −1.95409
\(520\) −32114.3 + 55623.6i −0.118766 + 0.205709i
\(521\) 123766. 71456.2i 0.455958 0.263248i −0.254385 0.967103i \(-0.581873\pi\)
0.710343 + 0.703855i \(0.248540\pi\)
\(522\) 94742.4 + 164099.i 0.347699 + 0.602232i
\(523\) 19228.8 + 11101.8i 0.0702990 + 0.0405871i 0.534737 0.845018i \(-0.320411\pi\)
−0.464439 + 0.885605i \(0.653744\pi\)
\(524\) 9357.85i 0.0340811i
\(525\) 0 0
\(526\) 23610.5 0.0853361
\(527\) 107897. 186882.i 0.388496 0.672894i
\(528\) 123823. 71489.1i 0.444153 0.256432i
\(529\) 113552. + 196677.i 0.405772 + 0.702818i
\(530\) −352553. 203546.i −1.25508 0.724622i
\(531\) 726606.i 2.57697i
\(532\) 0 0
\(533\) −67056.3 −0.236040
\(534\) 94717.1 164055.i 0.332159 0.575316i
\(535\) −204496. + 118066.i −0.714459 + 0.412493i
\(536\) −71452.5 123759.i −0.248707 0.430773i
\(537\) −66048.3 38133.0i −0.229041 0.132237i
\(538\) 259992.i 0.898246i
\(539\) 0 0
\(540\) −334494. −1.14710
\(541\) −105605. + 182912.i −0.360818 + 0.624955i −0.988096 0.153841i \(-0.950836\pi\)
0.627278 + 0.778796i \(0.284169\pi\)
\(542\) −12576.6 + 7261.09i −0.0428118 + 0.0247174i
\(543\) 281489. + 487554.i 0.954689 + 1.65357i
\(544\) 85106.9 + 49136.5i 0.287586 + 0.166038i
\(545\) 325204.i 1.09487i
\(546\) 0 0
\(547\) 254227. 0.849664 0.424832 0.905272i \(-0.360333\pi\)
0.424832 + 0.905272i \(0.360333\pi\)
\(548\) 83538.3 144693.i 0.278179 0.481821i
\(549\) −278658. + 160883.i −0.924543 + 0.533785i
\(550\) 29724.9 + 51485.0i 0.0982641 + 0.170198i
\(551\) −46434.5 26809.0i −0.152946 0.0883032i
\(552\) 83119.1i 0.272786i
\(553\) 0 0
\(554\) 187395. 0.610575
\(555\) 200208. 346771.i 0.649974 1.12579i
\(556\) −24247.8 + 13999.5i −0.0784373 + 0.0452858i
\(557\) −23069.6 39957.7i −0.0743584 0.128792i 0.826449 0.563012i \(-0.190358\pi\)
−0.900807 + 0.434220i \(0.857024\pi\)
\(558\) −170258. 98298.3i −0.546812 0.315702i
\(559\) 117801.i 0.376987i
\(560\) 0 0
\(561\) −1.21283e6 −3.85366
\(562\) 53961.2 93463.6i 0.170848 0.295917i
\(563\) −302788. + 174814.i −0.955259 + 0.551519i −0.894711 0.446646i \(-0.852618\pi\)
−0.0605484 + 0.998165i \(0.519285\pi\)
\(564\) 82826.6 + 143460.i 0.260382 + 0.450996i
\(565\) −474710. 274074.i −1.48707 0.858560i
\(566\) 311787.i 0.973251i
\(567\) 0 0
\(568\) −28584.8 −0.0886010
\(569\) 88098.2 152591.i 0.272109 0.471306i −0.697293 0.716786i \(-0.745612\pi\)
0.969402 + 0.245480i \(0.0789457\pi\)
\(570\) 152705. 88164.4i 0.470007 0.271358i
\(571\) 88263.5 + 152877.i 0.270713 + 0.468889i 0.969045 0.246886i \(-0.0794072\pi\)
−0.698332 + 0.715774i \(0.746074\pi\)
\(572\) 98630.1 + 56944.1i 0.301452 + 0.174043i
\(573\) 372943.i 1.13588i
\(574\) 0 0
\(575\) −34560.6 −0.104531
\(576\) 44765.4 77536.0i 0.134927 0.233700i
\(577\) 196469. 113432.i 0.590124 0.340708i −0.175023 0.984564i \(-0.556000\pi\)
0.765147 + 0.643856i \(0.222667\pi\)
\(578\) −298689. 517345.i −0.894054 1.54855i
\(579\) 819858. + 473345.i 2.44558 + 1.41196i
\(580\) 85350.5i 0.253717i
\(581\) 0 0
\(582\) 172569. 0.509468
\(583\) −360922. + 625135.i −1.06188 + 1.83923i
\(584\) 78294.2 45203.2i 0.229564 0.132539i
\(585\) −248180. 429860.i −0.725195 1.25608i
\(586\) −193538. 111739.i −0.563601 0.325395i
\(587\) 349659.i 1.01477i −0.861719 0.507386i \(-0.830612\pi\)
0.861719 0.507386i \(-0.169388\pi\)
\(588\) 0 0
\(589\) 55630.3 0.160354
\(590\) −163644. + 283440.i −0.470107 + 0.814249i
\(591\) 843663. 487089.i 2.41543 1.39455i
\(592\) 28765.2 + 49822.7i 0.0820774 + 0.142162i
\(593\) 119299. + 68877.4i 0.339256 + 0.195870i 0.659943 0.751316i \(-0.270580\pi\)
−0.320687 + 0.947185i \(0.603914\pi\)
\(594\) 593115.i 1.68099i
\(595\) 0 0
\(596\) 236271. 0.665146
\(597\) 320849. 555727.i 0.900228 1.55924i
\(598\) −57337.7 + 33103.9i −0.160339 + 0.0925715i
\(599\) −40438.6 70041.7i −0.112705 0.195210i 0.804155 0.594420i \(-0.202618\pi\)
−0.916860 + 0.399209i \(0.869285\pi\)
\(600\) 47172.8 + 27235.2i 0.131036 + 0.0756534i
\(601\) 228798.i 0.633438i 0.948519 + 0.316719i \(0.102581\pi\)
−0.948519 + 0.316719i \(0.897419\pi\)
\(602\) 0 0
\(603\) 1.10437e6 3.03725
\(604\) −103123. + 178615.i −0.282672 + 0.489602i
\(605\) 117329. 67740.0i 0.320549 0.185069i
\(606\) 111420. + 192985.i 0.303402 + 0.525507i
\(607\) 230320. + 132975.i 0.625107 + 0.360906i 0.778855 0.627204i \(-0.215801\pi\)
−0.153748 + 0.988110i \(0.549134\pi\)
\(608\) 25334.3i 0.0685332i
\(609\) 0 0
\(610\) 144935. 0.389505
\(611\) −65974.9 + 114272.i −0.176724 + 0.306096i
\(612\) −657708. + 379728.i −1.75602 + 1.01384i
\(613\) 153261. + 265456.i 0.407859 + 0.706433i 0.994650 0.103306i \(-0.0329421\pi\)
−0.586790 + 0.809739i \(0.699609\pi\)
\(614\) 6862.42 + 3962.02i 0.0182029 + 0.0105095i
\(615\) 293042.i 0.774782i
\(616\) 0 0
\(617\) 491906. 1.29215 0.646074 0.763275i \(-0.276410\pi\)
0.646074 + 0.763275i \(0.276410\pi\)
\(618\) −427379. + 740242.i −1.11902 + 1.93819i
\(619\) 99792.1 57615.0i 0.260444 0.150368i −0.364093 0.931363i \(-0.618621\pi\)
0.624537 + 0.780995i \(0.285288\pi\)
\(620\) 44276.9 + 76689.9i 0.115185 + 0.199506i
\(621\) −298607. 172401.i −0.774314 0.447050i
\(622\) 58433.5i 0.151036i
\(623\) 0 0
\(624\) 104349. 0.267991
\(625\) 231018. 400134.i 0.591405 1.02434i
\(626\) −91552.3 + 52857.8i −0.233626 + 0.134884i
\(627\) −156330. 270772.i −0.397657 0.688761i
\(628\) −177566. 102518.i −0.450235 0.259943i
\(629\) 488007.i 1.23346i
\(630\) 0 0
\(631\) 72815.9 0.182880 0.0914402 0.995811i \(-0.470853\pi\)
0.0914402 + 0.995811i \(0.470853\pi\)
\(632\) −120087. + 207996.i −0.300650 + 0.520741i
\(633\) −303777. + 175386.i −0.758136 + 0.437710i
\(634\) −150848. 261277.i −0.375286 0.650015i
\(635\) 674438. + 389387.i 1.67261 + 0.965682i
\(636\) 661385.i 1.63508i
\(637\) 0 0
\(638\) −151341. −0.371805
\(639\) 110452. 191308.i 0.270503 0.468524i
\(640\) −34924.9 + 20163.9i −0.0852658 + 0.0492282i
\(641\) 378897. + 656269.i 0.922157 + 1.59722i 0.796070 + 0.605204i \(0.206908\pi\)
0.126087 + 0.992019i \(0.459758\pi\)
\(642\) 332235. + 191816.i 0.806075 + 0.465388i
\(643\) 353082.i 0.853992i 0.904254 + 0.426996i \(0.140428\pi\)
−0.904254 + 0.426996i \(0.859572\pi\)
\(644\) 0 0
\(645\) 514802. 1.23743
\(646\) 107450. 186109.i 0.257479 0.445967i
\(647\) 185815. 107281.i 0.443888 0.256279i −0.261358 0.965242i \(-0.584170\pi\)
0.705245 + 0.708963i \(0.250837\pi\)
\(648\) 111471. + 193073.i 0.265467 + 0.459802i
\(649\) 502587. + 290169.i 1.19322 + 0.688908i
\(650\) 43388.1i 0.102694i
\(651\) 0 0
\(652\) −49462.3 −0.116353
\(653\) 248796. 430927.i 0.583467 1.01059i −0.411598 0.911366i \(-0.635029\pi\)
0.995065 0.0992289i \(-0.0316376\pi\)
\(654\) 457560. 264172.i 1.06978 0.617635i
\(655\) 16287.2 + 28210.2i 0.0379632 + 0.0657542i
\(656\) −36462.4 21051.6i −0.0847301 0.0489190i
\(657\) 698662.i 1.61859i
\(658\) 0 0
\(659\) −197464. −0.454692 −0.227346 0.973814i \(-0.573005\pi\)
−0.227346 + 0.973814i \(0.573005\pi\)
\(660\) 248851. 431022.i 0.571283 0.989491i
\(661\) 578871. 334211.i 1.32489 0.764924i 0.340383 0.940287i \(-0.389443\pi\)
0.984504 + 0.175363i \(0.0561099\pi\)
\(662\) 153248. + 265433.i 0.349687 + 0.605675i
\(663\) −766567. 442577.i −1.74390 1.00684i
\(664\) 130115.i 0.295114i
\(665\) 0 0
\(666\) −444595. −1.00234
\(667\) 43990.3 76193.4i 0.0988793 0.171264i
\(668\) 272076. 157083.i 0.609731 0.352028i
\(669\) −514729. 891536.i −1.15007 1.99199i
\(670\) −430802. 248724.i −0.959684 0.554074i
\(671\) 256994.i 0.570792i
\(672\) 0 0
\(673\) −404534. −0.893151 −0.446575 0.894746i \(-0.647357\pi\)
−0.446575 + 0.894746i \(0.647357\pi\)
\(674\) 264382. 457922.i 0.581984 1.00803i
\(675\) −195686. + 112980.i −0.429490 + 0.247966i
\(676\) −72684.6 125893.i −0.159056 0.275493i
\(677\) −182878. 105585.i −0.399010 0.230369i 0.287047 0.957917i \(-0.407327\pi\)
−0.686057 + 0.727548i \(0.740660\pi\)
\(678\) 890550.i 1.93731i
\(679\) 0 0
\(680\) 342085. 0.739803
\(681\) 350106. 606401.i 0.754927 1.30757i
\(682\) 135984. 78510.5i 0.292361 0.168795i
\(683\) 85054.3 + 147318.i 0.182329 + 0.315802i 0.942673 0.333718i \(-0.108303\pi\)
−0.760345 + 0.649520i \(0.774970\pi\)
\(684\) −169554. 97891.8i −0.362405 0.209235i
\(685\) 581588.i 1.23946i
\(686\) 0 0
\(687\) −455983. −0.966128
\(688\) −36982.4 + 64055.4i −0.0781301 + 0.135325i
\(689\) −456241. + 263411.i −0.961072 + 0.554875i
\(690\) 144667. + 250571.i 0.303859 + 0.526299i
\(691\) −146038. 84315.2i −0.305851 0.176583i 0.339217 0.940708i \(-0.389838\pi\)
−0.645068 + 0.764125i \(0.723171\pi\)
\(692\) 263247.i 0.549732i
\(693\) 0 0
\(694\) 178834. 0.371305
\(695\) −48731.6 + 84405.7i −0.100888 + 0.174744i
\(696\) −120087. + 69332.5i −0.247901 + 0.143126i
\(697\) 178572. + 309296.i 0.367577 + 0.636662i
\(698\) −229284. 132377.i −0.470613 0.271708i
\(699\) 35109.0i 0.0718562i
\(700\) 0 0
\(701\) −487646. −0.992359 −0.496179 0.868220i \(-0.665264\pi\)
−0.496179 + 0.868220i \(0.665264\pi\)
\(702\) −216436. + 374877.i −0.439192 + 0.760703i
\(703\) 108951. 62902.9i 0.220455 0.127280i
\(704\) 35754.0 + 61927.7i 0.0721405 + 0.124951i
\(705\) 499378. + 288316.i 1.00474 + 0.580084i
\(706\) 405174.i 0.812890i
\(707\) 0 0
\(708\) 531730. 1.06078
\(709\) 193465. 335090.i 0.384865 0.666606i −0.606885 0.794790i \(-0.707581\pi\)
0.991751 + 0.128183i \(0.0409145\pi\)
\(710\) −86171.8 + 49751.3i −0.170942 + 0.0986933i
\(711\) −928032. 1.60740e6i −1.83579 3.17969i
\(712\) 82049.1 + 47371.1i 0.161850 + 0.0934444i
\(713\) 91282.7i 0.179560i
\(714\) 0 0
\(715\) 396441. 0.775472
\(716\) 19071.5 33032.9i 0.0372014 0.0644348i
\(717\) −1.12128e6 + 647370.i −2.18110 + 1.25926i
\(718\) 144730. + 250680.i 0.280744 + 0.486263i
\(719\) −163137. 94187.2i −0.315569 0.182194i 0.333847 0.942627i \(-0.391653\pi\)
−0.649416 + 0.760433i \(0.724987\pi\)
\(720\) 311654.i 0.601184i
\(721\) 0 0
\(722\) −313203. −0.600830
\(723\) −344042. + 595899.i −0.658166 + 1.13998i
\(724\) −243841. + 140782.i −0.465189 + 0.268577i
\(725\) −28828.2 49931.9i −0.0548455 0.0949952i
\(726\) −190619. 110054.i −0.361654 0.208801i
\(727\) 901538.i 1.70575i 0.522115 + 0.852875i \(0.325143\pi\)
−0.522115 + 0.852875i \(0.674857\pi\)
\(728\) 0 0
\(729\) 222465. 0.418607
\(730\) 157351. 272539.i 0.295272 0.511427i
\(731\) 543357. 313707.i 1.01684 0.587070i
\(732\) −117734. 203922.i −0.219726 0.380577i
\(733\) −348560. 201241.i −0.648738 0.374549i 0.139235 0.990259i \(-0.455536\pi\)
−0.787972 + 0.615710i \(0.788869\pi\)
\(734\) 43462.9i 0.0806726i
\(735\) 0 0
\(736\) −41570.5 −0.0767414
\(737\) −441029. + 763885.i −0.811955 + 1.40635i
\(738\) 281782. 162687.i 0.517369 0.298703i
\(739\) 18650.6 + 32303.7i 0.0341510 + 0.0591513i 0.882596 0.470133i \(-0.155794\pi\)
−0.848445 + 0.529284i \(0.822461\pi\)
\(740\) 173431. + 100130.i 0.316711 + 0.182853i
\(741\) 228188.i 0.415582i
\(742\) 0 0
\(743\) −831221. −1.50570 −0.752851 0.658191i \(-0.771322\pi\)
−0.752851 + 0.658191i \(0.771322\pi\)
\(744\) 71934.7 124595.i 0.129955 0.225089i
\(745\) 712262. 411224.i 1.28330 0.740912i
\(746\) 137873. + 238803.i 0.247743 + 0.429103i
\(747\) 870813. + 502764.i 1.56057 + 0.900997i
\(748\) 606574.i 1.08413i
\(749\) 0 0
\(750\) −597835. −1.06282
\(751\) 125549. 217458.i 0.222605 0.385562i −0.732994 0.680236i \(-0.761877\pi\)
0.955598 + 0.294673i \(0.0952108\pi\)
\(752\) −71748.9 + 41424.2i −0.126876 + 0.0732519i
\(753\) 252482. + 437311.i 0.445287 + 0.771260i
\(754\) −95654.8 55226.3i −0.168253 0.0971412i
\(755\) 717936.i 1.25948i
\(756\) 0 0
\(757\) −422399. −0.737108 −0.368554 0.929606i \(-0.620147\pi\)
−0.368554 + 0.929606i \(0.620147\pi\)
\(758\) −93466.3 + 161888.i −0.162673 + 0.281759i
\(759\) 444305. 256519.i 0.771254 0.445284i
\(760\) 44093.8 + 76372.7i 0.0763397 + 0.132224i
\(761\) −214084. 123602.i −0.369671 0.213430i 0.303644 0.952786i \(-0.401797\pi\)
−0.673315 + 0.739356i \(0.735130\pi\)
\(762\) 1.26524e6i 2.17903i
\(763\) 0 0
\(764\) 186520. 0.319551
\(765\) −1.32182e6 + 2.28946e6i −2.25865 + 3.91209i
\(766\) 511700. 295430.i 0.872083 0.503497i
\(767\) 211773. + 366802.i 0.359981 + 0.623506i
\(768\) 56740.9 + 32759.4i 0.0961997 + 0.0555409i
\(769\) 903767.i 1.52828i −0.645049 0.764141i \(-0.723163\pi\)
0.645049 0.764141i \(-0.276837\pi\)
\(770\) 0 0
\(771\) 1.08941e6 1.83266
\(772\) −236735. + 410037.i −0.397217 + 0.688000i
\(773\) −211888. + 122333.i −0.354606 + 0.204732i −0.666712 0.745315i \(-0.732299\pi\)
0.312106 + 0.950047i \(0.398966\pi\)
\(774\) −285801. 495021.i −0.477069 0.826308i
\(775\) 51805.9 + 29910.2i 0.0862534 + 0.0497984i
\(776\) 86307.3i 0.143326i
\(777\) 0 0
\(778\) 407291. 0.672893
\(779\) −46035.0 + 79735.0i −0.0758601 + 0.131393i
\(780\) 314572. 181618.i 0.517048 0.298518i
\(781\) 88217.5 + 152797.i 0.144628 + 0.250503i
\(782\) 305383. + 176313.i 0.499381 + 0.288318i
\(783\) 575222.i 0.938236i
\(784\) 0 0
\(785\) −713719. −1.15821
\(786\) 26461.0 45831.8i 0.0428313 0.0741860i
\(787\) −823098. + 475216.i −1.32893 + 0.767258i −0.985134 0.171787i \(-0.945046\pi\)
−0.343795 + 0.939045i \(0.611713\pi\)
\(788\) 243609. + 421943.i 0.392320 + 0.679518i
\(789\) −115637. 66762.8i −0.185755 0.107246i
\(790\) 836035.i 1.33958i
\(791\) 0 0
\(792\) −552615. −0.880992
\(793\) 93780.5 162433.i 0.149130 0.258301i
\(794\) −697070. + 402453.i −1.10569 + 0.638373i
\(795\) 1.15113e6 + 1.99381e6i 1.82133 + 3.15464i
\(796\) 277937. + 160467.i 0.438652 + 0.253256i
\(797\) 560412.i 0.882248i −0.897446 0.441124i \(-0.854580\pi\)
0.897446 0.441124i \(-0.145420\pi\)
\(798\) 0 0
\(799\) 702771. 1.10083
\(800\) −13621.2 + 23592.6i −0.0212831 + 0.0368635i
\(801\) −634076. + 366084.i −0.988272 + 0.570579i
\(802\) −152517. 264168.i −0.237121 0.410706i
\(803\) −483258. 279009.i −0.749459 0.432701i
\(804\) 808180.i 1.25025i
\(805\) 0 0
\(806\) 114598. 0.176404
\(807\) 735174. 1.27336e6i 1.12887 1.95526i
\(808\) −96518.0 + 55724.7i −0.147838 + 0.0853542i
\(809\) 25932.1 + 44915.7i 0.0396224 + 0.0686279i 0.885157 0.465293i \(-0.154051\pi\)
−0.845534 + 0.533921i \(0.820718\pi\)
\(810\) 672079. + 388025.i 1.02435 + 0.591412i
\(811\) 978879.i 1.48829i −0.668019 0.744145i \(-0.732857\pi\)
0.668019 0.744145i \(-0.267143\pi\)
\(812\) 0 0
\(813\) 82128.1 0.124254
\(814\) 177548. 307523.i 0.267959 0.464118i
\(815\) −149109. + 86088.1i −0.224486 + 0.129607i
\(816\) −277885. 481311.i −0.417335 0.722845i
\(817\) 140075. + 80872.1i 0.209853 + 0.121159i
\(818\) 240224.i 0.359013i
\(819\) 0 0
\(820\) −146560. −0.217965
\(821\) −74399.0 + 128863.i −0.110377 + 0.191179i −0.915923 0.401355i \(-0.868539\pi\)
0.805545 + 0.592535i \(0.201873\pi\)
\(822\) −818289. + 472440.i −1.21105 + 0.699202i
\(823\) −669533. 1.15966e6i −0.988490 1.71211i −0.625263 0.780414i \(-0.715008\pi\)
−0.363227 0.931701i \(-0.618325\pi\)
\(824\) −370219. 213746.i −0.545260 0.314806i
\(825\) 336210.i 0.493972i
\(826\) 0 0
\(827\) −127284. −0.186108 −0.0930538 0.995661i \(-0.529663\pi\)
−0.0930538 + 0.995661i \(0.529663\pi\)
\(828\) 160629. 278217.i 0.234295 0.405810i
\(829\) −385899. + 222799.i −0.561519 + 0.324193i −0.753755 0.657156i \(-0.771759\pi\)
0.192236 + 0.981349i \(0.438426\pi\)
\(830\) −226462. 392244.i −0.328730 0.569377i
\(831\) −917803. 529894.i −1.32907 0.767338i
\(832\) 52188.5i 0.0753924i
\(833\) 0 0
\(834\) 158344. 0.227651
\(835\) 546802. 947088.i 0.784254 1.35837i
\(836\) 135422. 78185.8i 0.193765 0.111870i
\(837\) 298406. + 516854.i 0.425948 + 0.737763i
\(838\) 812997. + 469384.i 1.15771 + 0.668406i
\(839\) 552232.i 0.784509i −0.919857 0.392254i \(-0.871695\pi\)
0.919857 0.392254i \(-0.128305\pi\)
\(840\) 0 0
\(841\) −560506. −0.792479
\(842\) 143528. 248598.i 0.202448 0.350650i
\(843\) −528571. + 305170.i −0.743786 + 0.429425i
\(844\) −87716.0 151928.i −0.123138 0.213282i
\(845\) −438230. 253012.i −0.613747 0.354347i
\(846\) 640254.i 0.894564i
\(847\) 0 0
\(848\) −330780. −0.459989
\(849\) −881634. + 1.52703e6i −1.22313 + 2.11852i
\(850\) 200127. 115543.i 0.276992 0.159922i
\(851\) 103216. + 178775.i 0.142524 + 0.246859i
\(852\) 139999. + 80828.7i 0.192862 + 0.111349i
\(853\) 753308.i 1.03532i 0.855586 + 0.517660i \(0.173197\pi\)
−0.855586 + 0.517660i \(0.826803\pi\)
\(854\) 0 0
\(855\) −681515. −0.932274
\(856\) −95933.4 + 166161.i −0.130925 + 0.226769i
\(857\) 1.12685e6 650586.i 1.53428 0.885816i 0.535120 0.844776i \(-0.320266\pi\)
0.999158 0.0410399i \(-0.0130671\pi\)
\(858\) −322040. 557789.i −0.437456 0.757697i
\(859\) −850759. 491186.i −1.15298 0.665671i −0.203366 0.979103i \(-0.565188\pi\)
−0.949611 + 0.313432i \(0.898521\pi\)
\(860\) 257469.i 0.348119i
\(861\) 0 0
\(862\) −649966. −0.874734
\(863\) 360718. 624781.i 0.484335 0.838893i −0.515503 0.856888i \(-0.672395\pi\)
0.999838 + 0.0179949i \(0.00572826\pi\)
\(864\) −235377. + 135895.i −0.315310 + 0.182044i
\(865\) −458177. 793585.i −0.612351 1.06062i
\(866\) 279888. + 161593.i 0.373205 + 0.215470i
\(867\) 3.37839e6i 4.49440i
\(868\) 0 0
\(869\) 1.48243e6 1.96307
\(870\) −241344. + 418020.i −0.318858 + 0.552279i
\(871\) −557504. + 321875.i −0.734872 + 0.424278i
\(872\) 132121. + 228840.i 0.173756 + 0.300954i
\(873\) −577625. 333492.i −0.757910 0.437579i
\(874\) 90905.2i 0.119005i
\(875\) 0 0
\(876\) −511281. −0.666272
\(877\) 358504. 620947.i 0.466117 0.807338i −0.533134 0.846031i \(-0.678986\pi\)
0.999251 + 0.0386923i \(0.0123192\pi\)
\(878\) −863050. + 498282.i −1.11956 + 0.646378i
\(879\) 631927. + 1.09453e6i 0.817879 + 1.41661i
\(880\) 215568. + 124458.i 0.278368 + 0.160716i
\(881\) 79128.9i 0.101949i 0.998700 + 0.0509745i \(0.0162327\pi\)
−0.998700 + 0.0509745i \(0.983767\pi\)
\(882\) 0 0
\(883\) −286591. −0.367571 −0.183786 0.982966i \(-0.558835\pi\)
−0.183786 + 0.982966i \(0.558835\pi\)
\(884\) 221347. 383384.i 0.283250 0.490603i
\(885\) 1.60296e6 925467.i 2.04661 1.18161i
\(886\) −277633. 480875.i −0.353675 0.612583i
\(887\) 725266. + 418733.i 0.921829 + 0.532218i 0.884218 0.467074i \(-0.154692\pi\)
0.0376108 + 0.999292i \(0.488025\pi\)
\(888\) 325355.i 0.412602i
\(889\) 0 0
\(890\) 329794. 0.416354
\(891\) 688034. 1.19171e6i 0.866672 1.50112i
\(892\) 445886. 257432.i 0.560394 0.323544i
\(893\) 90585.3 + 156898.i 0.113594 + 0.196750i
\(894\) −1.15718e6 668098.i −1.44786 0.835920i
\(895\) 132775.i 0.165756i
\(896\) 0 0
\(897\) 374430. 0.465356
\(898\) 109630. 189885.i 0.135950 0.235472i
\(899\) −131882. + 76142.1i −0.163180 + 0.0942118i
\(900\) −105265. 182324.i −0.129957 0.225092i
\(901\) 2.42996e6 + 1.40294e6i 2.99329 + 1.72818i
\(902\) 259875.i 0.319412i
\(903\) 0 0
\(904\) −445393. −0.545012
\(905\) −490056. + 848802.i −0.598341 + 1.03636i
\(906\) 1.01013e6 583199.i 1.23061 0.710494i
\(907\) 423285. + 733150.i 0.514538 + 0.891207i 0.999858 + 0.0168697i \(0.00537006\pi\)
−0.485319 + 0.874337i \(0.661297\pi\)
\(908\) 303281. + 175099.i 0.367852 + 0.212379i
\(909\) 861283.i 1.04236i
\(910\) 0 0
\(911\) 167017. 0.201244 0.100622 0.994925i \(-0.467917\pi\)
0.100622 + 0.994925i \(0.467917\pi\)
\(912\) 71637.2 124079.i 0.0861289 0.149180i
\(913\) −695515. + 401556.i −0.834382 + 0.481731i
\(914\) 268520. + 465090.i 0.321428 + 0.556730i
\(915\) −709845. 409829.i −0.847854 0.489509i
\(916\) 228051.i 0.271795i
\(917\) 0 0
\(918\) 2.30549e6 2.73576
\(919\) −561015. + 971707.i −0.664268 + 1.15055i 0.315215 + 0.949020i \(0.397923\pi\)
−0.979483 + 0.201526i \(0.935410\pi\)
\(920\) −125319. + 72352.7i −0.148061 + 0.0854829i
\(921\) −22406.7 38809.5i −0.0264154 0.0457529i
\(922\) 128843. + 74387.5i 0.151565 + 0.0875061i
\(923\) 128767.i 0.151148i
\(924\) 0 0
\(925\) 135281. 0.158108
\(926\) −345447. + 598331.i −0.402864 + 0.697782i
\(927\) 2.86106e6 1.65183e6i 3.32941 1.92223i
\(928\) −34675.4 60059.6i −0.0402648 0.0697407i
\(929\) −1.23549e6 713313.i −1.43156 0.826511i −0.434319 0.900759i \(-0.643011\pi\)
−0.997240 + 0.0742487i \(0.976344\pi\)
\(930\) 500804.i 0.579032i
\(931\) 0 0
\(932\) −17559.1 −0.0202149
\(933\) 165231. 286189.i 0.189814 0.328768i
\(934\) 729004. 420891.i 0.835673 0.482476i
\(935\) −1.05573e6 1.82858e6i −1.20762 2.09166i
\(936\) −349279. 201657.i −0.398677 0.230176i
\(937\) 265587.i 0.302502i −0.988495 0.151251i \(-0.951670\pi\)
0.988495 0.151251i \(-0.0483301\pi\)
\(938\) 0 0
\(939\) 597860. 0.678060
\(940\) −144196. + 249755.i −0.163192 + 0.282656i
\(941\) −518395. + 299295.i −0.585439 + 0.338003i −0.763292 0.646054i \(-0.776418\pi\)
0.177853 + 0.984057i \(0.443085\pi\)
\(942\) 579774. + 1.00420e6i 0.653366 + 1.13166i
\(943\) −130836. 75537.9i −0.147130 0.0849458i
\(944\) 265935.i 0.298423i
\(945\) 0 0
\(946\) 456536. 0.510144
\(947\) −575427. + 996669.i −0.641639 + 1.11135i 0.343428 + 0.939179i \(0.388412\pi\)
−0.985067 + 0.172172i \(0.944922\pi\)
\(948\) 1.17629e6 679134.i 1.30888 0.755681i
\(949\) −203629. 352695.i −0.226103 0.391622i
\(950\) 51591.7 + 29786.5i 0.0571653 + 0.0330044i
\(951\) 1.70621e6i 1.88656i
\(952\) 0 0
\(953\) 464604. 0.511561 0.255781 0.966735i \(-0.417668\pi\)
0.255781 + 0.966735i \(0.417668\pi\)
\(954\) 1.27814e6 2.21380e6i 1.40437 2.43243i
\(955\) 562285. 324635.i 0.616524 0.355950i
\(956\) −323770. 560787.i −0.354259 0.613595i
\(957\) 741220. + 427944.i 0.809325 + 0.467264i
\(958\) 132571.i 0.144450i
\(959\) 0 0
\(960\) 228068. 0.247470
\(961\) −382761. + 662961.i −0.414458 + 0.717862i
\(962\) 224438. 129580.i 0.242520 0.140019i
\(963\) −741374. 1.28410e6i −0.799438 1.38467i
\(964\) −298028. 172066.i −0.320703 0.185158i
\(965\) 1.64813e6i 1.76985i
\(966\) 0 0
\(967\) 101298. 0.108330 0.0541648 0.998532i \(-0.482750\pi\)
0.0541648 + 0.998532i \(0.482750\pi\)
\(968\) 55041.6 95334.8i 0.0587408 0.101742i
\(969\) −1.05252e6 + 607670.i −1.12094 + 0.647173i
\(970\) 150216. + 260182.i 0.159652 + 0.276525i
\(971\) −282567. 163140.i −0.299697 0.173030i 0.342610 0.939478i \(-0.388689\pi\)
−0.642307 + 0.766448i \(0.722022\pi\)
\(972\) 287878.i 0.304702i
\(973\) 0 0
\(974\) −303162. −0.319563
\(975\) 122688. 212501.i 0.129060 0.223538i
\(976\) 101988. 58882.7i 0.107065 0.0618142i
\(977\) −370964. 642529.i −0.388636 0.673137i 0.603630 0.797264i \(-0.293720\pi\)
−0.992266 + 0.124127i \(0.960387\pi\)
\(978\) 242251. + 139864.i 0.253272 + 0.146227i
\(979\) 584780.i 0.610137i
\(980\) 0 0
\(981\) −2.04207e6 −2.12193
\(982\) −164567. + 285039.i −0.170656 + 0.295584i
\(983\) 506189. 292248.i 0.523849 0.302444i −0.214659 0.976689i \(-0.568864\pi\)
0.738508 + 0.674245i \(0.235531\pi\)
\(984\) 119054. + 206208.i 0.122958 + 0.212969i
\(985\) 1.46877e6 + 847993.i 1.51384 + 0.874017i
\(986\) 588276.i 0.605100i
\(987\) 0 0
\(988\) 114124. 0.116913
\(989\) −132701. + 229846.i −0.135670 + 0.234987i
\(990\) −1.66591e6 + 961815.i −1.69974 + 0.981344i
\(991\) −291172. 504324.i −0.296484 0.513526i 0.678845 0.734282i \(-0.262481\pi\)
−0.975329 + 0.220756i \(0.929148\pi\)
\(992\) 62313.7 + 35976.9i 0.0633229 + 0.0365595i
\(993\) 1.73335e6i 1.75787i
\(994\) 0 0
\(995\) 1.11716e6 1.12842
\(996\) −367923. + 637261.i −0.370884 + 0.642390i
\(997\) −1.18588e6 + 684671.i −1.19303 + 0.688797i −0.958993 0.283430i \(-0.908528\pi\)
−0.234039 + 0.972227i \(0.575194\pi\)
\(998\) 626366. + 1.08490e6i 0.628879 + 1.08925i
\(999\) 1.16884e6 + 674833.i 1.17119 + 0.676185i
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 98.5.d.c.19.3 8
7.2 even 3 98.5.b.a.97.1 4
7.3 odd 6 inner 98.5.d.c.31.3 8
7.4 even 3 inner 98.5.d.c.31.4 8
7.5 odd 6 98.5.b.a.97.2 yes 4
7.6 odd 2 inner 98.5.d.c.19.4 8
21.2 odd 6 882.5.c.c.685.3 4
21.5 even 6 882.5.c.c.685.4 4
28.19 even 6 784.5.c.a.97.1 4
28.23 odd 6 784.5.c.a.97.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
98.5.b.a.97.1 4 7.2 even 3
98.5.b.a.97.2 yes 4 7.5 odd 6
98.5.d.c.19.3 8 1.1 even 1 trivial
98.5.d.c.19.4 8 7.6 odd 2 inner
98.5.d.c.31.3 8 7.3 odd 6 inner
98.5.d.c.31.4 8 7.4 even 3 inner
784.5.c.a.97.1 4 28.19 even 6
784.5.c.a.97.4 4 28.23 odd 6
882.5.c.c.685.3 4 21.2 odd 6
882.5.c.c.685.4 4 21.5 even 6