Properties

Label 21.5.b.a.8.6
Level $21$
Weight $5$
Character 21.8
Analytic conductor $2.171$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,5,Mod(8,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.8");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 21.b (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: \(2.17076922476\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 82x^{6} + 2017x^{4} + 13020x^{2} + 756 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 3^{3}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 8.6
Root \(3.15624i\) of defining polynomial
Character \(\chi\) \(=\) 21.8
Dual form 21.5.b.a.8.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.15624i q^{2} +(7.09942 - 5.53157i) q^{3} +6.03813 q^{4} +16.3361i q^{5} +(17.4590 + 22.4075i) q^{6} -18.5203 q^{7} +69.5577i q^{8} +(19.8035 - 78.5418i) q^{9} +O(q^{10})\) \(q+3.15624i q^{2} +(7.09942 - 5.53157i) q^{3} +6.03813 q^{4} +16.3361i q^{5} +(17.4590 + 22.4075i) q^{6} -18.5203 q^{7} +69.5577i q^{8} +(19.8035 - 78.5418i) q^{9} -51.5608 q^{10} -179.202i q^{11} +(42.8672 - 33.4003i) q^{12} -208.099 q^{13} -58.4544i q^{14} +(90.3643 + 115.977i) q^{15} -122.931 q^{16} +160.272i q^{17} +(247.897 + 62.5048i) q^{18} -212.754 q^{19} +98.6396i q^{20} +(-131.483 + 102.446i) q^{21} +565.606 q^{22} -222.053i q^{23} +(384.763 + 493.819i) q^{24} +358.131 q^{25} -656.812i q^{26} +(-293.866 - 667.146i) q^{27} -111.828 q^{28} +1155.40i q^{29} +(-366.052 + 285.212i) q^{30} +428.142 q^{31} +724.923i q^{32} +(-991.270 - 1272.23i) q^{33} -505.857 q^{34} -302.549i q^{35} +(119.576 - 474.246i) q^{36} -235.617 q^{37} -671.503i q^{38} +(-1477.38 + 1151.12i) q^{39} -1136.30 q^{40} -1473.51i q^{41} +(-323.345 - 414.993i) q^{42} +3668.51 q^{43} -1082.05i q^{44} +(1283.07 + 323.513i) q^{45} +700.855 q^{46} +3735.71i q^{47} +(-872.738 + 680.001i) q^{48} +343.000 q^{49} +1130.35i q^{50} +(886.555 + 1137.84i) q^{51} -1256.53 q^{52} -2145.77i q^{53} +(2105.68 - 927.511i) q^{54} +2927.47 q^{55} -1288.23i q^{56} +(-1510.43 + 1176.86i) q^{57} -3646.72 q^{58} +1188.10i q^{59} +(545.632 + 700.284i) q^{60} -881.220 q^{61} +1351.32i q^{62} +(-366.767 + 1454.62i) q^{63} -4254.93 q^{64} -3399.54i q^{65} +(4015.48 - 3128.69i) q^{66} -218.549 q^{67} +967.743i q^{68} +(-1228.30 - 1576.45i) q^{69} +954.919 q^{70} -4245.30i q^{71} +(5463.19 + 1377.49i) q^{72} -9809.98 q^{73} -743.665i q^{74} +(2542.52 - 1981.03i) q^{75} -1284.64 q^{76} +3318.87i q^{77} +(-3633.20 - 4662.99i) q^{78} +2115.73 q^{79} -2008.21i q^{80} +(-5776.64 - 3110.81i) q^{81} +4650.74 q^{82} +9614.45i q^{83} +(-793.912 + 618.582i) q^{84} -2618.22 q^{85} +11578.7i q^{86} +(6391.16 + 8202.65i) q^{87} +12464.9 q^{88} -6522.50i q^{89} +(-1021.09 + 4049.68i) q^{90} +3854.05 q^{91} -1340.79i q^{92} +(3039.56 - 2368.29i) q^{93} -11790.8 q^{94} -3475.57i q^{95} +(4009.96 + 5146.54i) q^{96} +15210.9 q^{97} +1082.59i q^{98} +(-14074.9 - 3548.84i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} - 36 q^{4} - 34 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{3} - 36 q^{4} - 34 q^{6} + 64 q^{9} - 4 q^{10} + 98 q^{12} + 420 q^{13} + 76 q^{15} - 444 q^{16} - 712 q^{18} - 372 q^{19} + 98 q^{21} - 16 q^{22} + 1146 q^{24} + 1056 q^{25} - 1862 q^{27} + 392 q^{28} + 2348 q^{30} - 2776 q^{31} + 1396 q^{33} + 2928 q^{34} - 3268 q^{36} - 2560 q^{37} - 2540 q^{39} - 1980 q^{40} - 2450 q^{42} + 4720 q^{43} + 9700 q^{45} + 7536 q^{46} - 2962 q^{48} + 2744 q^{49} + 4764 q^{51} - 20252 q^{52} + 4886 q^{54} + 184 q^{55} - 14144 q^{57} - 7504 q^{58} - 13828 q^{60} + 972 q^{61} - 6076 q^{63} + 22772 q^{64} + 36020 q^{66} + 10200 q^{67} - 5760 q^{69} + 10780 q^{70} + 14304 q^{72} - 32008 q^{73} + 2114 q^{75} + 17332 q^{76} - 29668 q^{78} - 23168 q^{79} - 17216 q^{81} - 31976 q^{82} - 14798 q^{84} + 32016 q^{85} + 50764 q^{87} + 29208 q^{88} - 24352 q^{90} + 11956 q^{91} + 31848 q^{93} - 64992 q^{94} + 28630 q^{96} + 28112 q^{97} - 32432 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.15624i 0.789061i 0.918883 + 0.394530i \(0.129093\pi\)
−0.918883 + 0.394530i \(0.870907\pi\)
\(3\) 7.09942 5.53157i 0.788825 0.614618i
\(4\) 6.03813 0.377383
\(5\) 16.3361i 0.653445i 0.945120 + 0.326722i \(0.105944\pi\)
−0.945120 + 0.326722i \(0.894056\pi\)
\(6\) 17.4590 + 22.4075i 0.484971 + 0.622430i
\(7\) −18.5203 −0.377964
\(8\) 69.5577i 1.08684i
\(9\) 19.8035 78.5418i 0.244488 0.969652i
\(10\) −51.5608 −0.515608
\(11\) 179.202i 1.48101i −0.672050 0.740506i \(-0.734586\pi\)
0.672050 0.740506i \(-0.265414\pi\)
\(12\) 42.8672 33.4003i 0.297689 0.231947i
\(13\) −208.099 −1.23136 −0.615679 0.787997i \(-0.711118\pi\)
−0.615679 + 0.787997i \(0.711118\pi\)
\(14\) 58.4544i 0.298237i
\(15\) 90.3643 + 115.977i 0.401619 + 0.515453i
\(16\) −122.931 −0.480199
\(17\) 160.272i 0.554574i 0.960787 + 0.277287i \(0.0894354\pi\)
−0.960787 + 0.277287i \(0.910565\pi\)
\(18\) 247.897 + 62.5048i 0.765115 + 0.192916i
\(19\) −212.754 −0.589346 −0.294673 0.955598i \(-0.595211\pi\)
−0.294673 + 0.955598i \(0.595211\pi\)
\(20\) 98.6396i 0.246599i
\(21\) −131.483 + 102.446i −0.298148 + 0.232304i
\(22\) 565.606 1.16861
\(23\) 222.053i 0.419761i −0.977727 0.209880i \(-0.932693\pi\)
0.977727 0.209880i \(-0.0673075\pi\)
\(24\) 384.763 + 493.819i 0.667991 + 0.857325i
\(25\) 358.131 0.573010
\(26\) 656.812i 0.971616i
\(27\) −293.866 667.146i −0.403108 0.915152i
\(28\) −111.828 −0.142637
\(29\) 1155.40i 1.37384i 0.726734 + 0.686919i \(0.241037\pi\)
−0.726734 + 0.686919i \(0.758963\pi\)
\(30\) −366.052 + 285.212i −0.406724 + 0.316902i
\(31\) 428.142 0.445517 0.222758 0.974874i \(-0.428494\pi\)
0.222758 + 0.974874i \(0.428494\pi\)
\(32\) 724.923i 0.707933i
\(33\) −991.270 1272.23i −0.910257 1.16826i
\(34\) −505.857 −0.437593
\(35\) 302.549i 0.246979i
\(36\) 119.576 474.246i 0.0922657 0.365930i
\(37\) −235.617 −0.172109 −0.0860545 0.996290i \(-0.527426\pi\)
−0.0860545 + 0.996290i \(0.527426\pi\)
\(38\) 671.503i 0.465030i
\(39\) −1477.38 + 1151.12i −0.971325 + 0.756815i
\(40\) −1136.30 −0.710189
\(41\) 1473.51i 0.876565i −0.898837 0.438282i \(-0.855587\pi\)
0.898837 0.438282i \(-0.144413\pi\)
\(42\) −323.345 414.993i −0.183302 0.235257i
\(43\) 3668.51 1.98405 0.992025 0.126043i \(-0.0402276\pi\)
0.992025 + 0.126043i \(0.0402276\pi\)
\(44\) 1082.05i 0.558909i
\(45\) 1283.07 + 323.513i 0.633614 + 0.159760i
\(46\) 700.855 0.331217
\(47\) 3735.71i 1.69113i 0.533872 + 0.845565i \(0.320736\pi\)
−0.533872 + 0.845565i \(0.679264\pi\)
\(48\) −872.738 + 680.001i −0.378793 + 0.295139i
\(49\) 343.000 0.142857
\(50\) 1130.35i 0.452140i
\(51\) 886.555 + 1137.84i 0.340852 + 0.437462i
\(52\) −1256.53 −0.464693
\(53\) 2145.77i 0.763891i −0.924185 0.381946i \(-0.875254\pi\)
0.924185 0.381946i \(-0.124746\pi\)
\(54\) 2105.68 927.511i 0.722111 0.318077i
\(55\) 2927.47 0.967759
\(56\) 1288.23i 0.410787i
\(57\) −1510.43 + 1176.86i −0.464890 + 0.362223i
\(58\) −3646.72 −1.08404
\(59\) 1188.10i 0.341310i 0.985331 + 0.170655i \(0.0545883\pi\)
−0.985331 + 0.170655i \(0.945412\pi\)
\(60\) 545.632 + 700.284i 0.151564 + 0.194523i
\(61\) −881.220 −0.236823 −0.118412 0.992965i \(-0.537780\pi\)
−0.118412 + 0.992965i \(0.537780\pi\)
\(62\) 1351.32i 0.351540i
\(63\) −366.767 + 1454.62i −0.0924079 + 0.366494i
\(64\) −4254.93 −1.03880
\(65\) 3399.54i 0.804624i
\(66\) 4015.48 3128.69i 0.921827 0.718248i
\(67\) −218.549 −0.0486854 −0.0243427 0.999704i \(-0.507749\pi\)
−0.0243427 + 0.999704i \(0.507749\pi\)
\(68\) 967.743i 0.209287i
\(69\) −1228.30 1576.45i −0.257993 0.331118i
\(70\) 954.919 0.194881
\(71\) 4245.30i 0.842155i −0.907025 0.421077i \(-0.861652\pi\)
0.907025 0.421077i \(-0.138348\pi\)
\(72\) 5463.19 + 1377.49i 1.05386 + 0.265719i
\(73\) −9809.98 −1.84087 −0.920434 0.390899i \(-0.872164\pi\)
−0.920434 + 0.390899i \(0.872164\pi\)
\(74\) 743.665i 0.135804i
\(75\) 2542.52 1981.03i 0.452004 0.352182i
\(76\) −1284.64 −0.222409
\(77\) 3318.87i 0.559770i
\(78\) −3633.20 4662.99i −0.597173 0.766434i
\(79\) 2115.73 0.339006 0.169503 0.985530i \(-0.445784\pi\)
0.169503 + 0.985530i \(0.445784\pi\)
\(80\) 2008.21i 0.313784i
\(81\) −5776.64 3110.81i −0.880451 0.474137i
\(82\) 4650.74 0.691663
\(83\) 9614.45i 1.39562i 0.716281 + 0.697812i \(0.245843\pi\)
−0.716281 + 0.697812i \(0.754157\pi\)
\(84\) −793.912 + 618.582i −0.112516 + 0.0876676i
\(85\) −2618.22 −0.362384
\(86\) 11578.7i 1.56554i
\(87\) 6391.16 + 8202.65i 0.844386 + 1.08372i
\(88\) 12464.9 1.60962
\(89\) 6522.50i 0.823444i −0.911309 0.411722i \(-0.864927\pi\)
0.911309 0.411722i \(-0.135073\pi\)
\(90\) −1021.09 + 4049.68i −0.126060 + 0.499960i
\(91\) 3854.05 0.465409
\(92\) 1340.79i 0.158411i
\(93\) 3039.56 2368.29i 0.351435 0.273823i
\(94\) −11790.8 −1.33440
\(95\) 3475.57i 0.385105i
\(96\) 4009.96 + 5146.54i 0.435109 + 0.558435i
\(97\) 15210.9 1.61663 0.808317 0.588748i \(-0.200379\pi\)
0.808317 + 0.588748i \(0.200379\pi\)
\(98\) 1082.59i 0.112723i
\(99\) −14074.9 3548.84i −1.43607 0.362090i
\(100\) 2162.44 0.216244
\(101\) 5857.05i 0.574164i −0.957906 0.287082i \(-0.907315\pi\)
0.957906 0.287082i \(-0.0926853\pi\)
\(102\) −3591.29 + 2798.18i −0.345184 + 0.268953i
\(103\) −1974.81 −0.186144 −0.0930722 0.995659i \(-0.529669\pi\)
−0.0930722 + 0.995659i \(0.529669\pi\)
\(104\) 14474.9i 1.33829i
\(105\) −1673.57 2147.92i −0.151798 0.194823i
\(106\) 6772.57 0.602757
\(107\) 2897.22i 0.253054i −0.991963 0.126527i \(-0.959617\pi\)
0.991963 0.126527i \(-0.0403831\pi\)
\(108\) −1774.40 4028.31i −0.152126 0.345363i
\(109\) −11832.0 −0.995872 −0.497936 0.867214i \(-0.665909\pi\)
−0.497936 + 0.867214i \(0.665909\pi\)
\(110\) 9239.81i 0.763621i
\(111\) −1672.75 + 1303.33i −0.135764 + 0.105781i
\(112\) 2276.71 0.181498
\(113\) 5282.24i 0.413677i −0.978375 0.206838i \(-0.933683\pi\)
0.978375 0.206838i \(-0.0663174\pi\)
\(114\) −3714.46 4767.28i −0.285816 0.366827i
\(115\) 3627.49 0.274291
\(116\) 6976.44i 0.518463i
\(117\) −4121.11 + 16344.5i −0.301052 + 1.19399i
\(118\) −3749.93 −0.269314
\(119\) 2968.28i 0.209609i
\(120\) −8067.09 + 6285.54i −0.560215 + 0.436496i
\(121\) −17472.5 −1.19340
\(122\) 2781.34i 0.186868i
\(123\) −8150.79 10461.0i −0.538753 0.691456i
\(124\) 2585.17 0.168131
\(125\) 16060.5i 1.02788i
\(126\) −4591.12 1157.61i −0.289186 0.0729154i
\(127\) 21180.9 1.31322 0.656609 0.754231i \(-0.271990\pi\)
0.656609 + 0.754231i \(0.271990\pi\)
\(128\) 1830.82i 0.111744i
\(129\) 26044.3 20292.6i 1.56507 1.21943i
\(130\) 10729.8 0.634897
\(131\) 9714.22i 0.566064i −0.959111 0.283032i \(-0.908660\pi\)
0.959111 0.283032i \(-0.0913402\pi\)
\(132\) −5985.42 7681.91i −0.343516 0.440881i
\(133\) 3940.26 0.222752
\(134\) 689.793i 0.0384157i
\(135\) 10898.6 4800.63i 0.598002 0.263409i
\(136\) −11148.2 −0.602733
\(137\) 18088.4i 0.963740i 0.876243 + 0.481870i \(0.160042\pi\)
−0.876243 + 0.481870i \(0.839958\pi\)
\(138\) 4975.66 3876.82i 0.261272 0.203572i
\(139\) −5463.03 −0.282751 −0.141376 0.989956i \(-0.545152\pi\)
−0.141376 + 0.989956i \(0.545152\pi\)
\(140\) 1826.83i 0.0932057i
\(141\) 20664.3 + 26521.4i 1.03940 + 1.33401i
\(142\) 13399.2 0.664511
\(143\) 37291.9i 1.82365i
\(144\) −2434.47 + 9655.22i −0.117403 + 0.465626i
\(145\) −18874.7 −0.897727
\(146\) 30962.7i 1.45256i
\(147\) 2435.10 1897.33i 0.112689 0.0878026i
\(148\) −1422.69 −0.0649510
\(149\) 5998.91i 0.270209i 0.990831 + 0.135104i \(0.0431370\pi\)
−0.990831 + 0.135104i \(0.956863\pi\)
\(150\) 6252.60 + 8024.82i 0.277893 + 0.356659i
\(151\) −121.613 −0.00533366 −0.00266683 0.999996i \(-0.500849\pi\)
−0.00266683 + 0.999996i \(0.500849\pi\)
\(152\) 14798.7i 0.640524i
\(153\) 12588.1 + 3173.95i 0.537744 + 0.135587i
\(154\) −10475.2 −0.441692
\(155\) 6994.17i 0.291121i
\(156\) −8920.64 + 6950.58i −0.366562 + 0.285609i
\(157\) −4449.79 −0.180526 −0.0902631 0.995918i \(-0.528771\pi\)
−0.0902631 + 0.995918i \(0.528771\pi\)
\(158\) 6677.77i 0.267496i
\(159\) −11869.5 15233.7i −0.469502 0.602576i
\(160\) −11842.4 −0.462595
\(161\) 4112.49i 0.158655i
\(162\) 9818.48 18232.5i 0.374123 0.694729i
\(163\) −35624.1 −1.34082 −0.670408 0.741993i \(-0.733881\pi\)
−0.670408 + 0.741993i \(0.733881\pi\)
\(164\) 8897.22i 0.330801i
\(165\) 20783.4 16193.5i 0.763392 0.594803i
\(166\) −30345.6 −1.10123
\(167\) 11825.6i 0.424025i −0.977267 0.212013i \(-0.931998\pi\)
0.977267 0.212013i \(-0.0680018\pi\)
\(168\) −7125.91 9145.66i −0.252477 0.324038i
\(169\) 14744.3 0.516241
\(170\) 8263.75i 0.285943i
\(171\) −4213.28 + 16710.1i −0.144088 + 0.571461i
\(172\) 22150.9 0.748747
\(173\) 50680.7i 1.69337i −0.532098 0.846683i \(-0.678596\pi\)
0.532098 0.846683i \(-0.321404\pi\)
\(174\) −25889.6 + 20172.0i −0.855118 + 0.666272i
\(175\) −6632.68 −0.216577
\(176\) 22029.5i 0.711180i
\(177\) 6572.05 + 8434.81i 0.209775 + 0.269233i
\(178\) 20586.6 0.649747
\(179\) 36735.0i 1.14650i −0.819381 0.573249i \(-0.805683\pi\)
0.819381 0.573249i \(-0.194317\pi\)
\(180\) 7747.34 + 1953.41i 0.239115 + 0.0602906i
\(181\) −16220.5 −0.495115 −0.247558 0.968873i \(-0.579628\pi\)
−0.247558 + 0.968873i \(0.579628\pi\)
\(182\) 12164.3i 0.367236i
\(183\) −6256.15 + 4874.52i −0.186812 + 0.145556i
\(184\) 15445.5 0.456212
\(185\) 3849.07i 0.112464i
\(186\) 7474.91 + 9593.58i 0.216063 + 0.277303i
\(187\) 28721.1 0.821331
\(188\) 22556.7i 0.638204i
\(189\) 5442.47 + 12355.7i 0.152360 + 0.345895i
\(190\) 10969.8 0.303871
\(191\) 12814.6i 0.351268i −0.984456 0.175634i \(-0.943802\pi\)
0.984456 0.175634i \(-0.0561975\pi\)
\(192\) −30207.5 + 23536.4i −0.819432 + 0.638466i
\(193\) −15443.2 −0.414594 −0.207297 0.978278i \(-0.566467\pi\)
−0.207297 + 0.978278i \(0.566467\pi\)
\(194\) 48009.3i 1.27562i
\(195\) −18804.8 24134.7i −0.494537 0.634707i
\(196\) 2071.08 0.0539119
\(197\) 35593.4i 0.917142i 0.888658 + 0.458571i \(0.151639\pi\)
−0.888658 + 0.458571i \(0.848361\pi\)
\(198\) 11201.0 44423.8i 0.285711 1.13314i
\(199\) 33236.5 0.839285 0.419642 0.907689i \(-0.362155\pi\)
0.419642 + 0.907689i \(0.362155\pi\)
\(200\) 24910.8i 0.622769i
\(201\) −1551.57 + 1208.92i −0.0384042 + 0.0299229i
\(202\) 18486.3 0.453051
\(203\) 21398.3i 0.519262i
\(204\) 5353.14 + 6870.42i 0.128632 + 0.165091i
\(205\) 24071.4 0.572787
\(206\) 6232.97i 0.146879i
\(207\) −17440.5 4397.45i −0.407022 0.102627i
\(208\) 25581.8 0.591296
\(209\) 38126.0i 0.872828i
\(210\) 6779.37 5282.20i 0.153727 0.119778i
\(211\) −31336.8 −0.703865 −0.351932 0.936025i \(-0.614475\pi\)
−0.351932 + 0.936025i \(0.614475\pi\)
\(212\) 12956.4i 0.288280i
\(213\) −23483.2 30139.2i −0.517604 0.664312i
\(214\) 9144.33 0.199675
\(215\) 59929.2i 1.29647i
\(216\) 46405.1 20440.6i 0.994623 0.438113i
\(217\) −7929.29 −0.168390
\(218\) 37344.5i 0.785804i
\(219\) −69645.2 + 54264.6i −1.45212 + 1.13143i
\(220\) 17676.5 0.365216
\(221\) 33352.5i 0.682879i
\(222\) −4113.63 5279.59i −0.0834679 0.107126i
\(223\) 16649.0 0.334795 0.167397 0.985890i \(-0.446464\pi\)
0.167397 + 0.985890i \(0.446464\pi\)
\(224\) 13425.8i 0.267573i
\(225\) 7092.27 28128.3i 0.140094 0.555620i
\(226\) 16672.0 0.326416
\(227\) 51984.4i 1.00884i −0.863459 0.504419i \(-0.831707\pi\)
0.863459 0.504419i \(-0.168293\pi\)
\(228\) −9120.17 + 7106.05i −0.175442 + 0.136697i
\(229\) 37331.0 0.711866 0.355933 0.934511i \(-0.384163\pi\)
0.355933 + 0.934511i \(0.384163\pi\)
\(230\) 11449.2i 0.216432i
\(231\) 18358.6 + 23562.1i 0.344045 + 0.441560i
\(232\) −80366.8 −1.49314
\(233\) 24216.0i 0.446058i 0.974812 + 0.223029i \(0.0715944\pi\)
−0.974812 + 0.223029i \(0.928406\pi\)
\(234\) −51587.2 13007.2i −0.942129 0.237549i
\(235\) −61027.0 −1.10506
\(236\) 7173.89i 0.128804i
\(237\) 15020.5 11703.3i 0.267416 0.208359i
\(238\) 9368.61 0.165395
\(239\) 68021.6i 1.19083i −0.803417 0.595416i \(-0.796987\pi\)
0.803417 0.595416i \(-0.203013\pi\)
\(240\) −11108.6 14257.2i −0.192857 0.247520i
\(241\) −12198.6 −0.210027 −0.105014 0.994471i \(-0.533489\pi\)
−0.105014 + 0.994471i \(0.533489\pi\)
\(242\) 55147.4i 0.941661i
\(243\) −58218.5 + 9868.89i −0.985935 + 0.167130i
\(244\) −5320.92 −0.0893731
\(245\) 5603.29i 0.0933493i
\(246\) 33017.6 25725.9i 0.545601 0.425109i
\(247\) 44273.9 0.725695
\(248\) 29780.5i 0.484205i
\(249\) 53183.0 + 68257.1i 0.857776 + 1.10090i
\(250\) −50691.0 −0.811056
\(251\) 49873.6i 0.791633i −0.918330 0.395816i \(-0.870462\pi\)
0.918330 0.395816i \(-0.129538\pi\)
\(252\) −2214.59 + 8783.15i −0.0348732 + 0.138309i
\(253\) −39792.5 −0.621671
\(254\) 66852.1i 1.03621i
\(255\) −18587.9 + 14482.9i −0.285857 + 0.222728i
\(256\) −62300.4 −0.950628
\(257\) 37680.5i 0.570494i 0.958454 + 0.285247i \(0.0920756\pi\)
−0.958454 + 0.285247i \(0.907924\pi\)
\(258\) 64048.4 + 82202.1i 0.962207 + 1.23493i
\(259\) 4363.69 0.0650511
\(260\) 20526.8i 0.303652i
\(261\) 90747.0 + 22881.0i 1.33214 + 0.335887i
\(262\) 30660.4 0.446659
\(263\) 96710.2i 1.39817i 0.715037 + 0.699086i \(0.246410\pi\)
−0.715037 + 0.699086i \(0.753590\pi\)
\(264\) 88493.6 68950.4i 1.26971 0.989303i
\(265\) 35053.6 0.499161
\(266\) 12436.4i 0.175765i
\(267\) −36079.6 46306.0i −0.506104 0.649553i
\(268\) −1319.63 −0.0183730
\(269\) 32437.0i 0.448266i −0.974559 0.224133i \(-0.928045\pi\)
0.974559 0.224133i \(-0.0719551\pi\)
\(270\) 15151.9 + 34398.6i 0.207846 + 0.471860i
\(271\) 114921. 1.56481 0.782404 0.622771i \(-0.213993\pi\)
0.782404 + 0.622771i \(0.213993\pi\)
\(272\) 19702.4i 0.266306i
\(273\) 27361.6 21319.0i 0.367126 0.286049i
\(274\) −57091.5 −0.760449
\(275\) 64178.0i 0.848634i
\(276\) −7416.66 9518.82i −0.0973621 0.124958i
\(277\) −58013.0 −0.756077 −0.378038 0.925790i \(-0.623401\pi\)
−0.378038 + 0.925790i \(0.623401\pi\)
\(278\) 17242.7i 0.223108i
\(279\) 8478.72 33627.0i 0.108924 0.431996i
\(280\) 21044.6 0.268426
\(281\) 55194.8i 0.699013i 0.936934 + 0.349507i \(0.113651\pi\)
−0.936934 + 0.349507i \(0.886349\pi\)
\(282\) −83707.9 + 65221.6i −1.05261 + 0.820150i
\(283\) 70469.4 0.879888 0.439944 0.898025i \(-0.354998\pi\)
0.439944 + 0.898025i \(0.354998\pi\)
\(284\) 25633.7i 0.317815i
\(285\) −19225.4 24674.6i −0.236693 0.303780i
\(286\) −117702. −1.43897
\(287\) 27289.7i 0.331310i
\(288\) 56936.8 + 14356.1i 0.686449 + 0.173081i
\(289\) 57833.9 0.692447
\(290\) 59573.2i 0.708361i
\(291\) 107989. 84140.1i 1.27524 0.993613i
\(292\) −59233.9 −0.694712
\(293\) 103626.i 1.20707i 0.797335 + 0.603537i \(0.206243\pi\)
−0.797335 + 0.603537i \(0.793757\pi\)
\(294\) 5988.43 + 7685.77i 0.0692816 + 0.0889186i
\(295\) −19408.9 −0.223027
\(296\) 16389.0i 0.187055i
\(297\) −119554. + 52661.4i −1.35535 + 0.597007i
\(298\) −18934.0 −0.213211
\(299\) 46209.2i 0.516876i
\(300\) 15352.1 11961.7i 0.170579 0.132908i
\(301\) −67941.7 −0.749900
\(302\) 383.839i 0.00420858i
\(303\) −32398.7 41581.7i −0.352892 0.452915i
\(304\) 26154.0 0.283003
\(305\) 14395.7i 0.154751i
\(306\) −10017.8 + 39731.0i −0.106986 + 0.424313i
\(307\) −54478.8 −0.578030 −0.289015 0.957325i \(-0.593328\pi\)
−0.289015 + 0.957325i \(0.593328\pi\)
\(308\) 20039.8i 0.211248i
\(309\) −14020.0 + 10923.8i −0.146835 + 0.114408i
\(310\) −22075.3 −0.229712
\(311\) 119113.i 1.23152i 0.787935 + 0.615758i \(0.211150\pi\)
−0.787935 + 0.615758i \(0.788850\pi\)
\(312\) −80068.9 102763.i −0.822536 1.05567i
\(313\) −8174.96 −0.0834444 −0.0417222 0.999129i \(-0.513284\pi\)
−0.0417222 + 0.999129i \(0.513284\pi\)
\(314\) 14044.6i 0.142446i
\(315\) −23762.8 5991.55i −0.239484 0.0603834i
\(316\) 12775.1 0.127935
\(317\) 118540.i 1.17963i −0.807539 0.589814i \(-0.799201\pi\)
0.807539 0.589814i \(-0.200799\pi\)
\(318\) 48081.4 37462.9i 0.475469 0.370465i
\(319\) 207050. 2.03467
\(320\) 69509.0i 0.678799i
\(321\) −16026.2 20568.6i −0.155532 0.199615i
\(322\) −12980.0 −0.125188
\(323\) 34098.5i 0.326836i
\(324\) −34880.1 18783.5i −0.332267 0.178931i
\(325\) −74526.9 −0.705580
\(326\) 112438.i 1.05799i
\(327\) −84000.0 + 65449.2i −0.785568 + 0.612081i
\(328\) 102494. 0.952685
\(329\) 69186.3i 0.639187i
\(330\) 51110.6 + 65597.3i 0.469336 + 0.602363i
\(331\) −75489.4 −0.689017 −0.344508 0.938783i \(-0.611954\pi\)
−0.344508 + 0.938783i \(0.611954\pi\)
\(332\) 58053.3i 0.526685i
\(333\) −4666.06 + 18505.8i −0.0420786 + 0.166886i
\(334\) 37324.6 0.334582
\(335\) 3570.24i 0.0318132i
\(336\) 16163.3 12593.8i 0.143170 0.111552i
\(337\) 108658. 0.956757 0.478379 0.878154i \(-0.341225\pi\)
0.478379 + 0.878154i \(0.341225\pi\)
\(338\) 46536.8i 0.407345i
\(339\) −29219.0 37500.8i −0.254253 0.326318i
\(340\) −15809.2 −0.136758
\(341\) 76724.0i 0.659816i
\(342\) −52741.1 13298.1i −0.450917 0.113694i
\(343\) −6352.45 −0.0539949
\(344\) 255173.i 2.15634i
\(345\) 25753.1 20065.7i 0.216367 0.168584i
\(346\) 159961. 1.33617
\(347\) 125339.i 1.04094i 0.853879 + 0.520471i \(0.174244\pi\)
−0.853879 + 0.520471i \(0.825756\pi\)
\(348\) 38590.6 + 49528.7i 0.318657 + 0.408976i
\(349\) −71120.9 −0.583911 −0.291955 0.956432i \(-0.594306\pi\)
−0.291955 + 0.956432i \(0.594306\pi\)
\(350\) 20934.4i 0.170893i
\(351\) 61153.3 + 138833.i 0.496370 + 1.12688i
\(352\) 129908. 1.04846
\(353\) 54743.5i 0.439322i −0.975576 0.219661i \(-0.929505\pi\)
0.975576 0.219661i \(-0.0704951\pi\)
\(354\) −26622.3 + 20743.0i −0.212441 + 0.165525i
\(355\) 69351.8 0.550302
\(356\) 39383.7i 0.310754i
\(357\) −16419.2 21073.1i −0.128830 0.165345i
\(358\) 115944. 0.904657
\(359\) 117836.i 0.914302i 0.889389 + 0.457151i \(0.151130\pi\)
−0.889389 + 0.457151i \(0.848870\pi\)
\(360\) −22502.8 + 89247.3i −0.173633 + 0.688637i
\(361\) −85056.8 −0.652671
\(362\) 51195.8i 0.390676i
\(363\) −124045. + 96650.3i −0.941379 + 0.733483i
\(364\) 23271.3 0.175638
\(365\) 160257.i 1.20291i
\(366\) −15385.2 19745.9i −0.114853 0.147406i
\(367\) −14485.3 −0.107546 −0.0537732 0.998553i \(-0.517125\pi\)
−0.0537732 + 0.998553i \(0.517125\pi\)
\(368\) 27297.2i 0.201569i
\(369\) −115732. 29180.6i −0.849963 0.214310i
\(370\) 12148.6 0.0887407
\(371\) 39740.2i 0.288724i
\(372\) 18353.2 14300.1i 0.132625 0.103336i
\(373\) −87058.5 −0.625740 −0.312870 0.949796i \(-0.601290\pi\)
−0.312870 + 0.949796i \(0.601290\pi\)
\(374\) 90650.9i 0.648080i
\(375\) 88840.0 + 114021.i 0.631751 + 0.810813i
\(376\) −259847. −1.83799
\(377\) 240438.i 1.69169i
\(378\) −38997.7 + 17177.8i −0.272932 + 0.120222i
\(379\) 74378.7 0.517810 0.258905 0.965903i \(-0.416638\pi\)
0.258905 + 0.965903i \(0.416638\pi\)
\(380\) 20986.0i 0.145332i
\(381\) 150372. 117164.i 1.03590 0.807129i
\(382\) 40446.0 0.277172
\(383\) 170404.i 1.16167i −0.814022 0.580834i \(-0.802726\pi\)
0.814022 0.580834i \(-0.197274\pi\)
\(384\) −10127.3 12997.7i −0.0686801 0.0881466i
\(385\) −54217.5 −0.365779
\(386\) 48742.5i 0.327140i
\(387\) 72649.5 288131.i 0.485077 1.92384i
\(388\) 91845.4 0.610090
\(389\) 90053.1i 0.595113i 0.954704 + 0.297557i \(0.0961717\pi\)
−0.954704 + 0.297557i \(0.903828\pi\)
\(390\) 76175.1 59352.4i 0.500823 0.390220i
\(391\) 35589.0 0.232789
\(392\) 23858.3i 0.155263i
\(393\) −53734.8 68965.3i −0.347913 0.446525i
\(394\) −112341. −0.723681
\(395\) 34562.9i 0.221522i
\(396\) −84986.0 21428.4i −0.541947 0.136647i
\(397\) −96396.4 −0.611617 −0.305809 0.952093i \(-0.598927\pi\)
−0.305809 + 0.952093i \(0.598927\pi\)
\(398\) 104903.i 0.662247i
\(399\) 27973.5 21795.8i 0.175712 0.136907i
\(400\) −44025.4 −0.275159
\(401\) 299141.i 1.86032i 0.367157 + 0.930159i \(0.380331\pi\)
−0.367157 + 0.930159i \(0.619669\pi\)
\(402\) −3815.64 4897.13i −0.0236110 0.0303033i
\(403\) −89096.0 −0.548590
\(404\) 35365.6i 0.216680i
\(405\) 50818.6 94367.9i 0.309822 0.575326i
\(406\) 67538.1 0.409729
\(407\) 42223.2i 0.254895i
\(408\) −79145.4 + 61666.7i −0.475451 + 0.370451i
\(409\) −165389. −0.988692 −0.494346 0.869265i \(-0.664592\pi\)
−0.494346 + 0.869265i \(0.664592\pi\)
\(410\) 75975.1i 0.451964i
\(411\) 100057. + 128417.i 0.592332 + 0.760222i
\(412\) −11924.1 −0.0702478
\(413\) 22003.9i 0.129003i
\(414\) 13879.4 55046.4i 0.0809786 0.321165i
\(415\) −157063. −0.911963
\(416\) 150856.i 0.871718i
\(417\) −38784.4 + 30219.1i −0.223041 + 0.173784i
\(418\) −120335. −0.688714
\(419\) 155568.i 0.886119i −0.896492 0.443059i \(-0.853893\pi\)
0.896492 0.443059i \(-0.146107\pi\)
\(420\) −10105.2 12969.4i −0.0572859 0.0735229i
\(421\) −10503.6 −0.0592619 −0.0296310 0.999561i \(-0.509433\pi\)
−0.0296310 + 0.999561i \(0.509433\pi\)
\(422\) 98906.4i 0.555392i
\(423\) 293409. + 73980.3i 1.63981 + 0.413462i
\(424\) 149255. 0.830227
\(425\) 57398.4i 0.317777i
\(426\) 95126.6 74118.6i 0.524183 0.408421i
\(427\) 16320.4 0.0895108
\(428\) 17493.8i 0.0954984i
\(429\) 206283. + 264751.i 1.12085 + 1.43854i
\(430\) −189151. −1.02299
\(431\) 154084.i 0.829477i 0.909941 + 0.414738i \(0.136127\pi\)
−0.909941 + 0.414738i \(0.863873\pi\)
\(432\) 36125.2 + 82012.9i 0.193572 + 0.439455i
\(433\) 10755.0 0.0573631 0.0286816 0.999589i \(-0.490869\pi\)
0.0286816 + 0.999589i \(0.490869\pi\)
\(434\) 25026.8i 0.132870i
\(435\) −134000. + 104407.i −0.708149 + 0.551760i
\(436\) −71442.9 −0.375825
\(437\) 47242.7i 0.247384i
\(438\) −171272. 219817.i −0.892768 1.14581i
\(439\) 330676. 1.71583 0.857913 0.513796i \(-0.171761\pi\)
0.857913 + 0.513796i \(0.171761\pi\)
\(440\) 203628.i 1.05180i
\(441\) 6792.62 26939.8i 0.0349269 0.138522i
\(442\) 105269. 0.538833
\(443\) 283684.i 1.44553i −0.691092 0.722766i \(-0.742870\pi\)
0.691092 0.722766i \(-0.257130\pi\)
\(444\) −10100.3 + 7869.69i −0.0512350 + 0.0399201i
\(445\) 106552. 0.538075
\(446\) 52548.3i 0.264173i
\(447\) 33183.4 + 42588.8i 0.166075 + 0.213147i
\(448\) 78802.4 0.392630
\(449\) 26137.5i 0.129650i −0.997897 0.0648248i \(-0.979351\pi\)
0.997897 0.0648248i \(-0.0206489\pi\)
\(450\) 88779.7 + 22384.9i 0.438418 + 0.110543i
\(451\) −264056. −1.29820
\(452\) 31894.8i 0.156115i
\(453\) −863.380 + 672.709i −0.00420732 + 0.00327817i
\(454\) 164075. 0.796034
\(455\) 62960.3i 0.304119i
\(456\) −81859.8 105062.i −0.393678 0.505261i
\(457\) 269540. 1.29060 0.645299 0.763930i \(-0.276733\pi\)
0.645299 + 0.763930i \(0.276733\pi\)
\(458\) 117826.i 0.561706i
\(459\) 106925. 47098.4i 0.507520 0.223553i
\(460\) 21903.3 0.103513
\(461\) 305874.i 1.43926i 0.694356 + 0.719632i \(0.255689\pi\)
−0.694356 + 0.719632i \(0.744311\pi\)
\(462\) −74367.7 + 57944.1i −0.348418 + 0.271472i
\(463\) −103588. −0.483225 −0.241612 0.970373i \(-0.577676\pi\)
−0.241612 + 0.970373i \(0.577676\pi\)
\(464\) 142034.i 0.659715i
\(465\) 38688.7 + 49654.6i 0.178928 + 0.229643i
\(466\) −76431.7 −0.351967
\(467\) 321596.i 1.47461i 0.675561 + 0.737304i \(0.263901\pi\)
−0.675561 + 0.737304i \(0.736099\pi\)
\(468\) −24883.8 + 98690.2i −0.113612 + 0.450591i
\(469\) 4047.58 0.0184014
\(470\) 192616.i 0.871960i
\(471\) −31590.9 + 24614.3i −0.142404 + 0.110955i
\(472\) −82641.4 −0.370949
\(473\) 657405.i 2.93840i
\(474\) 36938.5 + 47408.3i 0.164408 + 0.211007i
\(475\) −76193.8 −0.337701
\(476\) 17922.9i 0.0791031i
\(477\) −168533. 42493.9i −0.740709 0.186762i
\(478\) 214693. 0.939639
\(479\) 441012.i 1.92211i −0.276352 0.961057i \(-0.589125\pi\)
0.276352 0.961057i \(-0.410875\pi\)
\(480\) −84074.4 + 65507.2i −0.364906 + 0.284319i
\(481\) 49031.8 0.211928
\(482\) 38501.7i 0.165724i
\(483\) 22748.5 + 29196.3i 0.0975121 + 0.125151i
\(484\) −105501. −0.450367
\(485\) 248487.i 1.05638i
\(486\) −31148.6 183752.i −0.131876 0.777962i
\(487\) −33119.4 −0.139645 −0.0698224 0.997559i \(-0.522243\pi\)
−0.0698224 + 0.997559i \(0.522243\pi\)
\(488\) 61295.6i 0.257389i
\(489\) −252911. + 197057.i −1.05767 + 0.824090i
\(490\) −17685.3 −0.0736582
\(491\) 134343.i 0.557252i 0.960400 + 0.278626i \(0.0898790\pi\)
−0.960400 + 0.278626i \(0.910121\pi\)
\(492\) −49215.6 63165.1i −0.203316 0.260944i
\(493\) −185178. −0.761895
\(494\) 139739.i 0.572618i
\(495\) 57974.3 229929.i 0.236606 0.938390i
\(496\) −52631.9 −0.213937
\(497\) 78624.1i 0.318305i
\(498\) −215436. + 167858.i −0.868679 + 0.676838i
\(499\) −441062. −1.77132 −0.885662 0.464330i \(-0.846295\pi\)
−0.885662 + 0.464330i \(0.846295\pi\)
\(500\) 96975.7i 0.387903i
\(501\) −65414.3 83955.1i −0.260614 0.334481i
\(502\) 157413. 0.624646
\(503\) 36433.5i 0.144001i −0.997405 0.0720004i \(-0.977062\pi\)
0.997405 0.0720004i \(-0.0229383\pi\)
\(504\) −101180. 25511.5i −0.398320 0.100432i
\(505\) 95681.5 0.375185
\(506\) 125595.i 0.490536i
\(507\) 104676. 81559.3i 0.407223 0.317291i
\(508\) 127893. 0.495587
\(509\) 223038.i 0.860881i 0.902619 + 0.430440i \(0.141642\pi\)
−0.902619 + 0.430440i \(0.858358\pi\)
\(510\) −45711.5 58667.8i −0.175746 0.225559i
\(511\) 181683. 0.695782
\(512\) 225928.i 0.861847i
\(513\) 62521.0 + 141938.i 0.237570 + 0.539341i
\(514\) −118929. −0.450154
\(515\) 32260.7i 0.121635i
\(516\) 157259. 122529.i 0.590630 0.460194i
\(517\) 669448. 2.50458
\(518\) 13772.9i 0.0513293i
\(519\) −280344. 359804.i −1.04077 1.33577i
\(520\) 236464. 0.874497
\(521\) 115397.i 0.425126i 0.977147 + 0.212563i \(0.0681811\pi\)
−0.977147 + 0.212563i \(0.931819\pi\)
\(522\) −72217.9 + 286420.i −0.265035 + 1.05114i
\(523\) −51941.3 −0.189893 −0.0949467 0.995482i \(-0.530268\pi\)
−0.0949467 + 0.995482i \(0.530268\pi\)
\(524\) 58655.7i 0.213623i
\(525\) −47088.2 + 36689.1i −0.170842 + 0.133112i
\(526\) −305241. −1.10324
\(527\) 68619.1i 0.247072i
\(528\) 121858. + 156397.i 0.437104 + 0.560996i
\(529\) 230533. 0.823801
\(530\) 110638.i 0.393868i
\(531\) 93315.4 + 23528.6i 0.330952 + 0.0834462i
\(532\) 23791.8 0.0840628
\(533\) 306636.i 1.07936i
\(534\) 146153. 113876.i 0.512537 0.399347i
\(535\) 47329.3 0.165357
\(536\) 15201.7i 0.0529132i
\(537\) −203202. 260797.i −0.704659 0.904386i
\(538\) 102379. 0.353709
\(539\) 61466.4i 0.211573i
\(540\) 65807.0 28986.8i 0.225676 0.0994060i
\(541\) 78629.5 0.268653 0.134326 0.990937i \(-0.457113\pi\)
0.134326 + 0.990937i \(0.457113\pi\)
\(542\) 362719.i 1.23473i
\(543\) −115156. + 89724.6i −0.390559 + 0.304307i
\(544\) −116185. −0.392601
\(545\) 193288.i 0.650747i
\(546\) 67287.8 + 86359.7i 0.225710 + 0.289685i
\(547\) 336673. 1.12521 0.562606 0.826725i \(-0.309799\pi\)
0.562606 + 0.826725i \(0.309799\pi\)
\(548\) 109220.i 0.363699i
\(549\) −17451.3 + 69212.6i −0.0579005 + 0.229636i
\(550\) 202561. 0.669624
\(551\) 245815.i 0.809666i
\(552\) 109654. 85438.0i 0.359872 0.280397i
\(553\) −39184.0 −0.128132
\(554\) 183103.i 0.596591i
\(555\) −21291.4 27326.2i −0.0691223 0.0887142i
\(556\) −32986.5 −0.106705
\(557\) 27917.5i 0.0899842i 0.998987 + 0.0449921i \(0.0143263\pi\)
−0.998987 + 0.0449921i \(0.985674\pi\)
\(558\) 106135. + 26760.9i 0.340871 + 0.0859474i
\(559\) −763414. −2.44307
\(560\) 37192.7i 0.118599i
\(561\) 203903. 158873.i 0.647886 0.504805i
\(562\) −174208. −0.551564
\(563\) 37494.7i 0.118291i 0.998249 + 0.0591456i \(0.0188376\pi\)
−0.998249 + 0.0591456i \(0.981162\pi\)
\(564\) 124774. + 160139.i 0.392252 + 0.503431i
\(565\) 86291.2 0.270315
\(566\) 222419.i 0.694285i
\(567\) 106985. + 57613.1i 0.332779 + 0.179207i
\(568\) 295293. 0.915286
\(569\) 164796.i 0.509004i 0.967072 + 0.254502i \(0.0819115\pi\)
−0.967072 + 0.254502i \(0.918088\pi\)
\(570\) 77878.9 60679.9i 0.239701 0.186765i
\(571\) −289109. −0.886725 −0.443363 0.896342i \(-0.646215\pi\)
−0.443363 + 0.896342i \(0.646215\pi\)
\(572\) 225173.i 0.688216i
\(573\) −70884.8 90976.3i −0.215896 0.277089i
\(574\) −86133.0 −0.261424
\(575\) 79524.3i 0.240527i
\(576\) −84262.7 + 334190.i −0.253975 + 1.00728i
\(577\) 110372. 0.331517 0.165758 0.986166i \(-0.446993\pi\)
0.165758 + 0.986166i \(0.446993\pi\)
\(578\) 182538.i 0.546383i
\(579\) −109638. + 85425.2i −0.327042 + 0.254817i
\(580\) −113968. −0.338787
\(581\) 178062.i 0.527496i
\(582\) 265567. + 340838.i 0.784021 + 1.00624i
\(583\) −384527. −1.13133
\(584\) 682360.i 2.00073i
\(585\) −267006. 67322.9i −0.780206 0.196721i
\(586\) −327069. −0.952455
\(587\) 86984.6i 0.252445i 0.992002 + 0.126222i \(0.0402853\pi\)
−0.992002 + 0.126222i \(0.959715\pi\)
\(588\) 14703.5 11456.3i 0.0425270 0.0331352i
\(589\) −91088.8 −0.262564
\(590\) 61259.3i 0.175982i
\(591\) 196887. + 252692.i 0.563693 + 0.723464i
\(592\) 28964.6 0.0826466
\(593\) 292146.i 0.830788i −0.909641 0.415394i \(-0.863644\pi\)
0.909641 0.415394i \(-0.136356\pi\)
\(594\) −166212. 377342.i −0.471075 1.06945i
\(595\) 48490.2 0.136968
\(596\) 36222.2i 0.101972i
\(597\) 235960. 183850.i 0.662049 0.515840i
\(598\) −145847. −0.407846
\(599\) 89429.2i 0.249245i 0.992204 + 0.124622i \(0.0397719\pi\)
−0.992204 + 0.124622i \(0.960228\pi\)
\(600\) 137796. + 176852.i 0.382766 + 0.491256i
\(601\) 547762. 1.51650 0.758251 0.651963i \(-0.226054\pi\)
0.758251 + 0.651963i \(0.226054\pi\)
\(602\) 214441.i 0.591717i
\(603\) −4328.04 + 17165.2i −0.0119030 + 0.0472079i
\(604\) −734.314 −0.00201283
\(605\) 285433.i 0.779818i
\(606\) 131242. 102258.i 0.357377 0.278453i
\(607\) −446082. −1.21070 −0.605351 0.795958i \(-0.706967\pi\)
−0.605351 + 0.795958i \(0.706967\pi\)
\(608\) 154230.i 0.417217i
\(609\) −118366. 151915.i −0.319148 0.409606i
\(610\) 45436.4 0.122108
\(611\) 777398.i 2.08239i
\(612\) 76008.3 + 19164.7i 0.202936 + 0.0511682i
\(613\) −697578. −1.85640 −0.928201 0.372079i \(-0.878645\pi\)
−0.928201 + 0.372079i \(0.878645\pi\)
\(614\) 171948.i 0.456101i
\(615\) 170893. 133152.i 0.451828 0.352045i
\(616\) −230853. −0.608380
\(617\) 470102.i 1.23487i 0.786621 + 0.617436i \(0.211829\pi\)
−0.786621 + 0.617436i \(0.788171\pi\)
\(618\) −34478.1 44250.5i −0.0902747 0.115862i
\(619\) 422811. 1.10348 0.551741 0.834015i \(-0.313964\pi\)
0.551741 + 0.834015i \(0.313964\pi\)
\(620\) 42231.7i 0.109864i
\(621\) −148142. + 65253.9i −0.384145 + 0.169209i
\(622\) −375951. −0.971741
\(623\) 120798.i 0.311233i
\(624\) 181616. 141508.i 0.466429 0.363422i
\(625\) −38535.1 −0.0986500
\(626\) 25802.2i 0.0658427i
\(627\) 210896. + 270673.i 0.536456 + 0.688508i
\(628\) −26868.4 −0.0681276
\(629\) 37762.9i 0.0954473i
\(630\) 18910.8 75001.1i 0.0476462 0.188967i
\(631\) 181730. 0.456424 0.228212 0.973612i \(-0.426712\pi\)
0.228212 + 0.973612i \(0.426712\pi\)
\(632\) 147166.i 0.368445i
\(633\) −222473. + 173341.i −0.555226 + 0.432608i
\(634\) 374140. 0.930798
\(635\) 346014.i 0.858116i
\(636\) −71669.4 91983.2i −0.177182 0.227402i
\(637\) −71378.1 −0.175908
\(638\) 653500.i 1.60548i
\(639\) −333434. 84072.0i −0.816597 0.205897i
\(640\) 29908.5 0.0730187
\(641\) 176756.i 0.430187i 0.976593 + 0.215093i \(0.0690056\pi\)
−0.976593 + 0.215093i \(0.930994\pi\)
\(642\) 64919.4 50582.5i 0.157509 0.122724i
\(643\) 414300. 1.00206 0.501029 0.865430i \(-0.332955\pi\)
0.501029 + 0.865430i \(0.332955\pi\)
\(644\) 24831.7i 0.0598736i
\(645\) 331502. + 425463.i 0.796833 + 1.02269i
\(646\) 107623. 0.257894
\(647\) 726996.i 1.73669i 0.495957 + 0.868347i \(0.334817\pi\)
−0.495957 + 0.868347i \(0.665183\pi\)
\(648\) 216381. 401810.i 0.515311 0.956908i
\(649\) 212910. 0.505483
\(650\) 235225.i 0.556745i
\(651\) −56293.4 + 43861.4i −0.132830 + 0.103495i
\(652\) −215103. −0.506001
\(653\) 212491.i 0.498326i 0.968462 + 0.249163i \(0.0801556\pi\)
−0.968462 + 0.249163i \(0.919844\pi\)
\(654\) −206574. 265125.i −0.482969 0.619861i
\(655\) 158693. 0.369891
\(656\) 181139.i 0.420926i
\(657\) −194272. + 770494.i −0.450070 + 1.78500i
\(658\) 218369. 0.504358
\(659\) 91061.6i 0.209684i 0.994489 + 0.104842i \(0.0334336\pi\)
−0.994489 + 0.104842i \(0.966566\pi\)
\(660\) 125493. 97778.5i 0.288091 0.224469i
\(661\) 533530. 1.22111 0.610556 0.791973i \(-0.290946\pi\)
0.610556 + 0.791973i \(0.290946\pi\)
\(662\) 238263.i 0.543676i
\(663\) −184492. 236783.i −0.419710 0.538672i
\(664\) −668759. −1.51682
\(665\) 64368.5i 0.145556i
\(666\) −58408.8 14727.2i −0.131683 0.0332026i
\(667\) 256560. 0.576683
\(668\) 71404.7i 0.160020i
\(669\) 118198. 92095.1i 0.264094 0.205771i
\(670\) 11268.5 0.0251026
\(671\) 157917.i 0.350738i
\(672\) −74265.5 95315.2i −0.164456 0.211069i
\(673\) 683682. 1.50947 0.754735 0.656030i \(-0.227766\pi\)
0.754735 + 0.656030i \(0.227766\pi\)
\(674\) 342951.i 0.754940i
\(675\) −105242. 238926.i −0.230985 0.524391i
\(676\) 89028.3 0.194821
\(677\) 579265.i 1.26386i −0.775025 0.631931i \(-0.782263\pi\)
0.775025 0.631931i \(-0.217737\pi\)
\(678\) 118362. 92222.4i 0.257485 0.200621i
\(679\) −281710. −0.611030
\(680\) 182118.i 0.393853i
\(681\) −287555. 369059.i −0.620050 0.795796i
\(682\) 242160. 0.520635
\(683\) 716617.i 1.53619i −0.640334 0.768096i \(-0.721204\pi\)
0.640334 0.768096i \(-0.278796\pi\)
\(684\) −25440.3 + 100898.i −0.0543764 + 0.215660i
\(685\) −295495. −0.629751
\(686\) 20049.9i 0.0426053i
\(687\) 265028. 206499.i 0.561538 0.437526i
\(688\) −450973. −0.952738
\(689\) 446534.i 0.940623i
\(690\) 63332.3 + 81283.0i 0.133023 + 0.170727i
\(691\) 397316. 0.832109 0.416054 0.909340i \(-0.363413\pi\)
0.416054 + 0.909340i \(0.363413\pi\)
\(692\) 306017.i 0.639048i
\(693\) 260671. + 65725.5i 0.542782 + 0.136857i
\(694\) −395600. −0.821366
\(695\) 89244.8i 0.184762i
\(696\) −570558. + 444554.i −1.17783 + 0.917712i
\(697\) 236162. 0.486121
\(698\) 224475.i 0.460741i
\(699\) 133953. + 171920.i 0.274155 + 0.351861i
\(700\) −40049.0 −0.0817326
\(701\) 736925.i 1.49964i −0.661642 0.749820i \(-0.730140\pi\)
0.661642 0.749820i \(-0.269860\pi\)
\(702\) −438190. + 193015.i −0.889177 + 0.391666i
\(703\) 50128.5 0.101432
\(704\) 762493.i 1.53848i
\(705\) −433256. + 337575.i −0.871699 + 0.679191i
\(706\) 172784. 0.346652
\(707\) 108474.i 0.217014i
\(708\) 39682.9 + 50930.5i 0.0791656 + 0.101604i
\(709\) 826597. 1.64438 0.822189 0.569215i \(-0.192753\pi\)
0.822189 + 0.569215i \(0.192753\pi\)
\(710\) 218891.i 0.434221i
\(711\) 41899.0 166174.i 0.0828829 0.328718i
\(712\) 453690. 0.894951
\(713\) 95070.3i 0.187011i
\(714\) 66511.7 51823.1i 0.130467 0.101655i
\(715\) −609205. −1.19166
\(716\) 221810.i 0.432669i
\(717\) −376266. 482914.i −0.731908 0.939358i
\(718\) −371920. −0.721440
\(719\) 402575.i 0.778734i −0.921083 0.389367i \(-0.872694\pi\)
0.921083 0.389367i \(-0.127306\pi\)
\(720\) −157729. 39769.8i −0.304261 0.0767164i
\(721\) 36573.9 0.0703560
\(722\) 268460.i 0.514997i
\(723\) −86603.0 + 67477.3i −0.165675 + 0.129087i
\(724\) −97941.3 −0.186848
\(725\) 413784.i 0.787222i
\(726\) −305052. 391515.i −0.578762 0.742805i
\(727\) −619831. −1.17275 −0.586373 0.810041i \(-0.699445\pi\)
−0.586373 + 0.810041i \(0.699445\pi\)
\(728\) 268079.i 0.505825i
\(729\) −358727. + 392103.i −0.675008 + 0.737810i
\(730\) 505810. 0.949165
\(731\) 587959.i 1.10030i
\(732\) −37775.4 + 29433.0i −0.0704997 + 0.0549304i
\(733\) −697215. −1.29765 −0.648827 0.760936i \(-0.724740\pi\)
−0.648827 + 0.760936i \(0.724740\pi\)
\(734\) 45719.2i 0.0848606i
\(735\) 30995.0 + 39780.1i 0.0573742 + 0.0736362i
\(736\) 160972. 0.297162
\(737\) 39164.5i 0.0721036i
\(738\) 92101.2 365278.i 0.169103 0.670673i
\(739\) −123136. −0.225474 −0.112737 0.993625i \(-0.535962\pi\)
−0.112737 + 0.993625i \(0.535962\pi\)
\(740\) 23241.2i 0.0424419i
\(741\) 314319. 244904.i 0.572446 0.446026i
\(742\) −125430. −0.227821
\(743\) 314455.i 0.569614i −0.958585 0.284807i \(-0.908070\pi\)
0.958585 0.284807i \(-0.0919295\pi\)
\(744\) 164733. + 211425.i 0.297601 + 0.381953i
\(745\) −97998.9 −0.176567
\(746\) 274778.i 0.493747i
\(747\) 755137. + 190400.i 1.35327 + 0.341214i
\(748\) 173422. 0.309957
\(749\) 53657.3i 0.0956456i
\(750\) −359877. + 280401.i −0.639781 + 0.498490i
\(751\) 10665.0 0.0189096 0.00945478 0.999955i \(-0.496990\pi\)
0.00945478 + 0.999955i \(0.496990\pi\)
\(752\) 459234.i 0.812079i
\(753\) −275879. 354074.i −0.486552 0.624459i
\(754\) 758879. 1.33484
\(755\) 1986.68i 0.00348525i
\(756\) 32862.3 + 74605.4i 0.0574983 + 0.130535i
\(757\) −816983. −1.42568 −0.712839 0.701328i \(-0.752591\pi\)
−0.712839 + 0.701328i \(0.752591\pi\)
\(758\) 234757.i 0.408583i
\(759\) −282504. + 220115.i −0.490389 + 0.382090i
\(760\) 241753. 0.418547
\(761\) 463428.i 0.800227i −0.916466 0.400114i \(-0.868971\pi\)
0.916466 0.400114i \(-0.131029\pi\)
\(762\) 369797. + 474611.i 0.636873 + 0.817387i
\(763\) 219131. 0.376404
\(764\) 77376.3i 0.132563i
\(765\) −51850.1 + 205640.i −0.0885986 + 0.351386i
\(766\) 537836. 0.916627
\(767\) 247243.i 0.420274i
\(768\) −442296. + 344619.i −0.749879 + 0.584274i
\(769\) 819869. 1.38641 0.693205 0.720740i \(-0.256198\pi\)
0.693205 + 0.720740i \(0.256198\pi\)
\(770\) 171124.i 0.288622i
\(771\) 208432. + 267510.i 0.350636 + 0.450020i
\(772\) −93248.1 −0.156461
\(773\) 674745.i 1.12923i −0.825356 0.564613i \(-0.809025\pi\)
0.825356 0.564613i \(-0.190975\pi\)
\(774\) 909413. + 229299.i 1.51803 + 0.382755i
\(775\) 153331. 0.255286
\(776\) 1.05804e6i 1.75702i
\(777\) 30979.7 24138.1i 0.0513139 0.0399816i
\(778\) −284230. −0.469580
\(779\) 313494.i 0.516600i
\(780\) −113546. 145729.i −0.186630 0.239528i
\(781\) −760768. −1.24724
\(782\) 112327.i 0.183684i
\(783\) 770819. 339532.i 1.25727 0.553805i
\(784\) −42165.3 −0.0685998
\(785\) 72692.3i 0.117964i
\(786\) 217671. 169600.i 0.352335 0.274525i
\(787\) 429936. 0.694152 0.347076 0.937837i \(-0.387175\pi\)
0.347076 + 0.937837i \(0.387175\pi\)
\(788\) 214917.i 0.346114i
\(789\) 534959. + 686587.i 0.859343 + 1.10291i
\(790\) −109089. −0.174794
\(791\) 97828.4i 0.156355i
\(792\) 246849. 979016.i 0.393533 1.56077i
\(793\) 183381. 0.291614
\(794\) 304250.i 0.482603i
\(795\) 248860. 193901.i 0.393750 0.306794i
\(796\) 200686. 0.316732
\(797\) 480208.i 0.755984i 0.925809 + 0.377992i \(0.123385\pi\)
−0.925809 + 0.377992i \(0.876615\pi\)
\(798\) 68792.8 + 88291.3i 0.108028 + 0.138648i
\(799\) −598729. −0.937858
\(800\) 259618.i 0.405652i
\(801\) −512289. 129169.i −0.798454 0.201322i
\(802\) −944162. −1.46790
\(803\) 1.75797e6i 2.72635i
\(804\) −9368.58 + 7299.60i −0.0144931 + 0.0112924i
\(805\) −67182.1 −0.103672
\(806\) 281209.i 0.432871i
\(807\) −179427. 230284.i −0.275513 0.353603i
\(808\) 407403. 0.624024
\(809\) 803515.i 1.22771i 0.789417 + 0.613857i \(0.210383\pi\)
−0.789417 + 0.613857i \(0.789617\pi\)
\(810\) 297848. + 160396.i 0.453967 + 0.244469i
\(811\) −374875. −0.569961 −0.284980 0.958533i \(-0.591987\pi\)
−0.284980 + 0.958533i \(0.591987\pi\)
\(812\) 129205.i 0.195961i
\(813\) 815873. 635694.i 1.23436 0.961761i
\(814\) −133267. −0.201128
\(815\) 581960.i 0.876149i
\(816\) −108985. 139876.i −0.163677 0.210069i
\(817\) −780489. −1.16929
\(818\) 522009.i 0.780138i
\(819\) 76323.9 302704.i 0.113787 0.451285i
\(820\) 145346. 0.216160
\(821\) 201261.i 0.298588i −0.988793 0.149294i \(-0.952300\pi\)
0.988793 0.149294i \(-0.0477001\pi\)
\(822\) −405316. + 315805.i −0.599861 + 0.467386i
\(823\) −645120. −0.952447 −0.476223 0.879324i \(-0.657995\pi\)
−0.476223 + 0.879324i \(0.657995\pi\)
\(824\) 137363.i 0.202309i
\(825\) −355005. 455626.i −0.521586 0.669423i
\(826\) 69449.6 0.101791
\(827\) 296113.i 0.432959i 0.976287 + 0.216479i \(0.0694574\pi\)
−0.976287 + 0.216479i \(0.930543\pi\)
\(828\) −105308. 26552.4i −0.153603 0.0387295i
\(829\) −1.08450e6 −1.57806 −0.789028 0.614357i \(-0.789415\pi\)
−0.789028 + 0.614357i \(0.789415\pi\)
\(830\) 495729.i 0.719595i
\(831\) −411859. + 320903.i −0.596412 + 0.464699i
\(832\) 885448. 1.27914
\(833\) 54973.3i 0.0792249i
\(834\) −95378.9 122413.i −0.137126 0.175993i
\(835\) 193185. 0.277077
\(836\) 230210.i 0.329391i
\(837\) −125816. 285633.i −0.179591 0.407716i
\(838\) 491010. 0.699202
\(839\) 1.22872e6i 1.74554i −0.488135 0.872768i \(-0.662322\pi\)
0.488135 0.872768i \(-0.337678\pi\)
\(840\) 149405. 116410.i 0.211741 0.164980i
\(841\) −627662. −0.887430
\(842\) 33152.1i 0.0467613i
\(843\) 305314. + 391851.i 0.429626 + 0.551399i
\(844\) −189215. −0.265627
\(845\) 240865.i 0.337335i
\(846\) −233500. + 926071.i −0.326246 + 1.29391i
\(847\) 323595. 0.451061
\(848\) 263782.i 0.366820i
\(849\) 500292. 389806.i 0.694078 0.540796i
\(850\) −181163. −0.250745
\(851\) 52319.6i 0.0722446i
\(852\) −141794. 181984.i −0.195335 0.250700i
\(853\) −635765. −0.873773 −0.436886 0.899517i \(-0.643919\pi\)
−0.436886 + 0.899517i \(0.643919\pi\)
\(854\) 51511.2i 0.0706295i
\(855\) −272978. 68828.7i −0.373418 0.0941537i
\(856\) 201524. 0.275029
\(857\) 1.07185e6i 1.45939i −0.683772 0.729696i \(-0.739662\pi\)
0.683772 0.729696i \(-0.260338\pi\)
\(858\) −835618. + 651078.i −1.13510 + 0.884420i
\(859\) 658219. 0.892039 0.446019 0.895023i \(-0.352841\pi\)
0.446019 + 0.895023i \(0.352841\pi\)
\(860\) 361860.i 0.489265i
\(861\) 150955. + 193741.i 0.203630 + 0.261346i
\(862\) −486328. −0.654508
\(863\) 407215.i 0.546767i 0.961905 + 0.273383i \(0.0881428\pi\)
−0.961905 + 0.273383i \(0.911857\pi\)
\(864\) 483630. 213030.i 0.647866 0.285373i
\(865\) 827927. 1.10652
\(866\) 33945.3i 0.0452630i
\(867\) 410587. 319912.i 0.546219 0.425591i
\(868\) −47878.1 −0.0635474
\(869\) 379145.i 0.502071i
\(870\) −329533. 422935.i −0.435372 0.558773i
\(871\) 45479.9 0.0599491
\(872\) 823004.i 1.08235i
\(873\) 301230. 1.19469e6i 0.395248 1.56757i
\(874\) −149110. −0.195201
\(875\) 297446.i 0.388500i
\(876\) −420527. + 327656.i −0.548006 + 0.426983i
\(877\) −1.05028e6 −1.36555 −0.682773 0.730630i \(-0.739226\pi\)
−0.682773 + 0.730630i \(0.739226\pi\)
\(878\) 1.04369e6i 1.35389i
\(879\) 573215. + 735685.i 0.741890 + 0.952170i
\(880\) −359877. −0.464717
\(881\) 940604.i 1.21187i 0.795515 + 0.605933i \(0.207200\pi\)
−0.795515 + 0.605933i \(0.792800\pi\)
\(882\) 85028.7 + 21439.1i 0.109302 + 0.0275594i
\(883\) 792858. 1.01689 0.508445 0.861095i \(-0.330221\pi\)
0.508445 + 0.861095i \(0.330221\pi\)
\(884\) 201387.i 0.257707i
\(885\) −137792. + 107362.i −0.175929 + 0.137076i
\(886\) 895377. 1.14061
\(887\) 673793.i 0.856406i −0.903683 0.428203i \(-0.859147\pi\)
0.903683 0.428203i \(-0.140853\pi\)
\(888\) −90656.8 116352.i −0.114967 0.147553i
\(889\) −392276. −0.496350
\(890\) 336305.i 0.424574i
\(891\) −557465. + 1.03519e6i −0.702203 + 1.30396i
\(892\) 100529. 0.126346
\(893\) 794786.i 0.996661i
\(894\) −134420. + 104735.i −0.168186 + 0.131044i
\(895\) 600107. 0.749174
\(896\) 33907.2i 0.0422353i
\(897\) 255609. + 328058.i 0.317681 + 0.407724i
\(898\) 82496.3 0.102301
\(899\) 494674.i 0.612068i
\(900\) 42824.0 169842.i 0.0528692 0.209682i
\(901\) 343907. 0.423635
\(902\) 833424.i 1.02436i
\(903\) −482347. + 375824.i −0.591540 + 0.460903i
\(904\) 367420. 0.449600
\(905\) 264980.i 0.323531i
\(906\) −2123.23 2725.04i −0.00258667 0.00331983i
\(907\) 672822. 0.817873 0.408936 0.912563i \(-0.365900\pi\)
0.408936 + 0.912563i \(0.365900\pi\)
\(908\) 313888.i 0.380718i
\(909\) −460023. 115990.i −0.556740 0.140376i
\(910\) −198718. −0.239969
\(911\) 200119.i 0.241130i −0.992705 0.120565i \(-0.961529\pi\)
0.992705 0.120565i \(-0.0384706\pi\)
\(912\) 185678. 144673.i 0.223240 0.173939i
\(913\) 1.72293e6 2.06694
\(914\) 850734.i 1.01836i
\(915\) −79630.8 102201.i −0.0951128 0.122071i
\(916\) 225409. 0.268646
\(917\) 179910.i 0.213952i
\(918\) 148654. + 337481.i 0.176397 + 0.400464i
\(919\) 1.29075e6 1.52831 0.764153 0.645035i \(-0.223157\pi\)
0.764153 + 0.645035i \(0.223157\pi\)
\(920\) 252320.i 0.298110i
\(921\) −386768. + 301353.i −0.455965 + 0.355268i
\(922\) −965412. −1.13567
\(923\) 883445.i 1.03699i
\(924\) 110851. + 142271.i 0.129837 + 0.166637i
\(925\) −84381.9 −0.0986202
\(926\) 326950.i 0.381294i
\(927\) −39108.2 + 155105.i −0.0455101 + 0.180495i
\(928\) −837575. −0.972585
\(929\) 602322.i 0.697906i 0.937140 + 0.348953i \(0.113463\pi\)
−0.937140 + 0.348953i \(0.886537\pi\)
\(930\) −156722. + 122111.i −0.181202 + 0.141185i
\(931\) −72974.6 −0.0841923
\(932\) 146220.i 0.168335i
\(933\) 658884. + 845636.i 0.756912 + 0.971450i
\(934\) −1.01503e6 −1.16356
\(935\) 469192.i 0.536695i
\(936\) −1.13689e6 286655.i −1.29767 0.327195i
\(937\) −1.35100e6 −1.53878 −0.769389 0.638780i \(-0.779439\pi\)
−0.769389 + 0.638780i \(0.779439\pi\)
\(938\) 12775.1i 0.0145198i
\(939\) −58037.5 + 45220.3i −0.0658230 + 0.0512864i
\(940\) −368489. −0.417031
\(941\) 83899.8i 0.0947505i −0.998877 0.0473753i \(-0.984914\pi\)
0.998877 0.0473753i \(-0.0150857\pi\)
\(942\) −77688.8 99708.7i −0.0875501 0.112365i
\(943\) −327197. −0.367948
\(944\) 146054.i 0.163896i
\(945\) −201845. + 88908.8i −0.226023 + 0.0995592i
\(946\) 2.07493e6 2.31858
\(947\) 356542.i 0.397567i 0.980043 + 0.198783i \(0.0636990\pi\)
−0.980043 + 0.198783i \(0.936301\pi\)
\(948\) 90695.7 70666.2i 0.100918 0.0786312i
\(949\) 2.04145e6 2.26677
\(950\) 240486.i 0.266467i
\(951\) −655710. 841563.i −0.725021 0.930519i
\(952\) 206467. 0.227812
\(953\) 1.05051e6i 1.15668i 0.815794 + 0.578342i \(0.196300\pi\)
−0.815794 + 0.578342i \(0.803700\pi\)
\(954\) 134121. 531930.i 0.147367 0.584464i
\(955\) 209341. 0.229534
\(956\) 410723.i 0.449400i
\(957\) 1.46994e6 1.14531e6i 1.60500 1.25055i
\(958\) 1.39194e6 1.51666
\(959\) 335002.i 0.364259i
\(960\) −384494. 493474.i −0.417203 0.535453i
\(961\) −740216. −0.801515
\(962\) 154756.i 0.167224i
\(963\) −227553. 57375.2i −0.245375 0.0618688i
\(964\) −73656.7 −0.0792607
\(965\) 252282.i 0.270914i
\(966\) −92150.6 + 71799.8i −0.0987515 + 0.0769430i
\(967\) −217775. −0.232892 −0.116446 0.993197i \(-0.537150\pi\)
−0.116446 + 0.993197i \(0.537150\pi\)
\(968\) 1.21535e6i 1.29703i
\(969\) −188618. 242080.i −0.200880 0.257816i
\(970\) −784286. −0.833549
\(971\) 1.29862e6i 1.37735i −0.725070 0.688675i \(-0.758193\pi\)
0.725070 0.688675i \(-0.241807\pi\)
\(972\) −351531. + 59589.6i −0.372075 + 0.0630722i
\(973\) 101177. 0.106870
\(974\) 104533.i 0.110188i
\(975\) −529098. + 412250.i −0.556579 + 0.433662i
\(976\) 108329. 0.113722
\(977\) 160654.i 0.168307i 0.996453 + 0.0841534i \(0.0268186\pi\)
−0.996453 + 0.0841534i \(0.973181\pi\)
\(978\) −621961. 798248.i −0.650257 0.834565i
\(979\) −1.16885e6 −1.21953
\(980\) 33833.4i 0.0352284i
\(981\) −234315. + 929303.i −0.243479 + 0.965650i
\(982\) −424019. −0.439706
\(983\) 1.41074e6i 1.45996i 0.683469 + 0.729979i \(0.260470\pi\)
−0.683469 + 0.729979i \(0.739530\pi\)
\(984\) 727646. 566950.i 0.751501 0.585538i
\(985\) −581458. −0.599302
\(986\) 584466.i 0.601182i
\(987\) −382708. 491182.i −0.392856 0.504207i
\(988\) 267332. 0.273865
\(989\) 814605.i 0.832826i
\(990\) 725712. + 182981.i 0.740447 + 0.186696i
\(991\) 46509.6 0.0473582 0.0236791 0.999720i \(-0.492462\pi\)
0.0236791 + 0.999720i \(0.492462\pi\)
\(992\) 310370.i 0.315396i
\(993\) −535931. + 417575.i −0.543513 + 0.423483i
\(994\) −248157. −0.251162
\(995\) 542956.i 0.548426i
\(996\) 321126. + 412145.i 0.323710 + 0.415462i
\(997\) −1.50451e6 −1.51358 −0.756789 0.653659i \(-0.773233\pi\)
−0.756789 + 0.653659i \(0.773233\pi\)
\(998\) 1.39210e6i 1.39768i
\(999\) 69239.8 + 157191.i 0.0693785 + 0.157506i
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 21.5.b.a.8.6 yes 8
3.2 odd 2 inner 21.5.b.a.8.3 8
4.3 odd 2 336.5.d.b.113.2 8
7.2 even 3 147.5.h.e.116.6 16
7.3 odd 6 147.5.h.c.128.3 16
7.4 even 3 147.5.h.e.128.3 16
7.5 odd 6 147.5.h.c.116.6 16
7.6 odd 2 147.5.b.e.50.6 8
12.11 even 2 336.5.d.b.113.1 8
21.2 odd 6 147.5.h.e.116.3 16
21.5 even 6 147.5.h.c.116.3 16
21.11 odd 6 147.5.h.e.128.6 16
21.17 even 6 147.5.h.c.128.6 16
21.20 even 2 147.5.b.e.50.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.5.b.a.8.3 8 3.2 odd 2 inner
21.5.b.a.8.6 yes 8 1.1 even 1 trivial
147.5.b.e.50.3 8 21.20 even 2
147.5.b.e.50.6 8 7.6 odd 2
147.5.h.c.116.3 16 21.5 even 6
147.5.h.c.116.6 16 7.5 odd 6
147.5.h.c.128.3 16 7.3 odd 6
147.5.h.c.128.6 16 21.17 even 6
147.5.h.e.116.3 16 21.2 odd 6
147.5.h.e.116.6 16 7.2 even 3
147.5.h.e.128.3 16 7.4 even 3
147.5.h.e.128.6 16 21.11 odd 6
336.5.d.b.113.1 8 12.11 even 2
336.5.d.b.113.2 8 4.3 odd 2