Properties

Label 189.4.s.a.17.20
Level $189$
Weight $4$
Character 189.17
Analytic conductor $11.151$
Analytic rank $0$
Dimension $44$
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] = [189,4,Mod(17,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.17");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.s (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: \(11.1513609911\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.20
Character \(\chi\) \(=\) 189.17
Dual form 189.4.s.a.89.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.26829 + 2.46430i) q^{2} +(8.14552 + 14.1085i) q^{4} +9.24869 q^{5} +(17.8986 - 4.75801i) q^{7} +40.8632i q^{8} +O(q^{10})\) \(q+(4.26829 + 2.46430i) q^{2} +(8.14552 + 14.1085i) q^{4} +9.24869 q^{5} +(17.8986 - 4.75801i) q^{7} +40.8632i q^{8} +(39.4761 + 22.7915i) q^{10} +15.2595i q^{11} +(-61.0927 - 35.2719i) q^{13} +(88.1217 + 23.7990i) q^{14} +(-35.5349 + 61.5483i) q^{16} +(-17.8844 + 30.9767i) q^{17} +(91.6472 - 52.9125i) q^{19} +(75.3354 + 130.485i) q^{20} +(-37.6039 + 65.1319i) q^{22} +92.4427i q^{23} -39.4618 q^{25} +(-173.841 - 301.101i) q^{26} +(212.922 + 213.766i) q^{28} +(-222.341 + 128.369i) q^{29} +(-123.551 + 71.3321i) q^{31} +(-20.2380 + 11.6844i) q^{32} +(-152.672 + 88.1451i) q^{34} +(165.539 - 44.0053i) q^{35} +(-100.112 - 173.399i) q^{37} +521.569 q^{38} +377.931i q^{40} +(162.085 - 280.739i) q^{41} +(-92.5782 - 160.350i) q^{43} +(-215.288 + 124.297i) q^{44} +(-227.806 + 394.572i) q^{46} +(235.747 - 408.326i) q^{47} +(297.723 - 170.324i) q^{49} +(-168.434 - 97.2457i) q^{50} -1149.23i q^{52} +(247.615 + 142.960i) q^{53} +141.130i q^{55} +(194.427 + 731.396i) q^{56} -1265.36 q^{58} +(-85.0742 - 147.353i) q^{59} +(222.571 + 128.501i) q^{61} -703.134 q^{62} +453.383 q^{64} +(-565.027 - 326.218i) q^{65} +(-501.367 - 868.394i) q^{67} -582.712 q^{68} +(815.010 + 220.110i) q^{70} +445.602i q^{71} +(-81.3323 - 46.9572i) q^{73} -986.820i q^{74} +(1493.03 + 862.001i) q^{76} +(72.6048 + 273.124i) q^{77} +(-231.624 + 401.185i) q^{79} +(-328.651 + 569.241i) q^{80} +(1383.65 - 798.851i) q^{82} +(348.156 + 603.023i) q^{83} +(-165.407 + 286.494i) q^{85} -912.561i q^{86} -623.552 q^{88} +(338.803 + 586.824i) q^{89} +(-1261.30 - 340.639i) q^{91} +(-1304.22 + 752.994i) q^{92} +(2012.47 - 1161.90i) q^{94} +(847.616 - 489.371i) q^{95} +(402.332 - 232.287i) q^{97} +(1690.49 + 6.68653i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.26829 + 2.46430i 1.50907 + 0.871261i 0.999944 + 0.0105673i \(0.00336375\pi\)
0.509124 + 0.860693i \(0.329970\pi\)
\(3\) 0 0
\(4\) 8.14552 + 14.1085i 1.01819 + 1.76356i
\(5\) 9.24869 0.827228 0.413614 0.910452i \(-0.364266\pi\)
0.413614 + 0.910452i \(0.364266\pi\)
\(6\) 0 0
\(7\) 17.8986 4.75801i 0.966436 0.256908i
\(8\) 40.8632i 1.80592i
\(9\) 0 0
\(10\) 39.4761 + 22.7915i 1.24834 + 0.720731i
\(11\) 15.2595i 0.418265i 0.977887 + 0.209132i \(0.0670639\pi\)
−0.977887 + 0.209132i \(0.932936\pi\)
\(12\) 0 0
\(13\) −61.0927 35.2719i −1.30339 0.752512i −0.322405 0.946602i \(-0.604491\pi\)
−0.980984 + 0.194090i \(0.937825\pi\)
\(14\) 88.1217 + 23.7990i 1.68225 + 0.454326i
\(15\) 0 0
\(16\) −35.5349 + 61.5483i −0.555233 + 0.961692i
\(17\) −17.8844 + 30.9767i −0.255154 + 0.441939i −0.964937 0.262481i \(-0.915459\pi\)
0.709784 + 0.704420i \(0.248793\pi\)
\(18\) 0 0
\(19\) 91.6472 52.9125i 1.10660 0.638893i 0.168650 0.985676i \(-0.446059\pi\)
0.937945 + 0.346783i \(0.112726\pi\)
\(20\) 75.3354 + 130.485i 0.842275 + 1.45886i
\(21\) 0 0
\(22\) −37.6039 + 65.1319i −0.364418 + 0.631190i
\(23\) 92.4427i 0.838071i 0.907970 + 0.419035i \(0.137632\pi\)
−0.907970 + 0.419035i \(0.862368\pi\)
\(24\) 0 0
\(25\) −39.4618 −0.315695
\(26\) −173.841 301.101i −1.31127 2.27118i
\(27\) 0 0
\(28\) 212.922 + 213.766i 1.43709 + 1.44278i
\(29\) −222.341 + 128.369i −1.42372 + 0.821983i −0.996614 0.0822202i \(-0.973799\pi\)
−0.427102 + 0.904203i \(0.640466\pi\)
\(30\) 0 0
\(31\) −123.551 + 71.3321i −0.715819 + 0.413278i −0.813212 0.581968i \(-0.802283\pi\)
0.0973929 + 0.995246i \(0.468950\pi\)
\(32\) −20.2380 + 11.6844i −0.111800 + 0.0645478i
\(33\) 0 0
\(34\) −152.672 + 88.1451i −0.770088 + 0.444611i
\(35\) 165.539 44.0053i 0.799462 0.212522i
\(36\) 0 0
\(37\) −100.112 173.399i −0.444818 0.770447i 0.553222 0.833034i \(-0.313398\pi\)
−0.998040 + 0.0625870i \(0.980065\pi\)
\(38\) 521.569 2.22657
\(39\) 0 0
\(40\) 377.931i 1.49390i
\(41\) 162.085 280.739i 0.617401 1.06937i −0.372558 0.928009i \(-0.621519\pi\)
0.989958 0.141360i \(-0.0451476\pi\)
\(42\) 0 0
\(43\) −92.5782 160.350i −0.328327 0.568679i 0.653853 0.756621i \(-0.273151\pi\)
−0.982180 + 0.187943i \(0.939818\pi\)
\(44\) −215.288 + 124.297i −0.737634 + 0.425873i
\(45\) 0 0
\(46\) −227.806 + 394.572i −0.730178 + 1.26471i
\(47\) 235.747 408.326i 0.731643 1.26724i −0.224538 0.974465i \(-0.572087\pi\)
0.956181 0.292778i \(-0.0945795\pi\)
\(48\) 0 0
\(49\) 297.723 170.324i 0.867996 0.496571i
\(50\) −168.434 97.2457i −0.476404 0.275052i
\(51\) 0 0
\(52\) 1149.23i 3.06480i
\(53\) 247.615 + 142.960i 0.641745 + 0.370512i 0.785286 0.619133i \(-0.212516\pi\)
−0.143541 + 0.989644i \(0.545849\pi\)
\(54\) 0 0
\(55\) 141.130i 0.346000i
\(56\) 194.427 + 731.396i 0.463955 + 1.74530i
\(57\) 0 0
\(58\) −1265.36 −2.86465
\(59\) −85.0742 147.353i −0.187724 0.325147i 0.756767 0.653685i \(-0.226778\pi\)
−0.944491 + 0.328537i \(0.893444\pi\)
\(60\) 0 0
\(61\) 222.571 + 128.501i 0.467169 + 0.269720i 0.715054 0.699069i \(-0.246402\pi\)
−0.247885 + 0.968789i \(0.579736\pi\)
\(62\) −703.134 −1.44029
\(63\) 0 0
\(64\) 453.383 0.885515
\(65\) −565.027 326.218i −1.07820 0.622499i
\(66\) 0 0
\(67\) −501.367 868.394i −0.914205 1.58345i −0.808061 0.589099i \(-0.799483\pi\)
−0.106145 0.994351i \(-0.533851\pi\)
\(68\) −582.712 −1.03918
\(69\) 0 0
\(70\) 815.010 + 220.110i 1.39160 + 0.375831i
\(71\) 445.602i 0.744835i 0.928065 + 0.372417i \(0.121471\pi\)
−0.928065 + 0.372417i \(0.878529\pi\)
\(72\) 0 0
\(73\) −81.3323 46.9572i −0.130400 0.0752867i 0.433381 0.901211i \(-0.357321\pi\)
−0.563781 + 0.825924i \(0.690654\pi\)
\(74\) 986.820i 1.55021i
\(75\) 0 0
\(76\) 1493.03 + 862.001i 2.25345 + 1.30103i
\(77\) 72.6048 + 273.124i 0.107456 + 0.404226i
\(78\) 0 0
\(79\) −231.624 + 401.185i −0.329871 + 0.571353i −0.982486 0.186337i \(-0.940338\pi\)
0.652615 + 0.757689i \(0.273672\pi\)
\(80\) −328.651 + 569.241i −0.459304 + 0.795538i
\(81\) 0 0
\(82\) 1383.65 798.851i 1.86340 1.07583i
\(83\) 348.156 + 603.023i 0.460422 + 0.797475i 0.998982 0.0451126i \(-0.0143647\pi\)
−0.538560 + 0.842587i \(0.681031\pi\)
\(84\) 0 0
\(85\) −165.407 + 286.494i −0.211070 + 0.365584i
\(86\) 912.561i 1.14423i
\(87\) 0 0
\(88\) −623.552 −0.755351
\(89\) 338.803 + 586.824i 0.403518 + 0.698913i 0.994148 0.108029i \(-0.0344541\pi\)
−0.590630 + 0.806942i \(0.701121\pi\)
\(90\) 0 0
\(91\) −1261.30 340.639i −1.45297 0.392403i
\(92\) −1304.22 + 752.994i −1.47799 + 0.853316i
\(93\) 0 0
\(94\) 2012.47 1161.90i 2.20820 1.27490i
\(95\) 847.616 489.371i 0.915406 0.528510i
\(96\) 0 0
\(97\) 402.332 232.287i 0.421141 0.243146i −0.274424 0.961609i \(-0.588487\pi\)
0.695565 + 0.718463i \(0.255154\pi\)
\(98\) 1690.49 + 6.68653i 1.74251 + 0.00689226i
\(99\) 0 0
\(100\) −321.437 556.745i −0.321437 0.556745i
\(101\) 508.150 0.500622 0.250311 0.968165i \(-0.419467\pi\)
0.250311 + 0.968165i \(0.419467\pi\)
\(102\) 0 0
\(103\) 657.703i 0.629179i 0.949228 + 0.314589i \(0.101867\pi\)
−0.949228 + 0.314589i \(0.898133\pi\)
\(104\) 1441.32 2496.44i 1.35897 2.35381i
\(105\) 0 0
\(106\) 704.594 + 1220.39i 0.645625 + 1.11825i
\(107\) −810.389 + 467.878i −0.732180 + 0.422724i −0.819219 0.573481i \(-0.805593\pi\)
0.0870393 + 0.996205i \(0.472259\pi\)
\(108\) 0 0
\(109\) −272.351 + 471.726i −0.239326 + 0.414524i −0.960521 0.278207i \(-0.910260\pi\)
0.721195 + 0.692732i \(0.243593\pi\)
\(110\) −347.787 + 602.385i −0.301456 + 0.522138i
\(111\) 0 0
\(112\) −343.180 + 1270.71i −0.289531 + 1.07206i
\(113\) −63.9011 36.8933i −0.0531974 0.0307135i 0.473165 0.880974i \(-0.343111\pi\)
−0.526363 + 0.850260i \(0.676445\pi\)
\(114\) 0 0
\(115\) 854.973i 0.693275i
\(116\) −3622.18 2091.26i −2.89923 1.67387i
\(117\) 0 0
\(118\) 838.592i 0.654226i
\(119\) −172.719 + 639.536i −0.133052 + 0.492657i
\(120\) 0 0
\(121\) 1098.15 0.825055
\(122\) 633.331 + 1096.96i 0.469993 + 0.814051i
\(123\) 0 0
\(124\) −2012.77 1162.07i −1.45768 0.841592i
\(125\) −1521.06 −1.08838
\(126\) 0 0
\(127\) −2142.49 −1.49697 −0.748484 0.663153i \(-0.769218\pi\)
−0.748484 + 0.663153i \(0.769218\pi\)
\(128\) 2097.08 + 1210.75i 1.44810 + 0.836062i
\(129\) 0 0
\(130\) −1607.80 2784.79i −1.08472 1.87879i
\(131\) −2060.85 −1.37448 −0.687242 0.726429i \(-0.741179\pi\)
−0.687242 + 0.726429i \(0.741179\pi\)
\(132\) 0 0
\(133\) 1388.60 1383.12i 0.905316 0.901742i
\(134\) 4942.07i 3.18604i
\(135\) 0 0
\(136\) −1265.81 730.815i −0.798105 0.460786i
\(137\) 47.4441i 0.0295870i 0.999891 + 0.0147935i \(0.00470909\pi\)
−0.999891 + 0.0147935i \(0.995291\pi\)
\(138\) 0 0
\(139\) −713.061 411.686i −0.435115 0.251214i 0.266408 0.963860i \(-0.414163\pi\)
−0.701523 + 0.712646i \(0.747496\pi\)
\(140\) 1969.25 + 1977.05i 1.18880 + 1.19351i
\(141\) 0 0
\(142\) −1098.10 + 1901.96i −0.648945 + 1.12401i
\(143\) 538.231 932.243i 0.314749 0.545162i
\(144\) 0 0
\(145\) −2056.37 + 1187.24i −1.17774 + 0.679967i
\(146\) −231.433 400.854i −0.131189 0.227225i
\(147\) 0 0
\(148\) 1630.92 2824.84i 0.905819 1.56892i
\(149\) 1150.98i 0.632830i 0.948621 + 0.316415i \(0.102479\pi\)
−0.948621 + 0.316415i \(0.897521\pi\)
\(150\) 0 0
\(151\) −593.799 −0.320018 −0.160009 0.987116i \(-0.551152\pi\)
−0.160009 + 0.987116i \(0.551152\pi\)
\(152\) 2162.18 + 3745.00i 1.15379 + 1.99842i
\(153\) 0 0
\(154\) −363.161 + 1344.69i −0.190028 + 0.703626i
\(155\) −1142.68 + 659.728i −0.592145 + 0.341875i
\(156\) 0 0
\(157\) −29.3249 + 16.9307i −0.0149069 + 0.00860649i −0.507435 0.861690i \(-0.669406\pi\)
0.492528 + 0.870297i \(0.336073\pi\)
\(158\) −1977.28 + 1141.58i −0.995594 + 0.574807i
\(159\) 0 0
\(160\) −187.175 + 108.065i −0.0924842 + 0.0533958i
\(161\) 439.843 + 1654.60i 0.215307 + 0.809942i
\(162\) 0 0
\(163\) 2034.98 + 3524.68i 0.977863 + 1.69371i 0.670142 + 0.742232i \(0.266233\pi\)
0.307721 + 0.951477i \(0.400434\pi\)
\(164\) 5281.07 2.51453
\(165\) 0 0
\(166\) 3431.84i 1.60459i
\(167\) 729.362 1263.29i 0.337962 0.585368i −0.646087 0.763264i \(-0.723596\pi\)
0.984049 + 0.177896i \(0.0569290\pi\)
\(168\) 0 0
\(169\) 1389.71 + 2407.05i 0.632548 + 1.09561i
\(170\) −1412.01 + 815.226i −0.637038 + 0.367794i
\(171\) 0 0
\(172\) 1508.20 2612.27i 0.668598 1.15805i
\(173\) 245.553 425.311i 0.107914 0.186912i −0.807011 0.590536i \(-0.798916\pi\)
0.914925 + 0.403624i \(0.132250\pi\)
\(174\) 0 0
\(175\) −706.313 + 187.760i −0.305098 + 0.0811045i
\(176\) −939.196 542.245i −0.402242 0.232234i
\(177\) 0 0
\(178\) 3339.65i 1.40628i
\(179\) 710.152 + 410.006i 0.296532 + 0.171203i 0.640884 0.767638i \(-0.278568\pi\)
−0.344352 + 0.938841i \(0.611901\pi\)
\(180\) 0 0
\(181\) 618.639i 0.254050i 0.991900 + 0.127025i \(0.0405429\pi\)
−0.991900 + 0.127025i \(0.959457\pi\)
\(182\) −4544.15 4562.16i −1.85074 1.85808i
\(183\) 0 0
\(184\) −3777.50 −1.51349
\(185\) −925.901 1603.71i −0.367966 0.637335i
\(186\) 0 0
\(187\) −472.689 272.907i −0.184847 0.106722i
\(188\) 7681.13 2.97981
\(189\) 0 0
\(190\) 4823.83 1.84188
\(191\) 1335.44 + 771.019i 0.505913 + 0.292089i 0.731152 0.682215i \(-0.238983\pi\)
−0.225239 + 0.974303i \(0.572316\pi\)
\(192\) 0 0
\(193\) 1405.23 + 2433.93i 0.524097 + 0.907763i 0.999606 + 0.0280523i \(0.00893050\pi\)
−0.475509 + 0.879711i \(0.657736\pi\)
\(194\) 2289.69 0.847373
\(195\) 0 0
\(196\) 4828.11 + 2813.03i 1.75952 + 1.02516i
\(197\) 1603.61i 0.579963i 0.957032 + 0.289982i \(0.0936492\pi\)
−0.957032 + 0.289982i \(0.906351\pi\)
\(198\) 0 0
\(199\) −597.100 344.736i −0.212700 0.122802i 0.389866 0.920872i \(-0.372521\pi\)
−0.602566 + 0.798069i \(0.705855\pi\)
\(200\) 1612.54i 0.570118i
\(201\) 0 0
\(202\) 2168.93 + 1252.23i 0.755473 + 0.436172i
\(203\) −3368.83 + 3355.53i −1.16476 + 1.16016i
\(204\) 0 0
\(205\) 1499.07 2596.47i 0.510731 0.884612i
\(206\) −1620.78 + 2807.27i −0.548179 + 0.949474i
\(207\) 0 0
\(208\) 4341.85 2506.77i 1.44737 0.835639i
\(209\) 807.419 + 1398.49i 0.267226 + 0.462850i
\(210\) 0 0
\(211\) 2341.89 4056.27i 0.764087 1.32344i −0.176641 0.984275i \(-0.556523\pi\)
0.940728 0.339162i \(-0.110143\pi\)
\(212\) 4657.95i 1.50901i
\(213\) 0 0
\(214\) −4611.96 −1.47321
\(215\) −856.227 1483.03i −0.271601 0.470427i
\(216\) 0 0
\(217\) −1871.99 + 1864.60i −0.585618 + 0.583307i
\(218\) −2324.95 + 1342.31i −0.722318 + 0.417030i
\(219\) 0 0
\(220\) −1991.13 + 1149.58i −0.610191 + 0.352294i
\(221\) 2185.21 1261.63i 0.665129 0.384012i
\(222\) 0 0
\(223\) 680.507 392.891i 0.204350 0.117982i −0.394333 0.918968i \(-0.629024\pi\)
0.598683 + 0.800986i \(0.295691\pi\)
\(224\) −306.638 + 305.428i −0.0914648 + 0.0911037i
\(225\) 0 0
\(226\) −181.832 314.942i −0.0535190 0.0926976i
\(227\) −1808.61 −0.528819 −0.264409 0.964411i \(-0.585177\pi\)
−0.264409 + 0.964411i \(0.585177\pi\)
\(228\) 0 0
\(229\) 2867.45i 0.827453i −0.910401 0.413726i \(-0.864227\pi\)
0.910401 0.413726i \(-0.135773\pi\)
\(230\) −2106.91 + 3649.27i −0.604024 + 1.04620i
\(231\) 0 0
\(232\) −5245.57 9085.59i −1.48443 2.57111i
\(233\) −2302.74 + 1329.49i −0.647456 + 0.373809i −0.787481 0.616339i \(-0.788615\pi\)
0.140025 + 0.990148i \(0.455282\pi\)
\(234\) 0 0
\(235\) 2180.35 3776.48i 0.605235 1.04830i
\(236\) 1385.95 2400.53i 0.382277 0.662124i
\(237\) 0 0
\(238\) −2313.22 + 2304.09i −0.630017 + 0.627530i
\(239\) 1674.76 + 966.920i 0.453267 + 0.261694i 0.709209 0.704998i \(-0.249052\pi\)
−0.255942 + 0.966692i \(0.582386\pi\)
\(240\) 0 0
\(241\) 4139.22i 1.10635i 0.833065 + 0.553175i \(0.186584\pi\)
−0.833065 + 0.553175i \(0.813416\pi\)
\(242\) 4687.21 + 2706.16i 1.24506 + 0.718838i
\(243\) 0 0
\(244\) 4186.84i 1.09851i
\(245\) 2753.54 1575.27i 0.718030 0.410777i
\(246\) 0 0
\(247\) −7465.29 −1.92310
\(248\) −2914.86 5048.68i −0.746346 1.29271i
\(249\) 0 0
\(250\) −6492.30 3748.33i −1.64244 0.948262i
\(251\) −370.848 −0.0932577 −0.0466289 0.998912i \(-0.514848\pi\)
−0.0466289 + 0.998912i \(0.514848\pi\)
\(252\) 0 0
\(253\) −1410.63 −0.350535
\(254\) −9144.75 5279.72i −2.25903 1.30425i
\(255\) 0 0
\(256\) 4153.75 + 7194.50i 1.01410 + 1.75647i
\(257\) −6849.66 −1.66253 −0.831265 0.555877i \(-0.812383\pi\)
−0.831265 + 0.555877i \(0.812383\pi\)
\(258\) 0 0
\(259\) −2616.89 2627.27i −0.627822 0.630310i
\(260\) 10628.9i 2.53529i
\(261\) 0 0
\(262\) −8796.30 5078.55i −2.07419 1.19753i
\(263\) 5271.14i 1.23587i 0.786231 + 0.617933i \(0.212030\pi\)
−0.786231 + 0.617933i \(0.787970\pi\)
\(264\) 0 0
\(265\) 2290.11 + 1322.20i 0.530869 + 0.306498i
\(266\) 9335.37 2481.63i 2.15184 0.572024i
\(267\) 0 0
\(268\) 8167.80 14147.0i 1.86167 3.22451i
\(269\) −553.460 + 958.621i −0.125446 + 0.217279i −0.921907 0.387410i \(-0.873370\pi\)
0.796461 + 0.604690i \(0.206703\pi\)
\(270\) 0 0
\(271\) 4357.92 2516.05i 0.976844 0.563981i 0.0755283 0.997144i \(-0.475936\pi\)
0.901316 + 0.433162i \(0.142602\pi\)
\(272\) −1271.04 2201.51i −0.283340 0.490758i
\(273\) 0 0
\(274\) −116.916 + 202.505i −0.0257780 + 0.0446488i
\(275\) 602.167i 0.132044i
\(276\) 0 0
\(277\) 8751.34 1.89826 0.949128 0.314890i \(-0.101968\pi\)
0.949128 + 0.314890i \(0.101968\pi\)
\(278\) −2029.03 3514.39i −0.437746 0.758197i
\(279\) 0 0
\(280\) 1798.20 + 6764.45i 0.383796 + 1.44376i
\(281\) 5849.25 3377.07i 1.24177 0.716936i 0.272315 0.962208i \(-0.412211\pi\)
0.969454 + 0.245273i \(0.0788775\pi\)
\(282\) 0 0
\(283\) 654.152 377.675i 0.137404 0.0793302i −0.429722 0.902961i \(-0.641389\pi\)
0.567126 + 0.823631i \(0.308055\pi\)
\(284\) −6286.76 + 3629.67i −1.31356 + 0.758384i
\(285\) 0 0
\(286\) 4594.65 2652.72i 0.949956 0.548457i
\(287\) 1565.34 5796.06i 0.321948 1.19209i
\(288\) 0 0
\(289\) 1816.79 + 3146.78i 0.369793 + 0.640501i
\(290\) −11702.9 −2.36971
\(291\) 0 0
\(292\) 1529.96i 0.306625i
\(293\) 3949.45 6840.64i 0.787472 1.36394i −0.140040 0.990146i \(-0.544723\pi\)
0.927511 0.373795i \(-0.121944\pi\)
\(294\) 0 0
\(295\) −786.824 1362.82i −0.155290 0.268971i
\(296\) 7085.62 4090.89i 1.39136 0.803304i
\(297\) 0 0
\(298\) −2836.35 + 4912.70i −0.551360 + 0.954983i
\(299\) 3260.63 5647.57i 0.630658 1.09233i
\(300\) 0 0
\(301\) −2419.97 2429.56i −0.463405 0.465241i
\(302\) −2534.50 1463.30i −0.482928 0.278819i
\(303\) 0 0
\(304\) 7520.97i 1.41894i
\(305\) 2058.49 + 1188.47i 0.386455 + 0.223120i
\(306\) 0 0
\(307\) 1715.02i 0.318832i −0.987212 0.159416i \(-0.949039\pi\)
0.987212 0.159416i \(-0.0509610\pi\)
\(308\) −3261.96 + 3249.08i −0.603466 + 0.601083i
\(309\) 0 0
\(310\) −6503.07 −1.19145
\(311\) 1576.29 + 2730.21i 0.287405 + 0.497800i 0.973190 0.230004i \(-0.0738740\pi\)
−0.685784 + 0.727805i \(0.740541\pi\)
\(312\) 0 0
\(313\) −4698.26 2712.54i −0.848440 0.489847i 0.0116844 0.999932i \(-0.496281\pi\)
−0.860124 + 0.510085i \(0.829614\pi\)
\(314\) −166.889 −0.0299940
\(315\) 0 0
\(316\) −7546.81 −1.34348
\(317\) −1209.31 698.194i −0.214263 0.123705i 0.389028 0.921226i \(-0.372811\pi\)
−0.603291 + 0.797521i \(0.706144\pi\)
\(318\) 0 0
\(319\) −1958.85 3392.82i −0.343807 0.595490i
\(320\) 4193.20 0.732522
\(321\) 0 0
\(322\) −2200.05 + 8146.21i −0.380757 + 1.40985i
\(323\) 3785.24i 0.652063i
\(324\) 0 0
\(325\) 2410.83 + 1391.89i 0.411473 + 0.237564i
\(326\) 20059.2i 3.40790i
\(327\) 0 0
\(328\) 11471.9 + 6623.31i 1.93119 + 1.11497i
\(329\) 2276.73 8430.16i 0.381521 1.41267i
\(330\) 0 0
\(331\) −844.559 + 1462.82i −0.140245 + 0.242912i −0.927589 0.373603i \(-0.878122\pi\)
0.787344 + 0.616514i \(0.211456\pi\)
\(332\) −5671.82 + 9823.88i −0.937595 + 1.62396i
\(333\) 0 0
\(334\) 6226.25 3594.73i 1.02002 0.588907i
\(335\) −4636.99 8031.50i −0.756256 1.30987i
\(336\) 0 0
\(337\) 823.056 1425.57i 0.133041 0.230433i −0.791807 0.610772i \(-0.790859\pi\)
0.924847 + 0.380339i \(0.124193\pi\)
\(338\) 13698.6i 2.20446i
\(339\) 0 0
\(340\) −5389.32 −0.859638
\(341\) −1088.49 1885.32i −0.172860 0.299402i
\(342\) 0 0
\(343\) 4518.43 4465.13i 0.711290 0.702899i
\(344\) 6552.43 3783.04i 1.02699 0.592930i
\(345\) 0 0
\(346\) 2096.18 1210.23i 0.325698 0.188042i
\(347\) 829.925 479.157i 0.128394 0.0741283i −0.434427 0.900707i \(-0.643049\pi\)
0.562821 + 0.826579i \(0.309716\pi\)
\(348\) 0 0
\(349\) −4992.01 + 2882.14i −0.765662 + 0.442055i −0.831325 0.555787i \(-0.812417\pi\)
0.0656629 + 0.997842i \(0.479084\pi\)
\(350\) −3477.44 939.153i −0.531078 0.143428i
\(351\) 0 0
\(352\) −178.298 308.822i −0.0269981 0.0467621i
\(353\) 2092.13 0.315447 0.157724 0.987483i \(-0.449584\pi\)
0.157724 + 0.987483i \(0.449584\pi\)
\(354\) 0 0
\(355\) 4121.24i 0.616148i
\(356\) −5519.46 + 9559.99i −0.821716 + 1.42325i
\(357\) 0 0
\(358\) 2020.76 + 3500.05i 0.298325 + 0.516713i
\(359\) −7692.73 + 4441.40i −1.13094 + 0.652948i −0.944171 0.329456i \(-0.893135\pi\)
−0.186768 + 0.982404i \(0.559801\pi\)
\(360\) 0 0
\(361\) 2169.97 3758.50i 0.316368 0.547966i
\(362\) −1524.51 + 2640.53i −0.221344 + 0.383379i
\(363\) 0 0
\(364\) −5468.05 20569.7i −0.787373 2.96193i
\(365\) −752.217 434.293i −0.107871 0.0622792i
\(366\) 0 0
\(367\) 7198.29i 1.02384i 0.859034 + 0.511918i \(0.171065\pi\)
−0.859034 + 0.511918i \(0.828935\pi\)
\(368\) −5689.69 3284.94i −0.805966 0.465325i
\(369\) 0 0
\(370\) 9126.79i 1.28238i
\(371\) 5112.17 + 1380.64i 0.715393 + 0.193206i
\(372\) 0 0
\(373\) 5497.21 0.763096 0.381548 0.924349i \(-0.375391\pi\)
0.381548 + 0.924349i \(0.375391\pi\)
\(374\) −1345.05 2329.69i −0.185965 0.322101i
\(375\) 0 0
\(376\) 16685.5 + 9633.38i 2.28853 + 1.32129i
\(377\) 18111.2 2.47421
\(378\) 0 0
\(379\) −2873.36 −0.389432 −0.194716 0.980860i \(-0.562379\pi\)
−0.194716 + 0.980860i \(0.562379\pi\)
\(380\) 13808.6 + 7972.37i 1.86412 + 1.07625i
\(381\) 0 0
\(382\) 3800.04 + 6581.86i 0.508971 + 0.881564i
\(383\) −1477.45 −0.197112 −0.0985561 0.995131i \(-0.531422\pi\)
−0.0985561 + 0.995131i \(0.531422\pi\)
\(384\) 0 0
\(385\) 671.499 + 2526.04i 0.0888903 + 0.334387i
\(386\) 13851.6i 1.82650i
\(387\) 0 0
\(388\) 6554.41 + 3784.19i 0.857603 + 0.495137i
\(389\) 10500.0i 1.36857i −0.729215 0.684284i \(-0.760115\pi\)
0.729215 0.684284i \(-0.239885\pi\)
\(390\) 0 0
\(391\) −2863.57 1653.28i −0.370376 0.213837i
\(392\) 6959.98 + 12165.9i 0.896765 + 1.56753i
\(393\) 0 0
\(394\) −3951.78 + 6844.69i −0.505299 + 0.875204i
\(395\) −2142.22 + 3710.44i −0.272878 + 0.472639i
\(396\) 0 0
\(397\) −3627.85 + 2094.54i −0.458631 + 0.264791i −0.711468 0.702718i \(-0.751970\pi\)
0.252838 + 0.967509i \(0.418636\pi\)
\(398\) −1699.06 2942.86i −0.213986 0.370634i
\(399\) 0 0
\(400\) 1402.27 2428.81i 0.175284 0.303601i
\(401\) 6712.82i 0.835966i −0.908455 0.417983i \(-0.862737\pi\)
0.908455 0.417983i \(-0.137263\pi\)
\(402\) 0 0
\(403\) 10064.1 1.24399
\(404\) 4139.15 + 7169.22i 0.509729 + 0.882876i
\(405\) 0 0
\(406\) −22648.2 + 6020.58i −2.76850 + 0.735951i
\(407\) 2645.97 1527.65i 0.322251 0.186052i
\(408\) 0 0
\(409\) 1922.39 1109.89i 0.232411 0.134183i −0.379273 0.925285i \(-0.623826\pi\)
0.611684 + 0.791102i \(0.290492\pi\)
\(410\) 12797.0 7388.32i 1.54145 0.889959i
\(411\) 0 0
\(412\) −9279.18 + 5357.34i −1.10959 + 0.640624i
\(413\) −2223.82 2232.63i −0.264956 0.266006i
\(414\) 0 0
\(415\) 3219.98 + 5577.17i 0.380874 + 0.659693i
\(416\) 1648.52 0.194292
\(417\) 0 0
\(418\) 7958.88i 0.931295i
\(419\) −3763.65 + 6518.82i −0.438821 + 0.760061i −0.997599 0.0692569i \(-0.977937\pi\)
0.558778 + 0.829318i \(0.311271\pi\)
\(420\) 0 0
\(421\) 297.422 + 515.151i 0.0344311 + 0.0596363i 0.882727 0.469885i \(-0.155705\pi\)
−0.848296 + 0.529522i \(0.822371\pi\)
\(422\) 19991.7 11542.2i 2.30612 1.33144i
\(423\) 0 0
\(424\) −5841.82 + 10118.3i −0.669113 + 1.15894i
\(425\) 705.752 1222.40i 0.0805506 0.139518i
\(426\) 0 0
\(427\) 4595.13 + 1241.01i 0.520782 + 0.140648i
\(428\) −13202.1 7622.23i −1.49100 0.860828i
\(429\) 0 0
\(430\) 8439.99i 0.946541i
\(431\) −9080.39 5242.57i −1.01482 0.585906i −0.102220 0.994762i \(-0.532595\pi\)
−0.912599 + 0.408856i \(0.865928\pi\)
\(432\) 0 0
\(433\) 7417.04i 0.823188i −0.911367 0.411594i \(-0.864972\pi\)
0.911367 0.411594i \(-0.135028\pi\)
\(434\) −12585.1 + 3345.52i −1.39195 + 0.370023i
\(435\) 0 0
\(436\) −8873.77 −0.974717
\(437\) 4891.38 + 8472.11i 0.535438 + 0.927405i
\(438\) 0 0
\(439\) −14857.3 8577.85i −1.61526 0.932570i −0.988124 0.153660i \(-0.950894\pi\)
−0.627136 0.778910i \(-0.715773\pi\)
\(440\) −5767.04 −0.624847
\(441\) 0 0
\(442\) 12436.2 1.33830
\(443\) 1474.37 + 851.230i 0.158126 + 0.0912938i 0.576975 0.816762i \(-0.304233\pi\)
−0.418849 + 0.908056i \(0.637566\pi\)
\(444\) 0 0
\(445\) 3133.48 + 5427.35i 0.333801 + 0.578160i
\(446\) 3872.80 0.411172
\(447\) 0 0
\(448\) 8114.95 2157.20i 0.855793 0.227496i
\(449\) 10147.0i 1.06651i 0.845953 + 0.533257i \(0.179032\pi\)
−0.845953 + 0.533257i \(0.820968\pi\)
\(450\) 0 0
\(451\) 4283.94 + 2473.34i 0.447279 + 0.258237i
\(452\) 1202.06i 0.125089i
\(453\) 0 0
\(454\) −7719.68 4456.96i −0.798023 0.460739i
\(455\) −11665.4 3150.46i −1.20194 0.324607i
\(456\) 0 0
\(457\) −3479.42 + 6026.53i −0.356150 + 0.616869i −0.987314 0.158780i \(-0.949244\pi\)
0.631164 + 0.775649i \(0.282577\pi\)
\(458\) 7066.26 12239.1i 0.720927 1.24868i
\(459\) 0 0
\(460\) −12062.4 + 6964.20i −1.22263 + 0.705886i
\(461\) 7791.99 + 13496.1i 0.787222 + 1.36351i 0.927663 + 0.373419i \(0.121815\pi\)
−0.140441 + 0.990089i \(0.544852\pi\)
\(462\) 0 0
\(463\) 6042.09 10465.2i 0.606479 1.05045i −0.385337 0.922776i \(-0.625915\pi\)
0.991816 0.127677i \(-0.0407520\pi\)
\(464\) 18246.3i 1.82557i
\(465\) 0 0
\(466\) −13105.0 −1.30274
\(467\) −8837.65 15307.3i −0.875712 1.51678i −0.856002 0.516972i \(-0.827059\pi\)
−0.0197099 0.999806i \(-0.506274\pi\)
\(468\) 0 0
\(469\) −13105.6 13157.6i −1.29032 1.29544i
\(470\) 18612.7 10746.1i 1.82668 1.05464i
\(471\) 0 0
\(472\) 6021.31 3476.40i 0.587189 0.339014i
\(473\) 2446.86 1412.70i 0.237858 0.137327i
\(474\) 0 0
\(475\) −3616.56 + 2088.02i −0.349346 + 0.201695i
\(476\) −10429.8 + 2772.55i −1.00430 + 0.266974i
\(477\) 0 0
\(478\) 4765.56 + 8254.19i 0.456007 + 0.789828i
\(479\) 11188.3 1.06724 0.533618 0.845726i \(-0.320832\pi\)
0.533618 + 0.845726i \(0.320832\pi\)
\(480\) 0 0
\(481\) 14124.5i 1.33892i
\(482\) −10200.3 + 17667.4i −0.963920 + 1.66956i
\(483\) 0 0
\(484\) 8944.99 + 15493.2i 0.840063 + 1.45503i
\(485\) 3721.04 2148.35i 0.348379 0.201137i
\(486\) 0 0
\(487\) 8832.68 15298.7i 0.821862 1.42351i −0.0824315 0.996597i \(-0.526269\pi\)
0.904294 0.426911i \(-0.140398\pi\)
\(488\) −5250.98 + 9094.96i −0.487092 + 0.843667i
\(489\) 0 0
\(490\) 15634.9 + 61.8416i 1.44145 + 0.00570147i
\(491\) −7981.84 4608.32i −0.733636 0.423565i 0.0861147 0.996285i \(-0.472555\pi\)
−0.819751 + 0.572720i \(0.805888\pi\)
\(492\) 0 0
\(493\) 9183.22i 0.838928i
\(494\) −31864.0 18396.7i −2.90209 1.67552i
\(495\) 0 0
\(496\) 10139.1i 0.917863i
\(497\) 2120.18 + 7975.68i 0.191354 + 0.719835i
\(498\) 0 0
\(499\) −461.057 −0.0413622 −0.0206811 0.999786i \(-0.506583\pi\)
−0.0206811 + 0.999786i \(0.506583\pi\)
\(500\) −12389.8 21459.8i −1.10818 1.91942i
\(501\) 0 0
\(502\) −1582.88 913.879i −0.140732 0.0812518i
\(503\) −12711.5 −1.12679 −0.563397 0.826186i \(-0.690506\pi\)
−0.563397 + 0.826186i \(0.690506\pi\)
\(504\) 0 0
\(505\) 4699.72 0.414129
\(506\) −6020.97 3476.21i −0.528982 0.305408i
\(507\) 0 0
\(508\) −17451.7 30227.2i −1.52420 2.63999i
\(509\) 5598.28 0.487504 0.243752 0.969838i \(-0.421622\pi\)
0.243752 + 0.969838i \(0.421622\pi\)
\(510\) 0 0
\(511\) −1679.16 453.491i −0.145365 0.0392588i
\(512\) 21572.3i 1.86205i
\(513\) 0 0
\(514\) −29236.3 16879.6i −2.50887 1.44850i
\(515\) 6082.89i 0.520474i
\(516\) 0 0
\(517\) 6230.84 + 3597.38i 0.530043 + 0.306020i
\(518\) −4695.30 17662.7i −0.398262 1.49818i
\(519\) 0 0
\(520\) 13330.3 23088.8i 1.12418 1.94714i
\(521\) −1390.74 + 2408.83i −0.116947 + 0.202558i −0.918556 0.395290i \(-0.870644\pi\)
0.801609 + 0.597848i \(0.203977\pi\)
\(522\) 0 0
\(523\) −7662.01 + 4423.66i −0.640605 + 0.369853i −0.784848 0.619689i \(-0.787259\pi\)
0.144243 + 0.989542i \(0.453925\pi\)
\(524\) −16786.7 29075.4i −1.39949 2.42398i
\(525\) 0 0
\(526\) −12989.7 + 22498.8i −1.07676 + 1.86500i
\(527\) 5102.94i 0.421798i
\(528\) 0 0
\(529\) 3621.35 0.297637
\(530\) 6516.57 + 11287.0i 0.534079 + 0.925051i
\(531\) 0 0
\(532\) 30824.6 + 8324.80i 2.51206 + 0.678432i
\(533\) −19804.4 + 11434.1i −1.60943 + 0.929203i
\(534\) 0 0
\(535\) −7495.03 + 4327.26i −0.605679 + 0.349689i
\(536\) 35485.4 20487.5i 2.85958 1.65098i
\(537\) 0 0
\(538\) −4724.66 + 2727.78i −0.378614 + 0.218593i
\(539\) 2599.05 + 4543.10i 0.207698 + 0.363052i
\(540\) 0 0
\(541\) 5968.54 + 10337.8i 0.474321 + 0.821548i 0.999568 0.0294020i \(-0.00936029\pi\)
−0.525247 + 0.850950i \(0.676027\pi\)
\(542\) 24801.1 1.96550
\(543\) 0 0
\(544\) 835.876i 0.0658785i
\(545\) −2518.89 + 4362.85i −0.197977 + 0.342906i
\(546\) 0 0
\(547\) −3335.96 5778.05i −0.260759 0.451648i 0.705685 0.708526i \(-0.250640\pi\)
−0.966444 + 0.256878i \(0.917306\pi\)
\(548\) −669.363 + 386.457i −0.0521784 + 0.0301252i
\(549\) 0 0
\(550\) 1483.92 2570.22i 0.115045 0.199263i
\(551\) −13584.6 + 23529.3i −1.05032 + 1.81920i
\(552\) 0 0
\(553\) −2236.92 + 8282.74i −0.172014 + 0.636922i
\(554\) 37353.2 + 21565.9i 2.86460 + 1.65388i
\(555\) 0 0
\(556\) 13413.6i 1.02313i
\(557\) 18890.9 + 10906.6i 1.43704 + 0.829675i 0.997643 0.0686176i \(-0.0218588\pi\)
0.439397 + 0.898293i \(0.355192\pi\)
\(558\) 0 0
\(559\) 13061.6i 0.988279i
\(560\) −3173.96 + 11752.4i −0.239508 + 0.886836i
\(561\) 0 0
\(562\) 33288.4 2.49855
\(563\) 3934.60 + 6814.92i 0.294536 + 0.510151i 0.974877 0.222745i \(-0.0715017\pi\)
−0.680341 + 0.732896i \(0.738168\pi\)
\(564\) 0 0
\(565\) −591.001 341.214i −0.0440064 0.0254071i
\(566\) 3722.81 0.276469
\(567\) 0 0
\(568\) −18208.7 −1.34511
\(569\) −8743.96 5048.33i −0.644228 0.371945i 0.142013 0.989865i \(-0.454642\pi\)
−0.786241 + 0.617919i \(0.787976\pi\)
\(570\) 0 0
\(571\) 4725.12 + 8184.15i 0.346305 + 0.599818i 0.985590 0.169152i \(-0.0541029\pi\)
−0.639285 + 0.768970i \(0.720770\pi\)
\(572\) 17536.7 1.28190
\(573\) 0 0
\(574\) 20964.5 20881.8i 1.52446 1.51845i
\(575\) 3647.96i 0.264574i
\(576\) 0 0
\(577\) 22282.2 + 12864.6i 1.60766 + 0.928184i 0.989892 + 0.141825i \(0.0452970\pi\)
0.617770 + 0.786359i \(0.288036\pi\)
\(578\) 17908.5i 1.28875i
\(579\) 0 0
\(580\) −33500.4 19341.4i −2.39832 1.38467i
\(581\) 9100.70 + 9136.77i 0.649846 + 0.652422i
\(582\) 0 0
\(583\) −2181.50 + 3778.48i −0.154972 + 0.268419i
\(584\) 1918.82 3323.50i 0.135961 0.235492i
\(585\) 0 0
\(586\) 33714.8 19465.2i 2.37670 1.37219i
\(587\) −7519.63 13024.4i −0.528736 0.915798i −0.999439 0.0335059i \(-0.989333\pi\)
0.470702 0.882292i \(-0.344001\pi\)
\(588\) 0 0
\(589\) −7548.72 + 13074.8i −0.528081 + 0.914663i
\(590\) 7755.87i 0.541194i
\(591\) 0 0
\(592\) 14229.8 0.987911
\(593\) 1728.25 + 2993.41i 0.119681 + 0.207293i 0.919641 0.392760i \(-0.128480\pi\)
−0.799960 + 0.600053i \(0.795146\pi\)
\(594\) 0 0
\(595\) −1597.43 + 5914.87i −0.110064 + 0.407539i
\(596\) −16238.5 + 9375.31i −1.11603 + 0.644341i
\(597\) 0 0
\(598\) 27834.6 16070.3i 1.90341 1.09894i
\(599\) 3692.69 2131.97i 0.251885 0.145426i −0.368742 0.929532i \(-0.620211\pi\)
0.620627 + 0.784106i \(0.286878\pi\)
\(600\) 0 0
\(601\) 18500.7 10681.4i 1.25567 0.724963i 0.283442 0.958989i \(-0.408524\pi\)
0.972230 + 0.234026i \(0.0751902\pi\)
\(602\) −4341.97 16333.6i −0.293963 1.10583i
\(603\) 0 0
\(604\) −4836.80 8377.59i −0.325839 0.564369i
\(605\) 10156.4 0.682508
\(606\) 0 0
\(607\) 12892.4i 0.862087i 0.902331 + 0.431043i \(0.141854\pi\)
−0.902331 + 0.431043i \(0.858146\pi\)
\(608\) −1236.50 + 2141.69i −0.0824783 + 0.142857i
\(609\) 0 0
\(610\) 5857.48 + 10145.5i 0.388791 + 0.673406i
\(611\) −28804.8 + 16630.5i −1.90723 + 1.10114i
\(612\) 0 0
\(613\) −2804.94 + 4858.29i −0.184813 + 0.320105i −0.943513 0.331334i \(-0.892501\pi\)
0.758701 + 0.651439i \(0.225835\pi\)
\(614\) 4226.32 7320.19i 0.277785 0.481138i
\(615\) 0 0
\(616\) −11160.7 + 2966.87i −0.729998 + 0.194056i
\(617\) −18116.5 10459.6i −1.18208 0.682473i −0.225583 0.974224i \(-0.572429\pi\)
−0.956494 + 0.291751i \(0.905762\pi\)
\(618\) 0 0
\(619\) 12344.6i 0.801568i −0.916173 0.400784i \(-0.868738\pi\)
0.916173 0.400784i \(-0.131262\pi\)
\(620\) −18615.5 10747.7i −1.20583 0.696188i
\(621\) 0 0
\(622\) 15537.8i 1.00162i
\(623\) 8856.23 + 8891.33i 0.569530 + 0.571788i
\(624\) 0 0
\(625\) −9135.04 −0.584642
\(626\) −13369.0 23155.8i −0.853569 1.47842i
\(627\) 0 0
\(628\) −477.733 275.819i −0.0303561 0.0175261i
\(629\) 7161.76 0.453987
\(630\) 0 0
\(631\) −5767.92 −0.363894 −0.181947 0.983308i \(-0.558240\pi\)
−0.181947 + 0.983308i \(0.558240\pi\)
\(632\) −16393.7 9464.92i −1.03182 0.595719i
\(633\) 0 0
\(634\) −3441.11 5960.18i −0.215558 0.373358i
\(635\) −19815.2 −1.23833
\(636\) 0 0
\(637\) −24196.3 95.7053i −1.50501 0.00595288i
\(638\) 19308.7i 1.19818i
\(639\) 0 0
\(640\) 19395.2 + 11197.8i 1.19791 + 0.691613i
\(641\) 27080.3i 1.66866i −0.551268 0.834328i \(-0.685856\pi\)
0.551268 0.834328i \(-0.314144\pi\)
\(642\) 0 0
\(643\) −14289.4 8250.01i −0.876392 0.505985i −0.00692488 0.999976i \(-0.502204\pi\)
−0.869467 + 0.493991i \(0.835538\pi\)
\(644\) −19761.1 + 19683.1i −1.20915 + 1.20438i
\(645\) 0 0
\(646\) −9327.96 + 16156.5i −0.568117 + 0.984008i
\(647\) 1814.64 3143.04i 0.110264 0.190983i −0.805613 0.592442i \(-0.798164\pi\)
0.915877 + 0.401460i \(0.131497\pi\)
\(648\) 0 0
\(649\) 2248.53 1298.19i 0.135998 0.0785183i
\(650\) 6860.07 + 11882.0i 0.413960 + 0.717000i
\(651\) 0 0
\(652\) −33151.9 + 57420.8i −1.99130 + 3.44904i
\(653\) 23075.3i 1.38286i 0.722444 + 0.691430i \(0.243019\pi\)
−0.722444 + 0.691430i \(0.756981\pi\)
\(654\) 0 0
\(655\) −19060.2 −1.13701
\(656\) 11519.4 + 19952.1i 0.685603 + 1.18750i
\(657\) 0 0
\(658\) 30492.2 30371.8i 1.80655 1.79942i
\(659\) −4090.21 + 2361.48i −0.241778 + 0.139591i −0.615994 0.787751i \(-0.711245\pi\)
0.374215 + 0.927342i \(0.377912\pi\)
\(660\) 0 0
\(661\) −2370.90 + 1368.84i −0.139512 + 0.0805471i −0.568131 0.822938i \(-0.692333\pi\)
0.428620 + 0.903485i \(0.359000\pi\)
\(662\) −7209.64 + 4162.49i −0.423279 + 0.244380i
\(663\) 0 0
\(664\) −24641.5 + 14226.8i −1.44017 + 0.831484i
\(665\) 12842.7 12792.0i 0.748903 0.745946i
\(666\) 0 0
\(667\) −11866.8 20553.8i −0.688880 1.19318i
\(668\) 23764.1 1.37644
\(669\) 0 0
\(670\) 45707.7i 2.63558i
\(671\) −1960.87 + 3396.32i −0.112814 + 0.195400i
\(672\) 0 0
\(673\) 9072.16 + 15713.4i 0.519623 + 0.900013i 0.999740 + 0.0228084i \(0.00726078\pi\)
−0.480117 + 0.877204i \(0.659406\pi\)
\(674\) 7026.08 4056.51i 0.401535 0.231826i
\(675\) 0 0
\(676\) −22639.8 + 39213.3i −1.28811 + 2.23107i
\(677\) 12329.9 21355.9i 0.699963 1.21237i −0.268515 0.963275i \(-0.586533\pi\)
0.968479 0.249097i \(-0.0801337\pi\)
\(678\) 0 0
\(679\) 6095.98 6071.92i 0.344539 0.343179i
\(680\) −11707.1 6759.08i −0.660214 0.381175i
\(681\) 0 0
\(682\) 10729.5i 0.602423i
\(683\) 13961.0 + 8060.40i 0.782143 + 0.451570i 0.837189 0.546913i \(-0.184197\pi\)
−0.0550463 + 0.998484i \(0.517531\pi\)
\(684\) 0 0
\(685\) 438.795i 0.0244752i
\(686\) 30289.4 7923.71i 1.68579 0.441004i
\(687\) 0 0
\(688\) 13159.0 0.729192
\(689\) −10085.0 17467.7i −0.557629 0.965842i
\(690\) 0 0
\(691\) −9861.10 5693.31i −0.542886 0.313435i 0.203362 0.979104i \(-0.434813\pi\)
−0.746248 + 0.665668i \(0.768147\pi\)
\(692\) 8000.64 0.439507
\(693\) 0 0
\(694\) 4723.14 0.258340
\(695\) −6594.87 3807.55i −0.359939 0.207811i
\(696\) 0 0
\(697\) 5797.60 + 10041.7i 0.315064 + 0.545707i
\(698\) −28409.8 −1.54058
\(699\) 0 0
\(700\) −8402.29 8435.59i −0.453681 0.455479i
\(701\) 19448.3i 1.04786i 0.851761 + 0.523930i \(0.175535\pi\)
−0.851761 + 0.523930i \(0.824465\pi\)
\(702\) 0 0
\(703\) −18349.9 10594.3i −0.984466 0.568382i
\(704\) 6918.40i 0.370379i
\(705\) 0 0
\(706\) 8929.82 + 5155.63i 0.476031 + 0.274837i
\(707\) 9095.20 2417.78i 0.483819 0.128614i
\(708\) 0 0
\(709\) 12475.9 21608.8i 0.660847 1.14462i −0.319546 0.947571i \(-0.603530\pi\)
0.980393 0.197050i \(-0.0631363\pi\)
\(710\) −10156.0 + 17590.6i −0.536826 + 0.929809i
\(711\) 0 0
\(712\) −23979.5 + 13844.6i −1.26218 + 0.728719i
\(713\) −6594.13 11421.4i −0.346356 0.599907i
\(714\) 0 0
\(715\) 4977.93 8622.02i 0.260369 0.450973i
\(716\) 13358.9i 0.697268i
\(717\) 0 0
\(718\) −43779.7 −2.27555
\(719\) 3243.11 + 5617.23i 0.168216 + 0.291359i 0.937793 0.347195i \(-0.112866\pi\)
−0.769576 + 0.638555i \(0.779533\pi\)
\(720\) 0 0
\(721\) 3129.36 + 11772.0i 0.161641 + 0.608061i
\(722\) 18524.1 10694.9i 0.954843 0.551279i
\(723\) 0 0
\(724\) −8728.05 + 5039.14i −0.448032 + 0.258671i
\(725\) 8774.00 5065.67i 0.449459 0.259496i
\(726\) 0 0
\(727\) 12957.4 7480.97i 0.661023 0.381642i −0.131643 0.991297i \(-0.542025\pi\)
0.792667 + 0.609655i \(0.208692\pi\)
\(728\) 13919.6 51540.7i 0.708647 2.62394i
\(729\) 0 0
\(730\) −2140.45 3707.37i −0.108523 0.187967i
\(731\) 6622.84 0.335095
\(732\) 0 0
\(733\) 12098.0i 0.609617i −0.952414 0.304808i \(-0.901408\pi\)
0.952414 0.304808i \(-0.0985925\pi\)
\(734\) −17738.7 + 30724.4i −0.892028 + 1.54504i
\(735\) 0 0
\(736\) −1080.14 1870.85i −0.0540957 0.0936964i
\(737\) 13251.2 7650.61i 0.662301 0.382380i
\(738\) 0 0
\(739\) 1933.82 3349.47i 0.0962606 0.166728i −0.813873 0.581042i \(-0.802645\pi\)
0.910134 + 0.414314i \(0.135978\pi\)
\(740\) 15083.9 26126.1i 0.749318 1.29786i
\(741\) 0 0
\(742\) 18417.9 + 18490.9i 0.911244 + 0.914855i
\(743\) 25571.4 + 14763.7i 1.26262 + 0.728972i 0.973580 0.228346i \(-0.0733317\pi\)
0.289037 + 0.957318i \(0.406665\pi\)
\(744\) 0 0
\(745\) 10645.0i 0.523494i
\(746\) 23463.7 + 13546.8i 1.15156 + 0.664855i
\(747\) 0 0
\(748\) 8891.90i 0.434652i
\(749\) −12278.7 + 12230.2i −0.599003 + 0.596639i
\(750\) 0 0
\(751\) 6081.58 0.295499 0.147750 0.989025i \(-0.452797\pi\)
0.147750 + 0.989025i \(0.452797\pi\)
\(752\) 16754.5 + 29019.6i 0.812465 + 1.40723i
\(753\) 0 0
\(754\) 77304.0 + 44631.5i 3.73375 + 2.15568i
\(755\) −5491.86 −0.264727
\(756\) 0 0
\(757\) −27611.0 −1.32568 −0.662840 0.748761i \(-0.730649\pi\)
−0.662840 + 0.748761i \(0.730649\pi\)
\(758\) −12264.3 7080.82i −0.587679 0.339297i
\(759\) 0 0
\(760\) 19997.3 + 34636.3i 0.954445 + 1.65315i
\(761\) 9596.16 0.457110 0.228555 0.973531i \(-0.426600\pi\)
0.228555 + 0.973531i \(0.426600\pi\)
\(762\) 0 0
\(763\) −2630.24 + 9739.10i −0.124798 + 0.462096i
\(764\) 25121.4i 1.18961i
\(765\) 0 0
\(766\) −6306.17 3640.87i −0.297456 0.171736i
\(767\) 12002.9i 0.565058i
\(768\) 0 0
\(769\) 612.746 + 353.769i 0.0287337 + 0.0165894i 0.514298 0.857612i \(-0.328053\pi\)
−0.485564 + 0.874201i \(0.661386\pi\)
\(770\) −3358.76 + 12436.6i −0.157197 + 0.582059i
\(771\) 0 0
\(772\) −22892.7 + 39651.3i −1.06726 + 1.84855i
\(773\) −2632.55 + 4559.71i −0.122492 + 0.212162i −0.920750 0.390154i \(-0.872422\pi\)
0.798258 + 0.602316i \(0.205755\pi\)
\(774\) 0 0
\(775\) 4875.54 2814.89i 0.225980 0.130470i
\(776\) 9491.98 + 16440.6i 0.439101 + 0.760545i
\(777\) 0 0
\(778\) 25875.2 44817.2i 1.19238 2.06526i
\(779\) 34305.3i 1.57781i
\(780\) 0 0
\(781\) −6799.67 −0.311538
\(782\) −8148.37 14113.4i −0.372615 0.645388i
\(783\) 0 0
\(784\) −96.4191 + 24376.8i −0.00439227 + 1.11046i
\(785\) −271.217 + 156.587i −0.0123314 + 0.00711953i
\(786\) 0 0
\(787\) −27206.6 + 15707.8i −1.23229 + 0.711463i −0.967507 0.252845i \(-0.918634\pi\)
−0.264783 + 0.964308i \(0.585300\pi\)
\(788\) −22624.5 + 13062.3i −1.02280 + 0.590513i
\(789\) 0 0
\(790\) −18287.2 + 10558.1i −0.823583 + 0.475496i
\(791\) −1319.28 356.298i −0.0593024 0.0160158i
\(792\) 0 0
\(793\) −9064.97 15701.0i −0.405935 0.703100i
\(794\) −20646.3 −0.922807
\(795\) 0 0
\(796\) 11232.2i 0.500145i
\(797\) 1477.45 2559.02i 0.0656637 0.113733i −0.831325 0.555787i \(-0.812417\pi\)
0.896988 + 0.442055i \(0.145750\pi\)
\(798\) 0 0
\(799\) 8432.40 + 14605.3i 0.373363 + 0.646683i
\(800\) 798.628 461.088i 0.0352947 0.0203774i
\(801\) 0 0
\(802\) 16542.4 28652.3i 0.728344 1.26153i
\(803\) 716.544 1241.09i 0.0314898 0.0545419i
\(804\) 0 0
\(805\) 4067.97 + 15302.9i 0.178108 + 0.670006i
\(806\) 42956.3 + 24800.9i 1.87726 + 1.08384i
\(807\) 0 0
\(808\) 20764.7i 0.904082i
\(809\) −1592.89 919.657i −0.0692251 0.0399671i 0.464988 0.885317i \(-0.346059\pi\)
−0.534213 + 0.845350i \(0.679392\pi\)
\(810\) 0 0
\(811\) 3301.11i 0.142932i −0.997443 0.0714658i \(-0.977232\pi\)
0.997443 0.0714658i \(-0.0227677\pi\)
\(812\) −74782.3 20196.4i −3.23195 0.872853i
\(813\) 0 0
\(814\) 15058.4 0.648398
\(815\) 18820.9 + 32598.7i 0.808916 + 1.40108i
\(816\) 0 0
\(817\) −16969.1 9797.10i −0.726649 0.419531i
\(818\) 10940.4 0.467633
\(819\) 0 0
\(820\) 48842.9 2.08008
\(821\) 7082.07 + 4088.84i 0.301055 + 0.173814i 0.642917 0.765936i \(-0.277724\pi\)
−0.341862 + 0.939750i \(0.611057\pi\)
\(822\) 0 0
\(823\) −15950.3 27626.7i −0.675567 1.17012i −0.976303 0.216409i \(-0.930565\pi\)
0.300735 0.953708i \(-0.402768\pi\)
\(824\) −26875.9 −1.13624
\(825\) 0 0
\(826\) −3990.03 15009.7i −0.168076 0.632267i
\(827\) 41211.0i 1.73283i −0.499327 0.866414i \(-0.666419\pi\)
0.499327 0.866414i \(-0.333581\pi\)
\(828\) 0 0
\(829\) 9494.26 + 5481.52i 0.397768 + 0.229651i 0.685520 0.728053i \(-0.259575\pi\)
−0.287753 + 0.957705i \(0.592908\pi\)
\(830\) 31740.0i 1.32736i
\(831\) 0 0
\(832\) −27698.4 15991.7i −1.15417 0.666360i
\(833\) −48.5269 + 12268.6i −0.00201844 + 0.510303i
\(834\) 0 0
\(835\) 6745.64 11683.8i 0.279572 0.484233i
\(836\) −13153.7 + 22782.9i −0.544175 + 0.942538i
\(837\) 0 0
\(838\) −32128.6 + 18549.5i −1.32442 + 0.764655i
\(839\) 10865.3 + 18819.2i 0.447093 + 0.774388i 0.998195 0.0600500i \(-0.0191260\pi\)
−0.551102 + 0.834438i \(0.685793\pi\)
\(840\) 0 0
\(841\) 20762.7 35962.0i 0.851312 1.47452i
\(842\) 2931.75i 0.119994i
\(843\) 0 0
\(844\) 76303.7 3.11194
\(845\) 12853.0 + 22262.0i 0.523261 + 0.906315i
\(846\) 0 0
\(847\) 19655.4 5225.00i 0.797362 0.211963i
\(848\) −17597.9 + 10160.2i −0.712637 + 0.411441i
\(849\) 0 0
\(850\) 6024.71 3478.37i 0.243113 0.140361i
\(851\) 16029.4 9254.59i 0.645689 0.372789i
\(852\) 0 0
\(853\) 33620.5 19410.8i 1.34952 0.779148i 0.361342 0.932433i \(-0.382319\pi\)
0.988182 + 0.153285i \(0.0489854\pi\)
\(854\) 16555.1 + 16620.7i 0.663354 + 0.665983i
\(855\) 0 0
\(856\) −19119.0 33115.1i −0.763405 1.32226i
\(857\) −24474.4 −0.975531 −0.487765 0.872975i \(-0.662188\pi\)
−0.487765 + 0.872975i \(0.662188\pi\)
\(858\) 0 0
\(859\) 33413.7i 1.32720i −0.748089 0.663599i \(-0.769028\pi\)
0.748089 0.663599i \(-0.230972\pi\)
\(860\) 13948.8 24160.1i 0.553083 0.957968i
\(861\) 0 0
\(862\) −25838.5 44753.6i −1.02095 1.76834i
\(863\) 20331.0 11738.1i 0.801942 0.463001i −0.0422080 0.999109i \(-0.513439\pi\)
0.844150 + 0.536108i \(0.180106\pi\)
\(864\) 0 0
\(865\) 2271.04 3933.56i 0.0892692 0.154619i
\(866\) 18277.8 31658.1i 0.717211 1.24225i
\(867\) 0 0
\(868\) −41555.1 11222.8i −1.62497 0.438855i
\(869\) −6121.89 3534.47i −0.238977 0.137973i
\(870\) 0 0
\(871\) 70736.6i 2.75180i
\(872\) −19276.2 11129.1i −0.748596 0.432202i
\(873\) 0 0
\(874\) 48215.2i 1.86602i
\(875\) −27224.8 + 7237.19i −1.05185 + 0.279613i
\(876\) 0 0
\(877\) 9596.84 0.369512 0.184756 0.982784i \(-0.440850\pi\)
0.184756 + 0.982784i \(0.440850\pi\)
\(878\) −42276.7 73225.5i −1.62502 2.81462i
\(879\) 0 0
\(880\) −8686.33 5015.06i −0.332746 0.192111i
\(881\) −48210.3 −1.84364 −0.921821 0.387617i \(-0.873298\pi\)
−0.921821 + 0.387617i \(0.873298\pi\)
\(882\) 0 0
\(883\) −21780.5 −0.830094 −0.415047 0.909800i \(-0.636235\pi\)
−0.415047 + 0.909800i \(0.636235\pi\)
\(884\) 35599.4 + 20553.3i 1.35446 + 0.781995i
\(885\) 0 0
\(886\) 4195.37 + 7266.59i 0.159081 + 0.275537i
\(887\) 32602.2 1.23413 0.617066 0.786911i \(-0.288321\pi\)
0.617066 + 0.786911i \(0.288321\pi\)
\(888\) 0 0
\(889\) −38347.6 + 10194.0i −1.44672 + 0.384583i
\(890\) 30887.4i 1.16331i
\(891\) 0 0
\(892\) 11086.2 + 6400.61i 0.416135 + 0.240256i
\(893\) 49895.9i 1.86977i
\(894\) 0 0
\(895\) 6567.97 + 3792.02i 0.245299 + 0.141624i
\(896\) 43295.5 + 11692.8i 1.61429 + 0.435971i
\(897\) 0 0
\(898\) −25005.1 + 43310.2i −0.929212 + 1.60944i
\(899\) 18313.7 31720.2i 0.679415 1.17678i
\(900\) 0 0
\(901\) −8856.89 + 5113.53i −0.327487 + 0.189075i
\(902\) 12190.1 + 21113.8i 0.449983 + 0.779394i
\(903\) 0 0
\(904\) 1507.58 2611.20i 0.0554661 0.0960700i
\(905\) 5721.60i 0.210157i
\(906\) 0 0
\(907\) 45098.6 1.65102 0.825510 0.564387i \(-0.190887\pi\)
0.825510 + 0.564387i \(0.190887\pi\)
\(908\) −14732.1 25516.7i −0.538438 0.932602i
\(909\) 0 0
\(910\) −42027.4 42194.0i −1.53098 1.53705i
\(911\) −27846.3 + 16077.1i −1.01272 + 0.584695i −0.911988 0.410218i \(-0.865453\pi\)
−0.100735 + 0.994913i \(0.532119\pi\)
\(912\) 0 0
\(913\) −9201.83 + 5312.68i −0.333556 + 0.192578i
\(914\) −29702.3 + 17148.7i −1.07491 + 0.620598i
\(915\) 0 0
\(916\) 40455.4 23356.9i 1.45926 0.842505i
\(917\) −36886.4 + 9805.54i −1.32835 + 0.353116i
\(918\) 0 0
\(919\) 8217.77 + 14233.6i 0.294972 + 0.510907i 0.974978 0.222300i \(-0.0713563\pi\)
−0.680006 + 0.733206i \(0.738023\pi\)
\(920\) −34937.0 −1.25200
\(921\) 0 0
\(922\) 76807.1i 2.74350i
\(923\) 15717.2 27223.0i 0.560497 0.970809i
\(924\) 0 0
\(925\) 3950.59 + 6842.62i 0.140427 + 0.243226i
\(926\) 51578.8 29779.0i 1.83044 1.05680i
\(927\) 0 0
\(928\) 2999.83 5195.86i 0.106114 0.183796i
\(929\) −11690.1 + 20247.9i −0.412852 + 0.715081i −0.995200 0.0978584i \(-0.968801\pi\)
0.582348 + 0.812940i \(0.302134\pi\)
\(930\) 0 0
\(931\) 18273.2 31363.0i 0.643265 1.10406i
\(932\) −37514.0 21658.7i −1.31847 0.761218i
\(933\) 0 0
\(934\) 87114.4i 3.05189i
\(935\) −4371.76 2524.03i −0.152911 0.0882832i
\(936\) 0 0
\(937\) 24806.5i 0.864880i −0.901663 0.432440i \(-0.857653\pi\)
0.901663 0.432440i \(-0.142347\pi\)
\(938\) −23514.4 88456.4i −0.818521 3.07911i
\(939\) 0 0
\(940\) 71040.3 2.46498
\(941\) −4448.30 7704.69i −0.154103 0.266914i 0.778629 0.627484i \(-0.215915\pi\)
−0.932732 + 0.360571i \(0.882582\pi\)
\(942\) 0 0
\(943\) 25952.3 + 14983.6i 0.896207 + 0.517425i
\(944\) 12092.4 0.416922
\(945\) 0 0
\(946\) 13925.2 0.478592
\(947\) −5275.81 3045.99i −0.181036 0.104521i 0.406744 0.913542i \(-0.366664\pi\)
−0.587779 + 0.809021i \(0.699998\pi\)
\(948\) 0 0
\(949\) 3312.54 + 5737.48i 0.113308 + 0.196256i
\(950\) −20582.1 −0.702916
\(951\) 0 0
\(952\) −26133.5 7057.87i −0.889697 0.240280i
\(953\) 50366.8i 1.71201i −0.516971 0.856003i \(-0.672941\pi\)
0.516971 0.856003i \(-0.327059\pi\)
\(954\) 0 0
\(955\) 12351.1 + 7130.91i 0.418505 + 0.241624i
\(956\) 31504.3i 1.06582i
\(957\) 0 0
\(958\) 47754.8 + 27571.3i 1.61053 + 0.929840i
\(959\) 225.739 + 849.184i 0.00760115 + 0.0285939i
\(960\) 0 0
\(961\) −4718.96 + 8173.48i −0.158402 + 0.274361i
\(962\) −34807.0 + 60287.4i −1.16655 + 2.02053i
\(963\) 0 0
\(964\) −58398.0 + 33716.1i −1.95111 + 1.12648i
\(965\) 12996.5 + 22510.7i 0.433548 + 0.750927i
\(966\) 0 0
\(967\) −3986.98 + 6905.65i −0.132588 + 0.229649i −0.924673 0.380761i \(-0.875662\pi\)
0.792085 + 0.610410i \(0.208995\pi\)
\(968\) 44873.8i 1.48998i
\(969\) 0 0
\(970\) 21176.7 0.700971
\(971\) 11779.8 + 20403.3i 0.389323 + 0.674327i 0.992359 0.123387i \(-0.0393757\pi\)
−0.603036 + 0.797714i \(0.706042\pi\)
\(972\) 0 0
\(973\) −14721.6 3975.87i −0.485050 0.130997i
\(974\) 75400.9 43532.7i 2.48049 1.43211i
\(975\) 0 0
\(976\) −15818.1 + 9132.58i −0.518775 + 0.299515i
\(977\) −17441.0 + 10069.6i −0.571124 + 0.329739i −0.757598 0.652721i \(-0.773627\pi\)
0.186474 + 0.982460i \(0.440294\pi\)
\(978\) 0 0
\(979\) −8954.65 + 5169.97i −0.292331 + 0.168777i
\(980\) 44653.7 + 26016.9i 1.45552 + 0.848039i
\(981\) 0 0
\(982\) −22712.5 39339.3i −0.738071 1.27838i
\(983\) 17607.8 0.571313 0.285656 0.958332i \(-0.407788\pi\)
0.285656 + 0.958332i \(0.407788\pi\)
\(984\) 0 0
\(985\) 14831.3i 0.479762i
\(986\) 22630.2 39196.6i 0.730925 1.26600i
\(987\) 0 0
\(988\) −60808.7 105324.i −1.95808 3.39149i
\(989\) 14823.2 8558.18i 0.476593 0.275161i
\(990\) 0 0
\(991\) −24487.2 + 42413.1i −0.784927 + 1.35953i 0.144116 + 0.989561i \(0.453966\pi\)
−0.929043 + 0.369972i \(0.879367\pi\)
\(992\) 1666.95 2887.24i 0.0533524 0.0924091i
\(993\) 0 0
\(994\) −10604.9 + 39267.2i −0.338398 + 1.25300i
\(995\) −5522.39 3188.35i −0.175951 0.101586i
\(996\) 0 0
\(997\) 56049.9i 1.78046i −0.455511 0.890230i \(-0.650544\pi\)
0.455511 0.890230i \(-0.349456\pi\)
\(998\) −1967.93 1136.18i −0.0624184 0.0360373i
\(999\) 0 0
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 189.4.s.a.17.20 44
3.2 odd 2 63.4.s.a.59.3 yes 44
7.5 odd 6 189.4.i.a.152.3 44
9.2 odd 6 189.4.i.a.143.20 44
9.7 even 3 63.4.i.a.38.3 yes 44
21.5 even 6 63.4.i.a.5.20 44
63.47 even 6 inner 189.4.s.a.89.20 44
63.61 odd 6 63.4.s.a.47.3 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.i.a.5.20 44 21.5 even 6
63.4.i.a.38.3 yes 44 9.7 even 3
63.4.s.a.47.3 yes 44 63.61 odd 6
63.4.s.a.59.3 yes 44 3.2 odd 2
189.4.i.a.143.20 44 9.2 odd 6
189.4.i.a.152.3 44 7.5 odd 6
189.4.s.a.17.20 44 1.1 even 1 trivial
189.4.s.a.89.20 44 63.47 even 6 inner