Properties

Label 189.4.o.a.62.20
Level $189$
Weight $4$
Character 189.62
Analytic conductor $11.151$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,4,Mod(62,189)]
 
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([1, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.62");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.o (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 62.20
Character \(\chi\) \(=\) 189.62
Dual form 189.4.o.a.125.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.38393 + 1.95371i) q^{2} +(3.63397 + 6.29422i) q^{4} +(5.82670 + 10.0921i) q^{5} +(17.1417 - 7.01157i) q^{7} -2.86048i q^{8} +O(q^{10})\) \(q+(3.38393 + 1.95371i) q^{2} +(3.63397 + 6.29422i) q^{4} +(5.82670 + 10.0921i) q^{5} +(17.1417 - 7.01157i) q^{7} -2.86048i q^{8} +45.5347i q^{10} +(41.2999 + 23.8445i) q^{11} +(-60.2061 + 34.7600i) q^{13} +(71.7048 + 9.76328i) q^{14} +(34.6603 - 60.0334i) q^{16} +25.6583 q^{17} +41.1363i q^{19} +(-42.3481 + 73.3490i) q^{20} +(93.1705 + 161.376i) q^{22} +(-145.611 + 84.0685i) q^{23} +(-5.40080 + 9.35446i) q^{25} -271.644 q^{26} +(106.425 + 82.4138i) q^{28} +(-28.2286 - 16.2978i) q^{29} +(148.499 - 85.7361i) q^{31} +(214.758 - 123.990i) q^{32} +(86.8259 + 50.1290i) q^{34} +(170.641 + 132.142i) q^{35} -3.86757 q^{37} +(-80.3685 + 139.202i) q^{38} +(28.8683 - 16.6671i) q^{40} +(-168.733 - 292.255i) q^{41} +(207.351 - 359.142i) q^{43} +346.601i q^{44} -656.982 q^{46} +(-74.3856 + 128.840i) q^{47} +(244.676 - 240.380i) q^{49} +(-36.5518 + 21.1032i) q^{50} +(-437.574 - 252.633i) q^{52} +59.7358i q^{53} +555.739i q^{55} +(-20.0564 - 49.0334i) q^{56} +(-63.6824 - 110.301i) q^{58} +(-282.056 - 488.535i) q^{59} +(-571.656 - 330.046i) q^{61} +670.014 q^{62} +414.401 q^{64} +(-701.605 - 405.072i) q^{65} +(145.989 + 252.861i) q^{67} +(93.2416 + 161.499i) q^{68} +(319.270 + 780.542i) q^{70} +3.05665i q^{71} -506.596i q^{73} +(-13.0876 - 7.55611i) q^{74} +(-258.921 + 149.488i) q^{76} +(875.138 + 119.158i) q^{77} +(-96.6430 + 167.391i) q^{79} +807.820 q^{80} -1318.62i q^{82} +(216.246 - 374.550i) q^{83} +(149.503 + 258.947i) q^{85} +(1403.32 - 810.206i) q^{86} +(68.2066 - 118.137i) q^{88} -924.591 q^{89} +(-788.312 + 1017.98i) q^{91} +(-1058.29 - 611.005i) q^{92} +(-503.430 + 290.656i) q^{94} +(-415.154 + 239.689i) q^{95} +(943.401 + 544.673i) q^{97} +(1297.60 - 335.404i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.38393 + 1.95371i 1.19640 + 0.690741i 0.959750 0.280855i \(-0.0906178\pi\)
0.236648 + 0.971595i \(0.423951\pi\)
\(3\) 0 0
\(4\) 3.63397 + 6.29422i 0.454246 + 0.786777i
\(5\) 5.82670 + 10.0921i 0.521156 + 0.902668i 0.999697 + 0.0246032i \(0.00783223\pi\)
−0.478542 + 0.878065i \(0.658834\pi\)
\(6\) 0 0
\(7\) 17.1417 7.01157i 0.925565 0.378589i
\(8\) 2.86048i 0.126416i
\(9\) 0 0
\(10\) 45.5347i 1.43993i
\(11\) 41.2999 + 23.8445i 1.13203 + 0.653581i 0.944446 0.328667i \(-0.106599\pi\)
0.187589 + 0.982248i \(0.439933\pi\)
\(12\) 0 0
\(13\) −60.2061 + 34.7600i −1.28447 + 0.741591i −0.977663 0.210179i \(-0.932595\pi\)
−0.306811 + 0.951770i \(0.599262\pi\)
\(14\) 71.7048 + 9.76328i 1.36885 + 0.186382i
\(15\) 0 0
\(16\) 34.6603 60.0334i 0.541567 0.938022i
\(17\) 25.6583 0.366062 0.183031 0.983107i \(-0.441409\pi\)
0.183031 + 0.983107i \(0.441409\pi\)
\(18\) 0 0
\(19\) 41.1363i 0.496701i 0.968670 + 0.248351i \(0.0798885\pi\)
−0.968670 + 0.248351i \(0.920111\pi\)
\(20\) −42.3481 + 73.3490i −0.473466 + 0.820067i
\(21\) 0 0
\(22\) 93.1705 + 161.376i 0.902910 + 1.56389i
\(23\) −145.611 + 84.0685i −1.32009 + 0.762152i −0.983742 0.179587i \(-0.942524\pi\)
−0.336344 + 0.941739i \(0.609191\pi\)
\(24\) 0 0
\(25\) −5.40080 + 9.35446i −0.0432064 + 0.0748357i
\(26\) −271.644 −2.04899
\(27\) 0 0
\(28\) 106.425 + 82.4138i 0.718300 + 0.556241i
\(29\) −28.2286 16.2978i −0.180756 0.104360i 0.406892 0.913476i \(-0.366613\pi\)
−0.587648 + 0.809117i \(0.699946\pi\)
\(30\) 0 0
\(31\) 148.499 85.7361i 0.860363 0.496731i −0.00377092 0.999993i \(-0.501200\pi\)
0.864134 + 0.503262i \(0.167867\pi\)
\(32\) 214.758 123.990i 1.18638 0.684957i
\(33\) 0 0
\(34\) 86.8259 + 50.1290i 0.437956 + 0.252854i
\(35\) 170.641 + 132.142i 0.824104 + 0.638174i
\(36\) 0 0
\(37\) −3.86757 −0.0171844 −0.00859222 0.999963i \(-0.502735\pi\)
−0.00859222 + 0.999963i \(0.502735\pi\)
\(38\) −80.3685 + 139.202i −0.343092 + 0.594253i
\(39\) 0 0
\(40\) 28.8683 16.6671i 0.114112 0.0658826i
\(41\) −168.733 292.255i −0.642725 1.11323i −0.984822 0.173568i \(-0.944471\pi\)
0.342097 0.939665i \(-0.388863\pi\)
\(42\) 0 0
\(43\) 207.351 359.142i 0.735364 1.27369i −0.219199 0.975680i \(-0.570344\pi\)
0.954563 0.298008i \(-0.0963223\pi\)
\(44\) 346.601i 1.18755i
\(45\) 0 0
\(46\) −656.982 −2.10580
\(47\) −74.3856 + 128.840i −0.230856 + 0.399855i −0.958060 0.286566i \(-0.907486\pi\)
0.727204 + 0.686421i \(0.240819\pi\)
\(48\) 0 0
\(49\) 244.676 240.380i 0.713340 0.700818i
\(50\) −36.5518 + 21.1032i −0.103384 + 0.0596888i
\(51\) 0 0
\(52\) −437.574 252.633i −1.16693 0.673730i
\(53\) 59.7358i 0.154818i 0.996999 + 0.0774089i \(0.0246647\pi\)
−0.996999 + 0.0774089i \(0.975335\pi\)
\(54\) 0 0
\(55\) 555.739i 1.36247i
\(56\) −20.0564 49.0334i −0.0478599 0.117007i
\(57\) 0 0
\(58\) −63.6824 110.301i −0.144171 0.249711i
\(59\) −282.056 488.535i −0.622382 1.07800i −0.989041 0.147642i \(-0.952832\pi\)
0.366659 0.930355i \(-0.380502\pi\)
\(60\) 0 0
\(61\) −571.656 330.046i −1.19989 0.692754i −0.239356 0.970932i \(-0.576936\pi\)
−0.960530 + 0.278178i \(0.910270\pi\)
\(62\) 670.014 1.37245
\(63\) 0 0
\(64\) 414.401 0.809377
\(65\) −701.605 405.072i −1.33882 0.772969i
\(66\) 0 0
\(67\) 145.989 + 252.861i 0.266200 + 0.461073i 0.967877 0.251423i \(-0.0808984\pi\)
−0.701677 + 0.712495i \(0.747565\pi\)
\(68\) 93.2416 + 161.499i 0.166282 + 0.288010i
\(69\) 0 0
\(70\) 319.270 + 780.542i 0.545144 + 1.33275i
\(71\) 3.05665i 0.00510927i 0.999997 + 0.00255464i \(0.000813166\pi\)
−0.999997 + 0.00255464i \(0.999187\pi\)
\(72\) 0 0
\(73\) 506.596i 0.812227i −0.913823 0.406114i \(-0.866884\pi\)
0.913823 0.406114i \(-0.133116\pi\)
\(74\) −13.0876 7.55611i −0.0205594 0.0118700i
\(75\) 0 0
\(76\) −258.921 + 149.488i −0.390793 + 0.225625i
\(77\) 875.138 + 119.158i 1.29521 + 0.176355i
\(78\) 0 0
\(79\) −96.6430 + 167.391i −0.137635 + 0.238391i −0.926601 0.376046i \(-0.877284\pi\)
0.788966 + 0.614437i \(0.210617\pi\)
\(80\) 807.820 1.12896
\(81\) 0 0
\(82\) 1318.62i 1.77583i
\(83\) 216.246 374.550i 0.285977 0.495327i −0.686868 0.726782i \(-0.741015\pi\)
0.972846 + 0.231454i \(0.0743484\pi\)
\(84\) 0 0
\(85\) 149.503 + 258.947i 0.190775 + 0.330433i
\(86\) 1403.32 810.206i 1.75958 1.01589i
\(87\) 0 0
\(88\) 68.2066 118.137i 0.0826233 0.143108i
\(89\) −924.591 −1.10120 −0.550598 0.834771i \(-0.685600\pi\)
−0.550598 + 0.834771i \(0.685600\pi\)
\(90\) 0 0
\(91\) −788.312 + 1017.98i −0.908105 + 1.17268i
\(92\) −1058.29 611.005i −1.19929 0.692409i
\(93\) 0 0
\(94\) −503.430 + 290.656i −0.552392 + 0.318924i
\(95\) −415.154 + 239.689i −0.448356 + 0.258859i
\(96\) 0 0
\(97\) 943.401 + 544.673i 0.987503 + 0.570135i 0.904527 0.426416i \(-0.140224\pi\)
0.0829763 + 0.996552i \(0.473557\pi\)
\(98\) 1297.60 335.404i 1.33752 0.345724i
\(99\) 0 0
\(100\) −78.5053 −0.0785053
\(101\) 168.799 292.369i 0.166298 0.288037i −0.770817 0.637056i \(-0.780152\pi\)
0.937116 + 0.349019i \(0.113485\pi\)
\(102\) 0 0
\(103\) −183.659 + 106.035i −0.175694 + 0.101437i −0.585268 0.810840i \(-0.699011\pi\)
0.409574 + 0.912277i \(0.365677\pi\)
\(104\) 99.4302 + 172.218i 0.0937493 + 0.162379i
\(105\) 0 0
\(106\) −116.706 + 202.142i −0.106939 + 0.185224i
\(107\) 399.253i 0.360722i 0.983600 + 0.180361i \(0.0577266\pi\)
−0.983600 + 0.180361i \(0.942273\pi\)
\(108\) 0 0
\(109\) 1847.45 1.62343 0.811714 0.584055i \(-0.198535\pi\)
0.811714 + 0.584055i \(0.198535\pi\)
\(110\) −1085.75 + 1880.58i −0.941113 + 1.63006i
\(111\) 0 0
\(112\) 173.208 1272.10i 0.146131 1.07323i
\(113\) −1101.72 + 636.078i −0.917177 + 0.529532i −0.882733 0.469874i \(-0.844299\pi\)
−0.0344435 + 0.999407i \(0.510966\pi\)
\(114\) 0 0
\(115\) −1696.86 979.684i −1.37594 0.794400i
\(116\) 236.903i 0.189620i
\(117\) 0 0
\(118\) 2204.22i 1.71962i
\(119\) 439.827 179.905i 0.338814 0.138587i
\(120\) 0 0
\(121\) 471.620 + 816.871i 0.354335 + 0.613727i
\(122\) −1289.63 2233.70i −0.957027 1.65762i
\(123\) 0 0
\(124\) 1079.28 + 623.124i 0.781633 + 0.451276i
\(125\) 1330.80 0.952242
\(126\) 0 0
\(127\) −1835.56 −1.28252 −0.641259 0.767325i \(-0.721588\pi\)
−0.641259 + 0.767325i \(0.721588\pi\)
\(128\) −315.760 182.304i −0.218043 0.125887i
\(129\) 0 0
\(130\) −1582.79 2741.47i −1.06784 1.84956i
\(131\) −673.698 1166.88i −0.449323 0.778250i 0.549019 0.835810i \(-0.315001\pi\)
−0.998342 + 0.0575597i \(0.981668\pi\)
\(132\) 0 0
\(133\) 288.430 + 705.147i 0.188046 + 0.459729i
\(134\) 1140.88i 0.735502i
\(135\) 0 0
\(136\) 73.3951i 0.0462763i
\(137\) 964.423 + 556.810i 0.601432 + 0.347237i 0.769605 0.638521i \(-0.220453\pi\)
−0.168173 + 0.985758i \(0.553787\pi\)
\(138\) 0 0
\(139\) −1140.22 + 658.307i −0.695772 + 0.401704i −0.805771 0.592228i \(-0.798249\pi\)
0.109999 + 0.993932i \(0.464915\pi\)
\(140\) −211.626 + 1554.25i −0.127755 + 0.938274i
\(141\) 0 0
\(142\) −5.97182 + 10.3435i −0.00352918 + 0.00611272i
\(143\) −3315.34 −1.93876
\(144\) 0 0
\(145\) 379.850i 0.217550i
\(146\) 989.742 1714.28i 0.561039 0.971747i
\(147\) 0 0
\(148\) −14.0546 24.3433i −0.00780596 0.0135203i
\(149\) 530.202 306.112i 0.291516 0.168307i −0.347110 0.937825i \(-0.612837\pi\)
0.638625 + 0.769518i \(0.279503\pi\)
\(150\) 0 0
\(151\) −1451.09 + 2513.36i −0.782040 + 1.35453i 0.148712 + 0.988881i \(0.452487\pi\)
−0.930752 + 0.365652i \(0.880846\pi\)
\(152\) 117.670 0.0627912
\(153\) 0 0
\(154\) 2728.60 + 2112.99i 1.42777 + 1.10565i
\(155\) 1730.52 + 999.116i 0.896766 + 0.517748i
\(156\) 0 0
\(157\) −1163.43 + 671.708i −0.591414 + 0.341453i −0.765657 0.643250i \(-0.777586\pi\)
0.174242 + 0.984703i \(0.444252\pi\)
\(158\) −654.065 + 377.625i −0.329333 + 0.190141i
\(159\) 0 0
\(160\) 2502.66 + 1444.91i 1.23658 + 0.713938i
\(161\) −1906.57 + 2462.04i −0.933283 + 1.20519i
\(162\) 0 0
\(163\) 974.519 0.468284 0.234142 0.972202i \(-0.424772\pi\)
0.234142 + 0.972202i \(0.424772\pi\)
\(164\) 1226.34 2124.09i 0.583911 1.01136i
\(165\) 0 0
\(166\) 1463.52 844.966i 0.684286 0.395073i
\(167\) 1421.47 + 2462.05i 0.658661 + 1.14083i 0.980963 + 0.194197i \(0.0622100\pi\)
−0.322302 + 0.946637i \(0.604457\pi\)
\(168\) 0 0
\(169\) 1318.01 2282.87i 0.599916 1.03908i
\(170\) 1168.34i 0.527106i
\(171\) 0 0
\(172\) 3014.02 1.33615
\(173\) −1990.91 + 3448.36i −0.874949 + 1.51546i −0.0181322 + 0.999836i \(0.505772\pi\)
−0.856817 + 0.515621i \(0.827561\pi\)
\(174\) 0 0
\(175\) −26.9894 + 198.219i −0.0116583 + 0.0856227i
\(176\) 2862.93 1652.91i 1.22615 0.707916i
\(177\) 0 0
\(178\) −3128.75 1806.38i −1.31747 0.760641i
\(179\) 2465.66i 1.02956i −0.857321 0.514782i \(-0.827873\pi\)
0.857321 0.514782i \(-0.172127\pi\)
\(180\) 0 0
\(181\) 2517.90i 1.03400i 0.855986 + 0.516999i \(0.172951\pi\)
−0.855986 + 0.516999i \(0.827049\pi\)
\(182\) −4656.44 + 1904.65i −1.89647 + 0.775726i
\(183\) 0 0
\(184\) 240.476 + 416.517i 0.0963485 + 0.166881i
\(185\) −22.5351 39.0320i −0.00895576 0.0155118i
\(186\) 0 0
\(187\) 1059.69 + 611.810i 0.414395 + 0.239251i
\(188\) −1081.26 −0.419462
\(189\) 0 0
\(190\) −1873.13 −0.715217
\(191\) 399.325 + 230.550i 0.151278 + 0.0873405i 0.573728 0.819046i \(-0.305497\pi\)
−0.422450 + 0.906386i \(0.638830\pi\)
\(192\) 0 0
\(193\) 1281.14 + 2219.00i 0.477815 + 0.827600i 0.999677 0.0254302i \(-0.00809554\pi\)
−0.521861 + 0.853030i \(0.674762\pi\)
\(194\) 2128.27 + 3686.26i 0.787632 + 1.36422i
\(195\) 0 0
\(196\) 2402.15 + 666.508i 0.875420 + 0.242896i
\(197\) 3764.93i 1.36162i −0.732458 0.680812i \(-0.761627\pi\)
0.732458 0.680812i \(-0.238373\pi\)
\(198\) 0 0
\(199\) 958.945i 0.341597i 0.985306 + 0.170799i \(0.0546347\pi\)
−0.985306 + 0.170799i \(0.945365\pi\)
\(200\) 26.7582 + 15.4489i 0.00946045 + 0.00546200i
\(201\) 0 0
\(202\) 1142.41 659.569i 0.397918 0.229738i
\(203\) −598.160 81.4451i −0.206811 0.0281592i
\(204\) 0 0
\(205\) 1966.32 3405.76i 0.669919 1.16033i
\(206\) −828.650 −0.280266
\(207\) 0 0
\(208\) 4819.17i 1.60649i
\(209\) −980.876 + 1698.93i −0.324634 + 0.562283i
\(210\) 0 0
\(211\) 2018.18 + 3495.59i 0.658471 + 1.14051i 0.981012 + 0.193949i \(0.0621298\pi\)
−0.322541 + 0.946556i \(0.604537\pi\)
\(212\) −375.990 + 217.078i −0.121807 + 0.0703254i
\(213\) 0 0
\(214\) −780.025 + 1351.04i −0.249165 + 0.431567i
\(215\) 4832.68 1.53296
\(216\) 0 0
\(217\) 1944.38 2510.87i 0.608265 0.785481i
\(218\) 6251.63 + 3609.38i 1.94227 + 1.12137i
\(219\) 0 0
\(220\) −3497.94 + 2019.54i −1.07196 + 0.618896i
\(221\) −1544.79 + 891.884i −0.470198 + 0.271469i
\(222\) 0 0
\(223\) −5069.18 2926.69i −1.52223 0.878860i −0.999655 0.0262676i \(-0.991638\pi\)
−0.522576 0.852593i \(-0.675029\pi\)
\(224\) 2811.95 3631.20i 0.838754 1.08312i
\(225\) 0 0
\(226\) −4970.85 −1.46308
\(227\) 3038.38 5262.62i 0.888388 1.53873i 0.0466072 0.998913i \(-0.485159\pi\)
0.841781 0.539820i \(-0.181508\pi\)
\(228\) 0 0
\(229\) 814.321 470.148i 0.234986 0.135669i −0.377884 0.925853i \(-0.623348\pi\)
0.612870 + 0.790184i \(0.290015\pi\)
\(230\) −3828.04 6630.35i −1.09745 1.90084i
\(231\) 0 0
\(232\) −46.6195 + 80.7473i −0.0131928 + 0.0228505i
\(233\) 3314.66i 0.931976i 0.884791 + 0.465988i \(0.154301\pi\)
−0.884791 + 0.465988i \(0.845699\pi\)
\(234\) 0 0
\(235\) −1733.69 −0.481248
\(236\) 2049.96 3550.64i 0.565429 0.979352i
\(237\) 0 0
\(238\) 1839.83 + 250.510i 0.501085 + 0.0682274i
\(239\) −2213.80 + 1278.14i −0.599158 + 0.345924i −0.768710 0.639597i \(-0.779101\pi\)
0.169552 + 0.985521i \(0.445768\pi\)
\(240\) 0 0
\(241\) −1800.75 1039.66i −0.481312 0.277886i 0.239651 0.970859i \(-0.422967\pi\)
−0.720963 + 0.692973i \(0.756300\pi\)
\(242\) 3685.64i 0.979016i
\(243\) 0 0
\(244\) 4797.50i 1.25872i
\(245\) 3851.60 + 1068.68i 1.00437 + 0.278674i
\(246\) 0 0
\(247\) −1429.90 2476.66i −0.368349 0.638000i
\(248\) −245.246 424.779i −0.0627949 0.108764i
\(249\) 0 0
\(250\) 4503.32 + 2600.00i 1.13926 + 0.657753i
\(251\) −4718.74 −1.18663 −0.593316 0.804970i \(-0.702181\pi\)
−0.593316 + 0.804970i \(0.702181\pi\)
\(252\) 0 0
\(253\) −8018.29 −1.99251
\(254\) −6211.40 3586.16i −1.53440 0.885888i
\(255\) 0 0
\(256\) −2369.94 4104.86i −0.578599 1.00216i
\(257\) 2401.45 + 4159.43i 0.582873 + 1.00957i 0.995137 + 0.0985008i \(0.0314047\pi\)
−0.412264 + 0.911064i \(0.635262\pi\)
\(258\) 0 0
\(259\) −66.2967 + 27.1177i −0.0159053 + 0.00650584i
\(260\) 5888.08i 1.40447i
\(261\) 0 0
\(262\) 5264.85i 1.24146i
\(263\) −2334.00 1347.54i −0.547227 0.315941i 0.200776 0.979637i \(-0.435654\pi\)
−0.748003 + 0.663696i \(0.768987\pi\)
\(264\) 0 0
\(265\) −602.862 + 348.062i −0.139749 + 0.0806842i
\(266\) −401.626 + 2949.67i −0.0925762 + 0.679910i
\(267\) 0 0
\(268\) −1061.04 + 1837.78i −0.241841 + 0.418881i
\(269\) 4182.34 0.947961 0.473981 0.880535i \(-0.342817\pi\)
0.473981 + 0.880535i \(0.342817\pi\)
\(270\) 0 0
\(271\) 654.173i 0.146635i −0.997309 0.0733176i \(-0.976641\pi\)
0.997309 0.0733176i \(-0.0233587\pi\)
\(272\) 889.325 1540.36i 0.198247 0.343374i
\(273\) 0 0
\(274\) 2175.69 + 3768.40i 0.479701 + 0.830867i
\(275\) −446.105 + 257.559i −0.0978223 + 0.0564777i
\(276\) 0 0
\(277\) 1828.75 3167.49i 0.396675 0.687061i −0.596638 0.802510i \(-0.703497\pi\)
0.993313 + 0.115449i \(0.0368306\pi\)
\(278\) −5144.57 −1.10989
\(279\) 0 0
\(280\) 377.989 488.115i 0.0806756 0.104180i
\(281\) −2453.28 1416.40i −0.520819 0.300695i 0.216450 0.976294i \(-0.430552\pi\)
−0.737270 + 0.675598i \(0.763885\pi\)
\(282\) 0 0
\(283\) 7878.39 4548.59i 1.65485 0.955426i 0.679808 0.733390i \(-0.262063\pi\)
0.975039 0.222035i \(-0.0712701\pi\)
\(284\) −19.2393 + 11.1078i −0.00401986 + 0.00232087i
\(285\) 0 0
\(286\) −11218.9 6477.21i −2.31953 1.33918i
\(287\) −4941.54 3826.66i −1.01634 0.787040i
\(288\) 0 0
\(289\) −4254.65 −0.865998
\(290\) 742.116 1285.38i 0.150271 0.260277i
\(291\) 0 0
\(292\) 3188.63 1840.95i 0.639042 0.368951i
\(293\) 1538.44 + 2664.66i 0.306747 + 0.531301i 0.977649 0.210245i \(-0.0674261\pi\)
−0.670902 + 0.741546i \(0.734093\pi\)
\(294\) 0 0
\(295\) 3286.91 5693.09i 0.648716 1.12361i
\(296\) 11.0631i 0.00217239i
\(297\) 0 0
\(298\) 2392.22 0.465025
\(299\) 5844.44 10122.9i 1.13041 1.95793i
\(300\) 0 0
\(301\) 1036.19 7610.15i 0.198423 1.45728i
\(302\) −9820.76 + 5670.02i −1.87126 + 1.08037i
\(303\) 0 0
\(304\) 2469.55 + 1425.80i 0.465917 + 0.268997i
\(305\) 7692.30i 1.44413i
\(306\) 0 0
\(307\) 3006.74i 0.558970i 0.960150 + 0.279485i \(0.0901637\pi\)
−0.960150 + 0.279485i \(0.909836\pi\)
\(308\) 2430.22 + 5941.32i 0.449592 + 1.09915i
\(309\) 0 0
\(310\) 3903.97 + 6761.87i 0.715260 + 1.23887i
\(311\) −2232.53 3866.86i −0.407059 0.705046i 0.587500 0.809224i \(-0.300112\pi\)
−0.994559 + 0.104178i \(0.966779\pi\)
\(312\) 0 0
\(313\) 6007.81 + 3468.61i 1.08492 + 0.626382i 0.932221 0.361890i \(-0.117869\pi\)
0.152704 + 0.988272i \(0.451202\pi\)
\(314\) −5249.29 −0.943423
\(315\) 0 0
\(316\) −1404.79 −0.250081
\(317\) 4933.94 + 2848.61i 0.874189 + 0.504713i 0.868738 0.495272i \(-0.164932\pi\)
0.00545096 + 0.999985i \(0.498265\pi\)
\(318\) 0 0
\(319\) −777.226 1346.20i −0.136415 0.236277i
\(320\) 2414.59 + 4182.19i 0.421811 + 0.730599i
\(321\) 0 0
\(322\) −11261.8 + 4606.48i −1.94905 + 0.797233i
\(323\) 1055.49i 0.181824i
\(324\) 0 0
\(325\) 750.927i 0.128166i
\(326\) 3297.70 + 1903.93i 0.560254 + 0.323463i
\(327\) 0 0
\(328\) −835.988 + 482.658i −0.140731 + 0.0812510i
\(329\) −371.727 + 2730.09i −0.0622917 + 0.457491i
\(330\) 0 0
\(331\) −3928.31 + 6804.03i −0.652325 + 1.12986i 0.330233 + 0.943900i \(0.392873\pi\)
−0.982557 + 0.185960i \(0.940461\pi\)
\(332\) 3143.33 0.519617
\(333\) 0 0
\(334\) 11108.5i 1.81986i
\(335\) −1701.27 + 2946.69i −0.277464 + 0.480581i
\(336\) 0 0
\(337\) 2447.80 + 4239.71i 0.395668 + 0.685317i 0.993186 0.116538i \(-0.0371798\pi\)
−0.597518 + 0.801855i \(0.703846\pi\)
\(338\) 8920.13 5150.04i 1.43548 0.828773i
\(339\) 0 0
\(340\) −1086.58 + 1882.01i −0.173318 + 0.300196i
\(341\) 8177.34 1.29861
\(342\) 0 0
\(343\) 2508.71 5836.09i 0.394921 0.918715i
\(344\) −1027.32 593.121i −0.161015 0.0929621i
\(345\) 0 0
\(346\) −13474.2 + 7779.33i −2.09358 + 1.20873i
\(347\) −1816.16 + 1048.56i −0.280969 + 0.162218i −0.633862 0.773446i \(-0.718531\pi\)
0.352893 + 0.935664i \(0.385198\pi\)
\(348\) 0 0
\(349\) 7325.59 + 4229.43i 1.12358 + 0.648700i 0.942313 0.334734i \(-0.108647\pi\)
0.181268 + 0.983434i \(0.441980\pi\)
\(350\) −478.593 + 618.030i −0.0730911 + 0.0943860i
\(351\) 0 0
\(352\) 11826.0 1.79070
\(353\) −316.445 + 548.099i −0.0477129 + 0.0826412i −0.888896 0.458110i \(-0.848527\pi\)
0.841183 + 0.540751i \(0.181860\pi\)
\(354\) 0 0
\(355\) −30.8482 + 17.8102i −0.00461197 + 0.00266272i
\(356\) −3359.93 5819.58i −0.500214 0.866396i
\(357\) 0 0
\(358\) 4817.18 8343.60i 0.711162 1.23177i
\(359\) 7038.13i 1.03470i −0.855773 0.517351i \(-0.826918\pi\)
0.855773 0.517351i \(-0.173082\pi\)
\(360\) 0 0
\(361\) 5166.80 0.753288
\(362\) −4919.24 + 8520.38i −0.714225 + 1.23707i
\(363\) 0 0
\(364\) −9272.12 1262.49i −1.33514 0.181792i
\(365\) 5112.64 2951.78i 0.733172 0.423297i
\(366\) 0 0
\(367\) −591.654 341.591i −0.0841528 0.0485856i 0.457333 0.889295i \(-0.348805\pi\)
−0.541486 + 0.840710i \(0.682138\pi\)
\(368\) 11655.4i 1.65103i
\(369\) 0 0
\(370\) 176.109i 0.0247445i
\(371\) 418.842 + 1023.97i 0.0586124 + 0.143294i
\(372\) 0 0
\(373\) −4524.00 7835.79i −0.627999 1.08773i −0.987953 0.154756i \(-0.950541\pi\)
0.359954 0.932970i \(-0.382792\pi\)
\(374\) 2390.60 + 4140.64i 0.330521 + 0.572480i
\(375\) 0 0
\(376\) 368.543 + 212.778i 0.0505482 + 0.0291840i
\(377\) 2266.05 0.309569
\(378\) 0 0
\(379\) 6790.65 0.920349 0.460175 0.887828i \(-0.347787\pi\)
0.460175 + 0.887828i \(0.347787\pi\)
\(380\) −3017.31 1742.04i −0.407328 0.235171i
\(381\) 0 0
\(382\) 900.857 + 1560.33i 0.120659 + 0.208988i
\(383\) 1170.59 + 2027.53i 0.156174 + 0.270501i 0.933486 0.358614i \(-0.116751\pi\)
−0.777312 + 0.629115i \(0.783417\pi\)
\(384\) 0 0
\(385\) 3896.60 + 9526.31i 0.515816 + 1.26105i
\(386\) 10011.9i 1.32019i
\(387\) 0 0
\(388\) 7917.29i 1.03593i
\(389\) −1522.53 879.032i −0.198445 0.114572i 0.397485 0.917609i \(-0.369883\pi\)
−0.595930 + 0.803036i \(0.703216\pi\)
\(390\) 0 0
\(391\) −3736.13 + 2157.06i −0.483234 + 0.278995i
\(392\) −687.603 699.889i −0.0885948 0.0901779i
\(393\) 0 0
\(394\) 7355.58 12740.2i 0.940530 1.62904i
\(395\) −2252.44 −0.286918
\(396\) 0 0
\(397\) 1120.19i 0.141614i 0.997490 + 0.0708071i \(0.0225575\pi\)
−0.997490 + 0.0708071i \(0.977443\pi\)
\(398\) −1873.50 + 3245.00i −0.235955 + 0.408686i
\(399\) 0 0
\(400\) 374.386 + 648.456i 0.0467983 + 0.0810571i
\(401\) 1528.43 882.440i 0.190340 0.109893i −0.401802 0.915727i \(-0.631616\pi\)
0.592142 + 0.805834i \(0.298283\pi\)
\(402\) 0 0
\(403\) −5960.37 + 10323.7i −0.736743 + 1.27608i
\(404\) 2453.64 0.302162
\(405\) 0 0
\(406\) −1865.01 1444.24i −0.227977 0.176542i
\(407\) −159.730 92.2202i −0.0194534 0.0112314i
\(408\) 0 0
\(409\) 5868.28 3388.05i 0.709456 0.409605i −0.101403 0.994845i \(-0.532333\pi\)
0.810860 + 0.585241i \(0.199000\pi\)
\(410\) 13307.7 7683.22i 1.60298 0.925481i
\(411\) 0 0
\(412\) −1334.82 770.659i −0.159616 0.0921545i
\(413\) −8260.31 6396.67i −0.984173 0.762129i
\(414\) 0 0
\(415\) 5040.01 0.596155
\(416\) −8619.81 + 14930.0i −1.01592 + 1.75962i
\(417\) 0 0
\(418\) −6638.42 + 3832.69i −0.776784 + 0.448477i
\(419\) 5353.56 + 9272.64i 0.624197 + 1.08114i 0.988696 + 0.149937i \(0.0479071\pi\)
−0.364498 + 0.931204i \(0.618760\pi\)
\(420\) 0 0
\(421\) 1424.86 2467.93i 0.164949 0.285700i −0.771688 0.636001i \(-0.780587\pi\)
0.936637 + 0.350301i \(0.113921\pi\)
\(422\) 15771.8i 1.81933i
\(423\) 0 0
\(424\) 170.873 0.0195715
\(425\) −138.575 + 240.020i −0.0158162 + 0.0273945i
\(426\) 0 0
\(427\) −12113.3 1649.34i −1.37284 0.186925i
\(428\) −2512.99 + 1450.87i −0.283808 + 0.163857i
\(429\) 0 0
\(430\) 16353.4 + 9441.65i 1.83403 + 1.05888i
\(431\) 10469.5i 1.17007i 0.811010 + 0.585033i \(0.198918\pi\)
−0.811010 + 0.585033i \(0.801082\pi\)
\(432\) 0 0
\(433\) 5079.76i 0.563782i 0.959446 + 0.281891i \(0.0909617\pi\)
−0.959446 + 0.281891i \(0.909038\pi\)
\(434\) 11485.2 4697.85i 1.27029 0.519594i
\(435\) 0 0
\(436\) 6713.58 + 11628.3i 0.737436 + 1.27728i
\(437\) −3458.27 5989.90i −0.378562 0.655689i
\(438\) 0 0
\(439\) −6497.04 3751.07i −0.706349 0.407811i 0.103359 0.994644i \(-0.467041\pi\)
−0.809708 + 0.586834i \(0.800374\pi\)
\(440\) 1589.68 0.172238
\(441\) 0 0
\(442\) −6969.93 −0.750058
\(443\) −2388.50 1379.00i −0.256165 0.147897i 0.366419 0.930450i \(-0.380584\pi\)
−0.622584 + 0.782553i \(0.713917\pi\)
\(444\) 0 0
\(445\) −5387.31 9331.09i −0.573894 0.994014i
\(446\) −11435.8 19807.4i −1.21413 2.10293i
\(447\) 0 0
\(448\) 7103.54 2905.60i 0.749131 0.306421i
\(449\) 8061.59i 0.847327i −0.905820 0.423663i \(-0.860744\pi\)
0.905820 0.423663i \(-0.139256\pi\)
\(450\) 0 0
\(451\) 16093.4i 1.68029i
\(452\) −8007.22 4622.97i −0.833248 0.481076i
\(453\) 0 0
\(454\) 20563.3 11872.2i 2.12573 1.22729i
\(455\) −14866.9 2024.27i −1.53180 0.208570i
\(456\) 0 0
\(457\) 108.316 187.608i 0.0110871 0.0192034i −0.860429 0.509571i \(-0.829804\pi\)
0.871516 + 0.490368i \(0.163137\pi\)
\(458\) 3674.14 0.374850
\(459\) 0 0
\(460\) 14240.6i 1.44341i
\(461\) −594.431 + 1029.59i −0.0600552 + 0.104019i −0.894490 0.447088i \(-0.852461\pi\)
0.834435 + 0.551107i \(0.185794\pi\)
\(462\) 0 0
\(463\) 2397.17 + 4152.02i 0.240617 + 0.416761i 0.960890 0.276929i \(-0.0893168\pi\)
−0.720273 + 0.693691i \(0.755983\pi\)
\(464\) −1956.82 + 1129.77i −0.195783 + 0.113035i
\(465\) 0 0
\(466\) −6475.88 + 11216.5i −0.643754 + 1.11501i
\(467\) −2953.79 −0.292687 −0.146344 0.989234i \(-0.546751\pi\)
−0.146344 + 0.989234i \(0.546751\pi\)
\(468\) 0 0
\(469\) 4275.46 + 3310.85i 0.420943 + 0.325972i
\(470\) −5866.67 3387.13i −0.575765 0.332418i
\(471\) 0 0
\(472\) −1397.44 + 806.814i −0.136277 + 0.0786793i
\(473\) 17127.1 9888.34i 1.66492 0.961240i
\(474\) 0 0
\(475\) −384.808 222.169i −0.0371710 0.0214607i
\(476\) 2730.68 + 2114.60i 0.262942 + 0.203619i
\(477\) 0 0
\(478\) −9988.44 −0.955775
\(479\) −54.6189 + 94.6028i −0.00521003 + 0.00902403i −0.868619 0.495481i \(-0.834992\pi\)
0.863409 + 0.504505i \(0.168325\pi\)
\(480\) 0 0
\(481\) 232.851 134.437i 0.0220730 0.0127438i
\(482\) −4062.39 7036.27i −0.383894 0.664924i
\(483\) 0 0
\(484\) −3427.71 + 5936.96i −0.321911 + 0.557566i
\(485\) 12694.6i 1.18852i
\(486\) 0 0
\(487\) −3614.94 −0.336363 −0.168182 0.985756i \(-0.553789\pi\)
−0.168182 + 0.985756i \(0.553789\pi\)
\(488\) −944.088 + 1635.21i −0.0875755 + 0.151685i
\(489\) 0 0
\(490\) 10945.7 + 11141.2i 1.00913 + 1.02716i
\(491\) −16280.5 + 9399.53i −1.49639 + 0.863940i −0.999991 0.00415517i \(-0.998677\pi\)
−0.496397 + 0.868096i \(0.665344\pi\)
\(492\) 0 0
\(493\) −724.300 418.175i −0.0661680 0.0382021i
\(494\) 11174.4i 1.01774i
\(495\) 0 0
\(496\) 11886.5i 1.07605i
\(497\) 21.4320 + 52.3963i 0.00193431 + 0.00472896i
\(498\) 0 0
\(499\) −1620.89 2807.46i −0.145413 0.251862i 0.784114 0.620617i \(-0.213118\pi\)
−0.929527 + 0.368755i \(0.879784\pi\)
\(500\) 4836.08 + 8376.34i 0.432552 + 0.749203i
\(501\) 0 0
\(502\) −15967.9 9219.06i −1.41968 0.819655i
\(503\) 4737.83 0.419979 0.209989 0.977704i \(-0.432657\pi\)
0.209989 + 0.977704i \(0.432657\pi\)
\(504\) 0 0
\(505\) 3934.16 0.346669
\(506\) −27133.3 15665.4i −2.38384 1.37631i
\(507\) 0 0
\(508\) −6670.37 11553.4i −0.582579 1.00906i
\(509\) 1272.38 + 2203.83i 0.110800 + 0.191912i 0.916093 0.400965i \(-0.131325\pi\)
−0.805293 + 0.592877i \(0.797992\pi\)
\(510\) 0 0
\(511\) −3552.03 8683.92i −0.307500 0.751769i
\(512\) 15603.9i 1.34687i
\(513\) 0 0
\(514\) 18766.9i 1.61046i
\(515\) −2140.25 1235.67i −0.183127 0.105729i
\(516\) 0 0
\(517\) −6144.23 + 3547.37i −0.522675 + 0.301767i
\(518\) −277.323 37.7602i −0.0235229 0.00320287i
\(519\) 0 0
\(520\) −1158.70 + 2006.93i −0.0977160 + 0.169249i
\(521\) −7623.86 −0.641089 −0.320545 0.947233i \(-0.603866\pi\)
−0.320545 + 0.947233i \(0.603866\pi\)
\(522\) 0 0
\(523\) 20941.4i 1.75087i −0.483335 0.875435i \(-0.660575\pi\)
0.483335 0.875435i \(-0.339425\pi\)
\(524\) 4896.40 8480.81i 0.408206 0.707034i
\(525\) 0 0
\(526\) −5265.39 9119.92i −0.436467 0.755984i
\(527\) 3810.24 2199.84i 0.314946 0.181834i
\(528\) 0 0
\(529\) 8051.53 13945.7i 0.661752 1.14619i
\(530\) −2720.05 −0.222927
\(531\) 0 0
\(532\) −3390.20 + 4377.93i −0.276286 + 0.356780i
\(533\) 20317.5 + 11730.3i 1.65113 + 0.953279i
\(534\) 0 0
\(535\) −4029.32 + 2326.33i −0.325612 + 0.187992i
\(536\) 723.302 417.599i 0.0582871 0.0336521i
\(537\) 0 0
\(538\) 14152.7 + 8171.07i 1.13414 + 0.654796i
\(539\) 15836.8 4093.52i 1.26557 0.327125i
\(540\) 0 0
\(541\) −6660.29 −0.529294 −0.264647 0.964345i \(-0.585255\pi\)
−0.264647 + 0.964345i \(0.585255\pi\)
\(542\) 1278.06 2213.67i 0.101287 0.175434i
\(543\) 0 0
\(544\) 5510.33 3181.39i 0.434289 0.250737i
\(545\) 10764.5 + 18644.7i 0.846059 + 1.46542i
\(546\) 0 0
\(547\) −10779.8 + 18671.2i −0.842616 + 1.45945i 0.0450599 + 0.998984i \(0.485652\pi\)
−0.887676 + 0.460469i \(0.847681\pi\)
\(548\) 8093.71i 0.630924i
\(549\) 0 0
\(550\) −2012.78 −0.156046
\(551\) 670.432 1161.22i 0.0518355 0.0897818i
\(552\) 0 0
\(553\) −482.954 + 3546.98i −0.0371380 + 0.272754i
\(554\) 12376.7 7145.70i 0.949163 0.547999i
\(555\) 0 0
\(556\) −8287.06 4784.54i −0.632103 0.364945i
\(557\) 15772.0i 1.19979i 0.800079 + 0.599895i \(0.204791\pi\)
−0.800079 + 0.599895i \(0.795209\pi\)
\(558\) 0 0
\(559\) 28830.0i 2.18136i
\(560\) 13847.4 5664.09i 1.04493 0.427413i
\(561\) 0 0
\(562\) −5534.47 9585.99i −0.415405 0.719503i
\(563\) 5842.23 + 10119.0i 0.437337 + 0.757489i 0.997483 0.0709043i \(-0.0225885\pi\)
−0.560146 + 0.828394i \(0.689255\pi\)
\(564\) 0 0
\(565\) −12838.8 7412.46i −0.955984 0.551937i
\(566\) 35546.5 2.63981
\(567\) 0 0
\(568\) 8.74349 0.000645896
\(569\) 5808.93 + 3353.79i 0.427984 + 0.247097i 0.698488 0.715622i \(-0.253857\pi\)
−0.270503 + 0.962719i \(0.587190\pi\)
\(570\) 0 0
\(571\) 9286.00 + 16083.8i 0.680573 + 1.17879i 0.974806 + 0.223053i \(0.0716022\pi\)
−0.294234 + 0.955733i \(0.595064\pi\)
\(572\) −12047.8 20867.5i −0.880674 1.52537i
\(573\) 0 0
\(574\) −9245.63 22603.5i −0.672308 1.64364i
\(575\) 1816.15i 0.131719i
\(576\) 0 0
\(577\) 8147.17i 0.587818i 0.955833 + 0.293909i \(0.0949563\pi\)
−0.955833 + 0.293909i \(0.905044\pi\)
\(578\) −14397.4 8312.35i −1.03608 0.598181i
\(579\) 0 0
\(580\) 2390.86 1380.36i 0.171164 0.0988213i
\(581\) 1080.65 7936.65i 0.0771650 0.566726i
\(582\) 0 0
\(583\) −1424.37 + 2467.08i −0.101186 + 0.175259i
\(584\) −1449.11 −0.102679
\(585\) 0 0
\(586\) 12022.7i 0.847531i
\(587\) 2070.04 3585.42i 0.145553 0.252106i −0.784026 0.620728i \(-0.786837\pi\)
0.929579 + 0.368622i \(0.120170\pi\)
\(588\) 0 0
\(589\) 3526.87 + 6108.72i 0.246727 + 0.427343i
\(590\) 22245.3 12843.3i 1.55224 0.896189i
\(591\) 0 0
\(592\) −134.051 + 232.183i −0.00930652 + 0.0161194i
\(593\) −14381.9 −0.995945 −0.497973 0.867193i \(-0.665922\pi\)
−0.497973 + 0.867193i \(0.665922\pi\)
\(594\) 0 0
\(595\) 4378.37 + 3390.54i 0.301673 + 0.233611i
\(596\) 3853.47 + 2224.80i 0.264840 + 0.152905i
\(597\) 0 0
\(598\) 39554.3 22836.7i 2.70484 1.56164i
\(599\) −12019.7 + 6939.59i −0.819887 + 0.473362i −0.850378 0.526173i \(-0.823626\pi\)
0.0304902 + 0.999535i \(0.490293\pi\)
\(600\) 0 0
\(601\) 12474.7 + 7202.28i 0.846680 + 0.488831i 0.859529 0.511087i \(-0.170757\pi\)
−0.0128495 + 0.999917i \(0.504090\pi\)
\(602\) 18374.4 23727.8i 1.24400 1.60643i
\(603\) 0 0
\(604\) −21092.9 −1.42095
\(605\) −5495.98 + 9519.31i −0.369328 + 0.639694i
\(606\) 0 0
\(607\) −17223.6 + 9944.08i −1.15171 + 0.664938i −0.949303 0.314364i \(-0.898209\pi\)
−0.202404 + 0.979302i \(0.564876\pi\)
\(608\) 5100.51 + 8834.35i 0.340219 + 0.589277i
\(609\) 0 0
\(610\) 15028.5 26030.2i 0.997520 1.72776i
\(611\) 10342.6i 0.684804i
\(612\) 0 0
\(613\) 8096.44 0.533462 0.266731 0.963771i \(-0.414057\pi\)
0.266731 + 0.963771i \(0.414057\pi\)
\(614\) −5874.30 + 10174.6i −0.386103 + 0.668751i
\(615\) 0 0
\(616\) 340.849 2503.31i 0.0222942 0.163736i
\(617\) 8145.01 4702.53i 0.531452 0.306834i −0.210155 0.977668i \(-0.567397\pi\)
0.741608 + 0.670834i \(0.234064\pi\)
\(618\) 0 0
\(619\) 467.098 + 269.679i 0.0303300 + 0.0175110i 0.515088 0.857137i \(-0.327759\pi\)
−0.484758 + 0.874648i \(0.661092\pi\)
\(620\) 14523.0i 0.940740i
\(621\) 0 0
\(622\) 17446.9i 1.12469i
\(623\) −15849.1 + 6482.83i −1.01923 + 0.416901i
\(624\) 0 0
\(625\) 8429.26 + 14599.9i 0.539473 + 0.934394i
\(626\) 13553.3 + 23475.0i 0.865335 + 1.49880i
\(627\) 0 0
\(628\) −8455.76 4881.93i −0.537295 0.310208i
\(629\) −99.2353 −0.00629057
\(630\) 0 0
\(631\) −14096.7 −0.889349 −0.444675 0.895692i \(-0.646681\pi\)
−0.444675 + 0.895692i \(0.646681\pi\)
\(632\) 478.817 + 276.445i 0.0301366 + 0.0173994i
\(633\) 0 0
\(634\) 11130.7 + 19279.0i 0.697252 + 1.20768i
\(635\) −10695.3 18524.7i −0.668391 1.15769i
\(636\) 0 0
\(637\) −6375.34 + 22977.3i −0.396547 + 1.42919i
\(638\) 6073.90i 0.376909i
\(639\) 0 0
\(640\) 4248.92i 0.262427i
\(641\) −18973.7 10954.5i −1.16914 0.675002i −0.215661 0.976468i \(-0.569191\pi\)
−0.953477 + 0.301466i \(0.902524\pi\)
\(642\) 0 0
\(643\) −14525.7 + 8386.40i −0.890881 + 0.514350i −0.874231 0.485511i \(-0.838634\pi\)
−0.0166504 + 0.999861i \(0.505300\pi\)
\(644\) −22425.0 3053.38i −1.37216 0.186832i
\(645\) 0 0
\(646\) −2062.12 + 3571.70i −0.125593 + 0.217534i
\(647\) −7088.41 −0.430717 −0.215359 0.976535i \(-0.569092\pi\)
−0.215359 + 0.976535i \(0.569092\pi\)
\(648\) 0 0
\(649\) 26901.9i 1.62711i
\(650\) 1467.09 2541.08i 0.0885295 0.153338i
\(651\) 0 0
\(652\) 3541.37 + 6133.84i 0.212716 + 0.368435i
\(653\) −3166.83 + 1828.37i −0.189782 + 0.109571i −0.591881 0.806026i \(-0.701614\pi\)
0.402098 + 0.915596i \(0.368281\pi\)
\(654\) 0 0
\(655\) 7850.87 13598.1i 0.468334 0.811179i
\(656\) −23393.4 −1.39231
\(657\) 0 0
\(658\) −6591.70 + 8512.17i −0.390534 + 0.504314i
\(659\) 6740.56 + 3891.66i 0.398444 + 0.230042i 0.685813 0.727778i \(-0.259447\pi\)
−0.287368 + 0.957820i \(0.592780\pi\)
\(660\) 0 0
\(661\) 6895.85 3981.32i 0.405775 0.234274i −0.283198 0.959062i \(-0.591395\pi\)
0.688973 + 0.724787i \(0.258062\pi\)
\(662\) −26586.2 + 15349.6i −1.56088 + 0.901175i
\(663\) 0 0
\(664\) −1071.39 618.568i −0.0626175 0.0361522i
\(665\) −5435.84 + 7019.56i −0.316982 + 0.409333i
\(666\) 0 0
\(667\) 5480.53 0.318151
\(668\) −10331.1 + 17894.0i −0.598388 + 1.03644i
\(669\) 0 0
\(670\) −11513.9 + 6647.58i −0.663914 + 0.383311i
\(671\) −15739.5 27261.7i −0.905542 1.56844i
\(672\) 0 0
\(673\) −494.666 + 856.786i −0.0283328 + 0.0490738i −0.879844 0.475262i \(-0.842353\pi\)
0.851511 + 0.524336i \(0.175686\pi\)
\(674\) 19129.2i 1.09322i
\(675\) 0 0
\(676\) 19158.5 1.09004
\(677\) 11083.3 19196.9i 0.629198 1.08980i −0.358515 0.933524i \(-0.616717\pi\)
0.987713 0.156279i \(-0.0499497\pi\)
\(678\) 0 0
\(679\) 19990.5 + 2721.89i 1.12985 + 0.153839i
\(680\) 740.713 427.651i 0.0417721 0.0241171i
\(681\) 0 0
\(682\) 27671.5 + 15976.1i 1.55366 + 0.897006i
\(683\) 2458.98i 0.137760i 0.997625 + 0.0688802i \(0.0219426\pi\)
−0.997625 + 0.0688802i \(0.978057\pi\)
\(684\) 0 0
\(685\) 12977.4i 0.723858i
\(686\) 19891.3 14847.6i 1.10708 0.826361i
\(687\) 0 0
\(688\) −14373.7 24895.9i −0.796498 1.37958i
\(689\) −2076.42 3596.46i −0.114812 0.198859i
\(690\) 0 0
\(691\) −21148.3 12210.0i −1.16428 0.672200i −0.211958 0.977279i \(-0.567984\pi\)
−0.952327 + 0.305079i \(0.901317\pi\)
\(692\) −28939.6 −1.58977
\(693\) 0 0
\(694\) −8194.32 −0.448202
\(695\) −13287.4 7671.51i −0.725211 0.418701i
\(696\) 0 0
\(697\) −4329.42 7498.77i −0.235277 0.407512i
\(698\) 16526.2 + 28624.1i 0.896167 + 1.55221i
\(699\) 0 0
\(700\) −1345.71 + 550.446i −0.0726618 + 0.0297213i
\(701\) 6521.09i 0.351353i 0.984448 + 0.175676i \(0.0562112\pi\)
−0.984448 + 0.175676i \(0.943789\pi\)
\(702\) 0 0
\(703\) 159.098i 0.00853553i
\(704\) 17114.7 + 9881.18i 0.916243 + 0.528993i
\(705\) 0 0
\(706\) −2141.65 + 1236.48i −0.114167 + 0.0659145i
\(707\) 843.540 6195.24i 0.0448721 0.329556i
\(708\) 0 0
\(709\) 5031.46 8714.75i 0.266517 0.461621i −0.701443 0.712726i \(-0.747461\pi\)
0.967960 + 0.251105i \(0.0807939\pi\)
\(710\) −139.184 −0.00735701
\(711\) 0 0
\(712\) 2644.77i 0.139209i
\(713\) −14415.4 + 24968.2i −0.757169 + 1.31145i
\(714\) 0 0
\(715\) −19317.5 33458.9i −1.01040 1.75006i
\(716\) 15519.4 8960.12i 0.810037 0.467675i
\(717\) 0 0
\(718\) 13750.5 23816.5i 0.714711 1.23792i
\(719\) 3449.87 0.178941 0.0894704 0.995989i \(-0.471483\pi\)
0.0894704 + 0.995989i \(0.471483\pi\)
\(720\) 0 0
\(721\) −2404.75 + 3105.36i −0.124213 + 0.160402i
\(722\) 17484.1 + 10094.4i 0.901232 + 0.520327i
\(723\) 0 0
\(724\) −15848.2 + 9149.96i −0.813527 + 0.469690i
\(725\) 304.914 176.042i 0.0156196 0.00901800i
\(726\) 0 0
\(727\) 18318.1 + 10575.9i 0.934497 + 0.539532i 0.888231 0.459397i \(-0.151935\pi\)
0.0462657 + 0.998929i \(0.485268\pi\)
\(728\) 2911.92 + 2254.95i 0.148246 + 0.114799i
\(729\) 0 0
\(730\) 23067.7 1.16955
\(731\) 5320.27 9214.98i 0.269189 0.466249i
\(732\) 0 0
\(733\) 8853.40 5111.51i 0.446122 0.257569i −0.260069 0.965590i \(-0.583745\pi\)
0.706191 + 0.708021i \(0.250412\pi\)
\(734\) −1334.74 2311.84i −0.0671202 0.116256i
\(735\) 0 0
\(736\) −20847.4 + 36108.7i −1.04408 + 1.80840i
\(737\) 13924.2i 0.695934i
\(738\) 0 0
\(739\) −38602.2 −1.92152 −0.960761 0.277378i \(-0.910534\pi\)
−0.960761 + 0.277378i \(0.910534\pi\)
\(740\) 163.784 283.682i 0.00813624 0.0140924i
\(741\) 0 0
\(742\) −583.218 + 4283.35i −0.0288552 + 0.211923i
\(743\) −12936.5 + 7468.90i −0.638755 + 0.368785i −0.784135 0.620591i \(-0.786893\pi\)
0.145380 + 0.989376i \(0.453560\pi\)
\(744\) 0 0
\(745\) 6178.65 + 3567.25i 0.303850 + 0.175428i
\(746\) 35354.3i 1.73514i
\(747\) 0 0
\(748\) 8893.20i 0.434716i
\(749\) 2799.39 + 6843.88i 0.136565 + 0.333872i
\(750\) 0 0
\(751\) 12330.2 + 21356.5i 0.599113 + 1.03769i 0.992952 + 0.118515i \(0.0378135\pi\)
−0.393839 + 0.919180i \(0.628853\pi\)
\(752\) 5156.45 + 8931.23i 0.250048 + 0.433097i
\(753\) 0 0
\(754\) 7668.13 + 4427.20i 0.370367 + 0.213832i
\(755\) −33820.2 −1.63026
\(756\) 0 0
\(757\) 31078.1 1.49214 0.746071 0.665867i \(-0.231938\pi\)
0.746071 + 0.665867i \(0.231938\pi\)
\(758\) 22979.1 + 13267.0i 1.10110 + 0.635723i
\(759\) 0 0
\(760\) 685.625 + 1187.54i 0.0327240 + 0.0566796i
\(761\) −1863.73 3228.07i −0.0887780 0.153768i 0.818217 0.574910i \(-0.194963\pi\)
−0.906995 + 0.421142i \(0.861630\pi\)
\(762\) 0 0
\(763\) 31668.4 12953.5i 1.50259 0.614612i
\(764\) 3351.25i 0.158696i
\(765\) 0 0
\(766\) 9148.01i 0.431503i
\(767\) 33962.9 + 19608.5i 1.59887 + 0.923106i
\(768\) 0 0
\(769\) −5266.10 + 3040.38i −0.246944 + 0.142573i −0.618364 0.785892i \(-0.712204\pi\)
0.371420 + 0.928465i \(0.378871\pi\)
\(770\) −5425.83 + 39849.1i −0.253940 + 1.86502i
\(771\) 0 0
\(772\) −9311.23 + 16127.5i −0.434091 + 0.751868i
\(773\) 34364.4 1.59897 0.799483 0.600688i \(-0.205107\pi\)
0.799483 + 0.600688i \(0.205107\pi\)
\(774\) 0 0
\(775\) 1852.17i 0.0858478i
\(776\) 1558.02 2698.58i 0.0720745 0.124837i
\(777\) 0 0
\(778\) −3434.75 5949.16i −0.158280 0.274149i
\(779\) 12022.3 6941.07i 0.552944 0.319242i
\(780\) 0 0
\(781\) −72.8844 + 126.239i −0.00333932 + 0.00578387i
\(782\) −16857.1 −0.770854
\(783\) 0 0
\(784\) −5950.32 23020.4i −0.271061 1.04867i
\(785\) −13557.9 7827.68i −0.616438 0.355900i
\(786\) 0 0
\(787\) 3382.03 1952.61i 0.153185 0.0884411i −0.421448 0.906852i \(-0.638478\pi\)
0.574633 + 0.818411i \(0.305145\pi\)
\(788\) 23697.3 13681.6i 1.07129 0.618512i
\(789\) 0 0
\(790\) −7622.08 4400.61i −0.343268 0.198186i
\(791\) −14425.4 + 18628.2i −0.648431 + 0.837350i
\(792\) 0 0
\(793\) 45889.5 2.05496
\(794\) −2188.53 + 3790.65i −0.0978188 + 0.169427i
\(795\) 0 0
\(796\) −6035.81 + 3484.78i −0.268761 + 0.155169i
\(797\) 2261.24 + 3916.59i 0.100499 + 0.174069i 0.911890 0.410434i \(-0.134623\pi\)
−0.811392 + 0.584503i \(0.801290\pi\)
\(798\) 0 0
\(799\) −1908.61 + 3305.81i −0.0845078 + 0.146372i
\(800\) 2678.59i 0.118378i
\(801\) 0 0
\(802\) 6896.13 0.303629
\(803\) 12079.5 20922.4i 0.530856 0.919470i
\(804\) 0 0
\(805\) −35956.2 4895.78i −1.57427 0.214352i
\(806\) −40338.9 + 23289.7i −1.76288 + 1.01780i
\(807\) 0 0
\(808\) −836.313 482.846i −0.0364126 0.0210228i
\(809\) 20951.2i 0.910513i −0.890360 0.455256i \(-0.849548\pi\)
0.890360 0.455256i \(-0.150452\pi\)
\(810\) 0 0
\(811\) 22578.2i 0.977592i −0.872398 0.488796i \(-0.837436\pi\)
0.872398 0.488796i \(-0.162564\pi\)
\(812\) −1661.06 4060.92i −0.0717880 0.175505i
\(813\) 0 0
\(814\) −360.343 624.133i −0.0155160 0.0268745i
\(815\) 5678.23 + 9834.98i 0.244049 + 0.422705i
\(816\) 0 0
\(817\) 14773.8 + 8529.64i 0.632643 + 0.365256i
\(818\) 26477.1 1.13172
\(819\) 0 0
\(820\) 28582.1 1.21723
\(821\) −35093.8 20261.4i −1.49182 0.861300i −0.491859 0.870675i \(-0.663683\pi\)
−0.999956 + 0.00937459i \(0.997016\pi\)
\(822\) 0 0
\(823\) 15823.1 + 27406.4i 0.670181 + 1.16079i 0.977853 + 0.209295i \(0.0671168\pi\)
−0.307672 + 0.951493i \(0.599550\pi\)
\(824\) 303.312 + 525.352i 0.0128233 + 0.0222105i
\(825\) 0 0
\(826\) −15455.1 37784.1i −0.651029 1.59162i
\(827\) 19924.2i 0.837766i −0.908040 0.418883i \(-0.862422\pi\)
0.908040 0.418883i \(-0.137578\pi\)
\(828\) 0 0
\(829\) 27088.6i 1.13489i 0.823410 + 0.567447i \(0.192069\pi\)
−0.823410 + 0.567447i \(0.807931\pi\)
\(830\) 17055.0 + 9846.72i 0.713239 + 0.411789i
\(831\) 0 0
\(832\) −24949.5 + 14404.6i −1.03962 + 0.600227i
\(833\) 6277.97 6167.76i 0.261127 0.256543i
\(834\) 0 0
\(835\) −16564.9 + 28691.3i −0.686529 + 1.18910i
\(836\) −14257.9 −0.589856
\(837\) 0 0
\(838\) 41837.2i 1.72463i
\(839\) −2785.92 + 4825.35i −0.114637 + 0.198557i −0.917635 0.397425i \(-0.869904\pi\)
0.802997 + 0.595982i \(0.203237\pi\)
\(840\) 0 0
\(841\) −11663.3 20201.4i −0.478218 0.828298i
\(842\) 9643.25 5567.53i 0.394689 0.227874i
\(843\) 0 0
\(844\) −14668.0 + 25405.8i −0.598216 + 1.03614i
\(845\) 30718.7 1.25060
\(846\) 0 0
\(847\) 13811.9 + 10695.7i 0.560311 + 0.433896i
\(848\) 3586.14 + 2070.46i 0.145222 + 0.0838442i
\(849\) 0 0
\(850\) −937.858 + 541.473i −0.0378450 + 0.0218498i
\(851\) 563.160 325.141i 0.0226849 0.0130972i
\(852\) 0 0
\(853\) −14771.1 8528.09i −0.592910 0.342317i 0.173337 0.984863i \(-0.444545\pi\)
−0.766247 + 0.642546i \(0.777878\pi\)
\(854\) −37768.1 29247.1i −1.51335 1.17191i
\(855\) 0 0
\(856\) 1142.05 0.0456012
\(857\) −3095.62 + 5361.77i −0.123389 + 0.213716i −0.921102 0.389321i \(-0.872710\pi\)
0.797713 + 0.603037i \(0.206043\pi\)
\(858\) 0 0
\(859\) 4145.84 2393.60i 0.164673 0.0950740i −0.415399 0.909640i \(-0.636358\pi\)
0.580072 + 0.814565i \(0.303025\pi\)
\(860\) 17561.8 + 30417.9i 0.696340 + 1.20610i
\(861\) 0 0
\(862\) −20454.4 + 35428.0i −0.808212 + 1.39986i
\(863\) 20578.3i 0.811694i −0.913941 0.405847i \(-0.866976\pi\)
0.913941 0.405847i \(-0.133024\pi\)
\(864\) 0 0
\(865\) −46401.8 −1.82394
\(866\) −9924.38 + 17189.5i −0.389427 + 0.674508i
\(867\) 0 0
\(868\) 22869.8 + 3113.94i 0.894300 + 0.121767i
\(869\) −7982.69 + 4608.81i −0.311616 + 0.179911i
\(870\) 0 0
\(871\) −17578.9 10149.2i −0.683855 0.394824i
\(872\) 5284.59i 0.205228i
\(873\) 0 0
\(874\) 27025.8i 1.04595i
\(875\) 22812.2 9330.99i 0.881362 0.360509i
\(876\) 0 0
\(877\) −18325.1 31740.0i −0.705581 1.22210i −0.966482 0.256736i \(-0.917353\pi\)
0.260901 0.965366i \(-0.415980\pi\)
\(878\) −14657.0 25386.7i −0.563383 0.975808i
\(879\) 0 0
\(880\) 33362.9 + 19262.1i 1.27803 + 0.737868i
\(881\) 13272.5 0.507561 0.253780 0.967262i \(-0.418326\pi\)
0.253780 + 0.967262i \(0.418326\pi\)
\(882\) 0 0
\(883\) 7209.05 0.274750 0.137375 0.990519i \(-0.456134\pi\)
0.137375 + 0.990519i \(0.456134\pi\)
\(884\) −11227.4 6482.15i −0.427171 0.246627i
\(885\) 0 0
\(886\) −5388.34 9332.88i −0.204317 0.353888i
\(887\) 12074.4 + 20913.5i 0.457068 + 0.791666i 0.998805 0.0488828i \(-0.0155661\pi\)
−0.541736 + 0.840549i \(0.682233\pi\)
\(888\) 0 0
\(889\) −31464.7 + 12870.2i −1.18705 + 0.485547i
\(890\) 42101.0i 1.58565i
\(891\) 0 0
\(892\) 42542.0i 1.59688i
\(893\) −5299.99 3059.95i −0.198608 0.114667i
\(894\) 0 0
\(895\) 24883.8 14366.6i 0.929354 0.536563i
\(896\) −6690.90 911.028i −0.249472 0.0339680i
\(897\) 0 0
\(898\) 15750.0 27279.8i 0.585283 1.01374i
\(899\) −5589.24 −0.207354
\(900\) 0 0
\(901\) 1532.72i 0.0566730i
\(902\) 31441.9 54459.0i 1.16065 2.01030i
\(903\) 0 0
\(904\) 1819.48 + 3151.44i 0.0669416 + 0.115946i
\(905\) −25411.0 + 14671.0i −0.933358 + 0.538874i
\(906\) 0 0
\(907\) 14615.6 25315.0i 0.535064 0.926758i −0.464096 0.885785i \(-0.653621\pi\)
0.999160 0.0409733i \(-0.0130459\pi\)
\(908\) 44165.4 1.61419
\(909\) 0 0
\(910\) −46353.6 35895.6i −1.68858 1.30761i
\(911\) 29195.6 + 16856.1i 1.06179 + 0.613027i 0.925928 0.377700i \(-0.123285\pi\)
0.135866 + 0.990727i \(0.456618\pi\)
\(912\) 0 0
\(913\) 17861.9 10312.6i 0.647473 0.373819i
\(914\) 733.065 423.235i 0.0265291 0.0153166i
\(915\) 0 0
\(916\) 5918.43 + 3417.01i 0.213483 + 0.123255i
\(917\) −19730.0 15278.6i −0.710515 0.550212i
\(918\) 0 0
\(919\) 12924.3 0.463912 0.231956 0.972726i \(-0.425488\pi\)
0.231956 + 0.972726i \(0.425488\pi\)
\(920\) −2802.36 + 4853.83i −0.100425 + 0.173941i
\(921\) 0 0
\(922\) −4023.02 + 2322.69i −0.143700 + 0.0829651i
\(923\) −106.249 184.029i −0.00378899 0.00656273i
\(924\) 0 0
\(925\) 20.8879 36.1790i 0.000742477 0.00128601i
\(926\) 18733.5i 0.664817i
\(927\) 0 0
\(928\) −8083.09 −0.285927
\(929\) 14691.7 25446.8i 0.518859 0.898690i −0.480901 0.876775i \(-0.659690\pi\)
0.999760 0.0219154i \(-0.00697643\pi\)
\(930\) 0 0
\(931\) 9888.38 + 10065.1i 0.348097 + 0.354317i
\(932\) −20863.2 + 12045.4i −0.733257 + 0.423346i
\(933\) 0 0
\(934\) −9995.40 5770.85i −0.350171 0.202171i
\(935\) 14259.3i 0.498749i
\(936\) 0 0
\(937\) 42385.1i 1.47776i −0.673837 0.738880i \(-0.735355\pi\)
0.673837 0.738880i \(-0.264645\pi\)
\(938\) 7999.38 + 19556.7i 0.278453 + 0.680755i
\(939\) 0 0
\(940\) −6300.17 10912.2i −0.218605 0.378635i
\(941\) −16870.2 29220.1i −0.584436 1.01227i −0.994946 0.100416i \(-0.967983\pi\)
0.410510 0.911856i \(-0.365351\pi\)
\(942\) 0 0
\(943\) 49138.8 + 28370.3i 1.69690 + 0.979708i
\(944\) −39104.5 −1.34825
\(945\) 0 0
\(946\) 77275.8 2.65587
\(947\) −26763.4 15451.8i −0.918366 0.530219i −0.0352526 0.999378i \(-0.511224\pi\)
−0.883113 + 0.469160i \(0.844557\pi\)
\(948\) 0 0
\(949\) 17609.3 + 30500.2i 0.602341 + 1.04328i
\(950\) −868.108 1503.61i −0.0296475 0.0513510i
\(951\) 0 0
\(952\) −514.615 1258.12i −0.0175197 0.0428317i
\(953\) 14796.1i 0.502931i −0.967866 0.251465i \(-0.919088\pi\)
0.967866 0.251465i \(-0.0809125\pi\)
\(954\) 0 0
\(955\) 5373.39i 0.182072i
\(956\) −16089.7 9289.42i −0.544330 0.314269i
\(957\) 0 0
\(958\) −369.653 + 213.419i −0.0124665 + 0.00719756i
\(959\) 20436.0 + 2782.55i 0.688124 + 0.0936946i
\(960\) 0 0
\(961\) −194.153 + 336.283i −0.00651716 + 0.0112881i
\(962\) 1050.60 0.0352107
\(963\) 0 0
\(964\) 15112.4i 0.504914i
\(965\) −14929.6 + 25858.8i −0.498032 + 0.862617i
\(966\) 0 0
\(967\) −9085.95 15737.3i −0.302156 0.523349i 0.674468 0.738304i \(-0.264373\pi\)
−0.976624 + 0.214955i \(0.931040\pi\)
\(968\) 2336.64 1349.06i 0.0775851 0.0447938i
\(969\) 0 0
\(970\) −24801.5 + 42957.5i −0.820957 + 1.42194i
\(971\) 36450.4 1.20468 0.602342 0.798238i \(-0.294234\pi\)
0.602342 + 0.798238i \(0.294234\pi\)
\(972\) 0 0
\(973\) −14929.6 + 19279.2i −0.491901 + 0.635215i
\(974\) −12232.7 7062.56i −0.402424 0.232340i
\(975\) 0 0
\(976\) −39627.5 + 22879.0i −1.29964 + 0.750346i
\(977\) −4369.47 + 2522.71i −0.143083 + 0.0826088i −0.569832 0.821761i \(-0.692992\pi\)
0.426750 + 0.904370i \(0.359659\pi\)
\(978\) 0 0
\(979\) −38185.5 22046.4i −1.24659 0.719720i
\(980\) 7270.12 + 28126.4i 0.236975 + 0.916800i
\(981\) 0 0
\(982\) −73455.8 −2.38704
\(983\) 24464.8 42374.3i 0.793802 1.37491i −0.129795 0.991541i \(-0.541432\pi\)
0.923597 0.383364i \(-0.125235\pi\)
\(984\) 0 0
\(985\) 37996.2 21937.1i 1.22909 0.709618i
\(986\) −1633.98 2830.14i −0.0527755 0.0914099i
\(987\) 0 0
\(988\) 10392.4 18000.2i 0.334643 0.579618i
\(989\) 69726.6i 2.24184i
\(990\) 0 0
\(991\) −41118.3 −1.31803 −0.659014 0.752131i \(-0.729026\pi\)
−0.659014 + 0.752131i \(0.729026\pi\)
\(992\) 21260.9 36825.0i 0.680478 1.17862i
\(993\) 0 0
\(994\) −29.8430 + 219.177i −0.000952276 + 0.00699383i
\(995\) −9677.80 + 5587.48i −0.308349 + 0.178025i
\(996\) 0 0
\(997\) −20713.0 11958.7i −0.657962 0.379874i 0.133538 0.991044i \(-0.457366\pi\)
−0.791500 + 0.611169i \(0.790699\pi\)
\(998\) 12667.0i 0.401770i
\(999\) 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.o.a.62.20 44
3.2 odd 2 63.4.o.a.20.4 yes 44
7.6 odd 2 inner 189.4.o.a.62.19 44
9.2 odd 6 567.4.c.c.566.10 44
9.4 even 3 63.4.o.a.41.3 yes 44
9.5 odd 6 inner 189.4.o.a.125.19 44
9.7 even 3 567.4.c.c.566.35 44
21.20 even 2 63.4.o.a.20.3 44
63.13 odd 6 63.4.o.a.41.4 yes 44
63.20 even 6 567.4.c.c.566.36 44
63.34 odd 6 567.4.c.c.566.9 44
63.41 even 6 inner 189.4.o.a.125.20 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.o.a.20.3 44 21.20 even 2
63.4.o.a.20.4 yes 44 3.2 odd 2
63.4.o.a.41.3 yes 44 9.4 even 3
63.4.o.a.41.4 yes 44 63.13 odd 6
189.4.o.a.62.19 44 7.6 odd 2 inner
189.4.o.a.62.20 44 1.1 even 1 trivial
189.4.o.a.125.19 44 9.5 odd 6 inner
189.4.o.a.125.20 44 63.41 even 6 inner
567.4.c.c.566.9 44 63.34 odd 6
567.4.c.c.566.10 44 9.2 odd 6
567.4.c.c.566.35 44 9.7 even 3
567.4.c.c.566.36 44 63.20 even 6