Properties

Label 189.4.i.a.143.4
Level $189$
Weight $4$
Character 189.143
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(143,189)]
 
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, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.143");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.i (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 143.4
Character \(\chi\) \(=\) 189.143
Dual form 189.4.i.a.152.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.10714i q^{2} -8.86861 q^{4} +(3.80591 - 6.59204i) q^{5} +(13.1152 - 13.0764i) q^{7} +3.56749i q^{8} +O(q^{10})\) \(q-4.10714i q^{2} -8.86861 q^{4} +(3.80591 - 6.59204i) q^{5} +(13.1152 - 13.0764i) q^{7} +3.56749i q^{8} +(-27.0744 - 15.6314i) q^{10} +(-6.20961 + 3.58512i) q^{11} +(59.6417 - 34.4342i) q^{13} +(-53.7066 - 53.8659i) q^{14} -56.2967 q^{16} +(11.4334 - 19.8032i) q^{17} +(-86.1218 + 49.7224i) q^{19} +(-33.7532 + 58.4622i) q^{20} +(14.7246 + 25.5037i) q^{22} +(-106.045 - 61.2248i) q^{23} +(33.5300 + 58.0757i) q^{25} +(-141.426 - 244.957i) q^{26} +(-116.313 + 115.969i) q^{28} +(-143.427 - 82.8076i) q^{29} -13.7877i q^{31} +259.758i q^{32} +(-81.3346 - 46.9585i) q^{34} +(-36.2848 - 136.223i) q^{35} +(126.544 + 219.181i) q^{37} +(204.217 + 353.714i) q^{38} +(23.5171 + 13.5776i) q^{40} +(159.598 + 276.433i) q^{41} +(156.693 - 271.399i) q^{43} +(55.0706 - 31.7950i) q^{44} +(-251.459 + 435.540i) q^{46} +70.7867 q^{47} +(1.01583 - 342.998i) q^{49} +(238.525 - 137.713i) q^{50} +(-528.939 + 305.383i) q^{52} +(254.574 + 146.979i) q^{53} +54.5786i q^{55} +(46.6500 + 46.7883i) q^{56} +(-340.103 + 589.075i) q^{58} -461.230 q^{59} -662.411i q^{61} -56.6280 q^{62} +616.491 q^{64} -524.214i q^{65} +718.278 q^{67} +(-101.398 + 175.627i) q^{68} +(-559.489 + 149.027i) q^{70} -92.9435i q^{71} +(-882.012 - 509.230i) q^{73} +(900.207 - 519.735i) q^{74} +(763.780 - 440.969i) q^{76} +(-34.5597 + 128.219i) q^{77} +796.225 q^{79} +(-214.260 + 371.110i) q^{80} +(1135.35 - 655.493i) q^{82} +(10.7079 - 18.5466i) q^{83} +(-87.0290 - 150.739i) q^{85} +(-1114.68 - 643.558i) q^{86} +(-12.7899 - 22.1527i) q^{88} +(-339.721 - 588.414i) q^{89} +(331.937 - 1231.51i) q^{91} +(940.467 + 542.979i) q^{92} -290.731i q^{94} +756.957i q^{95} +(984.068 + 568.152i) q^{97} +(-1408.74 - 4.17218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.10714i 1.45209i −0.687645 0.726047i \(-0.741356\pi\)
0.687645 0.726047i \(-0.258644\pi\)
\(3\) 0 0
\(4\) −8.86861 −1.10858
\(5\) 3.80591 6.59204i 0.340411 0.589610i −0.644098 0.764943i \(-0.722767\pi\)
0.984509 + 0.175333i \(0.0561004\pi\)
\(6\) 0 0
\(7\) 13.1152 13.0764i 0.708153 0.706059i
\(8\) 3.56749i 0.157662i
\(9\) 0 0
\(10\) −27.0744 15.6314i −0.856168 0.494309i
\(11\) −6.20961 + 3.58512i −0.170206 + 0.0982686i −0.582683 0.812699i \(-0.697997\pi\)
0.412477 + 0.910968i \(0.364664\pi\)
\(12\) 0 0
\(13\) 59.6417 34.4342i 1.27243 0.734640i 0.296988 0.954881i \(-0.404018\pi\)
0.975445 + 0.220241i \(0.0706844\pi\)
\(14\) −53.7066 53.8659i −1.02526 1.02830i
\(15\) 0 0
\(16\) −56.2967 −0.879635
\(17\) 11.4334 19.8032i 0.163118 0.282529i −0.772867 0.634568i \(-0.781178\pi\)
0.935985 + 0.352039i \(0.114512\pi\)
\(18\) 0 0
\(19\) −86.1218 + 49.7224i −1.03988 + 0.600374i −0.919799 0.392390i \(-0.871648\pi\)
−0.120079 + 0.992764i \(0.538315\pi\)
\(20\) −33.7532 + 58.4622i −0.377372 + 0.653627i
\(21\) 0 0
\(22\) 14.7246 + 25.5037i 0.142695 + 0.247155i
\(23\) −106.045 61.2248i −0.961383 0.555055i −0.0647848 0.997899i \(-0.520636\pi\)
−0.896598 + 0.442844i \(0.853969\pi\)
\(24\) 0 0
\(25\) 33.5300 + 58.0757i 0.268240 + 0.464606i
\(26\) −141.426 244.957i −1.06677 1.84769i
\(27\) 0 0
\(28\) −116.313 + 115.969i −0.785042 + 0.782720i
\(29\) −143.427 82.8076i −0.918404 0.530241i −0.0352788 0.999378i \(-0.511232\pi\)
−0.883126 + 0.469136i \(0.844565\pi\)
\(30\) 0 0
\(31\) 13.7877i 0.0798820i −0.999202 0.0399410i \(-0.987283\pi\)
0.999202 0.0399410i \(-0.0127170\pi\)
\(32\) 259.758i 1.43498i
\(33\) 0 0
\(34\) −81.3346 46.9585i −0.410258 0.236862i
\(35\) −36.2848 136.223i −0.175236 0.657884i
\(36\) 0 0
\(37\) 126.544 + 219.181i 0.562263 + 0.973868i 0.997299 + 0.0734549i \(0.0234025\pi\)
−0.435035 + 0.900413i \(0.643264\pi\)
\(38\) 204.217 + 353.714i 0.871799 + 1.51000i
\(39\) 0 0
\(40\) 23.5171 + 13.5776i 0.0929593 + 0.0536701i
\(41\) 159.598 + 276.433i 0.607929 + 1.05296i 0.991581 + 0.129486i \(0.0413328\pi\)
−0.383652 + 0.923478i \(0.625334\pi\)
\(42\) 0 0
\(43\) 156.693 271.399i 0.555707 0.962512i −0.442141 0.896945i \(-0.645781\pi\)
0.997848 0.0655670i \(-0.0208856\pi\)
\(44\) 55.0706 31.7950i 0.188686 0.108938i
\(45\) 0 0
\(46\) −251.459 + 435.540i −0.805992 + 1.39602i
\(47\) 70.7867 0.219687 0.109844 0.993949i \(-0.464965\pi\)
0.109844 + 0.993949i \(0.464965\pi\)
\(48\) 0 0
\(49\) 1.01583 342.998i 0.00296162 0.999996i
\(50\) 238.525 137.713i 0.674651 0.389510i
\(51\) 0 0
\(52\) −528.939 + 305.383i −1.41059 + 0.814404i
\(53\) 254.574 + 146.979i 0.659783 + 0.380926i 0.792194 0.610269i \(-0.208939\pi\)
−0.132412 + 0.991195i \(0.542272\pi\)
\(54\) 0 0
\(55\) 54.5786i 0.133807i
\(56\) 46.6500 + 46.7883i 0.111319 + 0.111649i
\(57\) 0 0
\(58\) −340.103 + 589.075i −0.769960 + 1.33361i
\(59\) −461.230 −1.01775 −0.508873 0.860842i \(-0.669938\pi\)
−0.508873 + 0.860842i \(0.669938\pi\)
\(60\) 0 0
\(61\) 662.411i 1.39038i −0.718827 0.695189i \(-0.755321\pi\)
0.718827 0.695189i \(-0.244679\pi\)
\(62\) −56.6280 −0.115996
\(63\) 0 0
\(64\) 616.491 1.20408
\(65\) 524.214i 1.00032i
\(66\) 0 0
\(67\) 718.278 1.30973 0.654863 0.755748i \(-0.272726\pi\)
0.654863 + 0.755748i \(0.272726\pi\)
\(68\) −101.398 + 175.627i −0.180829 + 0.313204i
\(69\) 0 0
\(70\) −559.489 + 149.027i −0.955310 + 0.254459i
\(71\) 92.9435i 0.155357i −0.996978 0.0776787i \(-0.975249\pi\)
0.996978 0.0776787i \(-0.0247508\pi\)
\(72\) 0 0
\(73\) −882.012 509.230i −1.41413 0.816450i −0.418358 0.908282i \(-0.637394\pi\)
−0.995774 + 0.0918323i \(0.970728\pi\)
\(74\) 900.207 519.735i 1.41415 0.816459i
\(75\) 0 0
\(76\) 763.780 440.969i 1.15278 0.665560i
\(77\) −34.5597 + 128.219i −0.0511486 + 0.189765i
\(78\) 0 0
\(79\) 796.225 1.13395 0.566977 0.823734i \(-0.308113\pi\)
0.566977 + 0.823734i \(0.308113\pi\)
\(80\) −214.260 + 371.110i −0.299438 + 0.518641i
\(81\) 0 0
\(82\) 1135.35 655.493i 1.52900 0.882770i
\(83\) 10.7079 18.5466i 0.0141608 0.0245272i −0.858858 0.512213i \(-0.828826\pi\)
0.873019 + 0.487686i \(0.162159\pi\)
\(84\) 0 0
\(85\) −87.0290 150.739i −0.111054 0.192352i
\(86\) −1114.68 643.558i −1.39766 0.806938i
\(87\) 0 0
\(88\) −12.7899 22.1527i −0.0154933 0.0268351i
\(89\) −339.721 588.414i −0.404611 0.700806i 0.589665 0.807648i \(-0.299260\pi\)
−0.994276 + 0.106841i \(0.965926\pi\)
\(90\) 0 0
\(91\) 331.937 1231.51i 0.382379 1.41865i
\(92\) 940.467 + 542.979i 1.06577 + 0.615320i
\(93\) 0 0
\(94\) 290.731i 0.319007i
\(95\) 756.957i 0.817496i
\(96\) 0 0
\(97\) 984.068 + 568.152i 1.03007 + 0.594713i 0.917005 0.398875i \(-0.130599\pi\)
0.113067 + 0.993587i \(0.463933\pi\)
\(98\) −1408.74 4.17218i −1.45209 0.00430054i
\(99\) 0 0
\(100\) −297.365 515.051i −0.297365 0.515051i
\(101\) 771.052 + 1335.50i 0.759629 + 1.31572i 0.943040 + 0.332679i \(0.107953\pi\)
−0.183411 + 0.983036i \(0.558714\pi\)
\(102\) 0 0
\(103\) 362.228 + 209.132i 0.346518 + 0.200062i 0.663151 0.748486i \(-0.269219\pi\)
−0.316632 + 0.948548i \(0.602552\pi\)
\(104\) 122.844 + 212.772i 0.115825 + 0.200615i
\(105\) 0 0
\(106\) 603.662 1045.57i 0.553140 0.958066i
\(107\) 1368.79 790.270i 1.23669 0.714003i 0.268273 0.963343i \(-0.413547\pi\)
0.968416 + 0.249340i \(0.0802138\pi\)
\(108\) 0 0
\(109\) 234.533 406.222i 0.206093 0.356964i −0.744387 0.667748i \(-0.767258\pi\)
0.950480 + 0.310784i \(0.100592\pi\)
\(110\) 224.162 0.194300
\(111\) 0 0
\(112\) −738.341 + 736.157i −0.622916 + 0.621074i
\(113\) 1733.74 1000.97i 1.44333 0.833306i 0.445259 0.895402i \(-0.353112\pi\)
0.998070 + 0.0620958i \(0.0197784\pi\)
\(114\) 0 0
\(115\) −807.193 + 466.033i −0.654531 + 0.377894i
\(116\) 1272.00 + 734.388i 1.01812 + 0.587813i
\(117\) 0 0
\(118\) 1894.34i 1.47786i
\(119\) −109.004 409.230i −0.0839693 0.315244i
\(120\) 0 0
\(121\) −639.794 + 1108.16i −0.480687 + 0.832574i
\(122\) −2720.61 −2.01896
\(123\) 0 0
\(124\) 122.278i 0.0885553i
\(125\) 1461.93 1.04607
\(126\) 0 0
\(127\) 522.832 0.365306 0.182653 0.983177i \(-0.441532\pi\)
0.182653 + 0.983177i \(0.441532\pi\)
\(128\) 453.948i 0.313466i
\(129\) 0 0
\(130\) −2153.02 −1.45256
\(131\) −1280.94 + 2218.65i −0.854321 + 1.47973i 0.0229522 + 0.999737i \(0.492693\pi\)
−0.877273 + 0.479991i \(0.840640\pi\)
\(132\) 0 0
\(133\) −479.312 + 1778.28i −0.312494 + 1.15937i
\(134\) 2950.07i 1.90184i
\(135\) 0 0
\(136\) 70.6479 + 40.7886i 0.0445441 + 0.0257176i
\(137\) 1.06378 0.614174i 0.000663394 0.000383011i −0.499668 0.866217i \(-0.666545\pi\)
0.500332 + 0.865834i \(0.333211\pi\)
\(138\) 0 0
\(139\) −1676.23 + 967.770i −1.02285 + 0.590541i −0.914927 0.403619i \(-0.867752\pi\)
−0.107920 + 0.994160i \(0.534419\pi\)
\(140\) 321.796 + 1208.11i 0.194262 + 0.729315i
\(141\) 0 0
\(142\) −381.732 −0.225593
\(143\) −246.901 + 427.645i −0.144384 + 0.250080i
\(144\) 0 0
\(145\) −1091.74 + 630.317i −0.625271 + 0.361000i
\(146\) −2091.48 + 3622.55i −1.18556 + 2.05345i
\(147\) 0 0
\(148\) −1122.27 1943.83i −0.623311 1.07961i
\(149\) 2102.67 + 1213.97i 1.15609 + 0.667468i 0.950363 0.311142i \(-0.100712\pi\)
0.205725 + 0.978610i \(0.434045\pi\)
\(150\) 0 0
\(151\) 698.188 + 1209.30i 0.376276 + 0.651730i 0.990517 0.137389i \(-0.0438710\pi\)
−0.614241 + 0.789119i \(0.710538\pi\)
\(152\) −177.384 307.239i −0.0946565 0.163950i
\(153\) 0 0
\(154\) 526.613 + 141.942i 0.275556 + 0.0742726i
\(155\) −90.8889 52.4747i −0.0470992 0.0271927i
\(156\) 0 0
\(157\) 733.416i 0.372822i −0.982472 0.186411i \(-0.940314\pi\)
0.982472 0.186411i \(-0.0596855\pi\)
\(158\) 3270.21i 1.64661i
\(159\) 0 0
\(160\) 1712.34 + 988.618i 0.846075 + 0.488482i
\(161\) −2191.39 + 583.705i −1.07271 + 0.285729i
\(162\) 0 0
\(163\) −1504.67 2606.16i −0.723036 1.25233i −0.959777 0.280762i \(-0.909413\pi\)
0.236742 0.971573i \(-0.423920\pi\)
\(164\) −1415.42 2451.57i −0.673935 1.16729i
\(165\) 0 0
\(166\) −76.1736 43.9789i −0.0356158 0.0205628i
\(167\) 40.1692 + 69.5751i 0.0186131 + 0.0322388i 0.875182 0.483794i \(-0.160742\pi\)
−0.856569 + 0.516033i \(0.827408\pi\)
\(168\) 0 0
\(169\) 1272.92 2204.77i 0.579392 1.00354i
\(170\) −619.105 + 357.440i −0.279313 + 0.161261i
\(171\) 0 0
\(172\) −1389.64 + 2406.94i −0.616043 + 1.06702i
\(173\) 2746.72 1.20711 0.603553 0.797323i \(-0.293751\pi\)
0.603553 + 0.797323i \(0.293751\pi\)
\(174\) 0 0
\(175\) 1199.17 + 323.222i 0.517994 + 0.139619i
\(176\) 349.580 201.830i 0.149719 0.0864405i
\(177\) 0 0
\(178\) −2416.70 + 1395.28i −1.01764 + 0.587533i
\(179\) −2491.90 1438.70i −1.04052 0.600745i −0.120540 0.992708i \(-0.538463\pi\)
−0.919981 + 0.391964i \(0.871796\pi\)
\(180\) 0 0
\(181\) 320.544i 0.131634i −0.997832 0.0658172i \(-0.979035\pi\)
0.997832 0.0658172i \(-0.0209654\pi\)
\(182\) −5057.98 1363.31i −2.06001 0.555250i
\(183\) 0 0
\(184\) 218.419 378.313i 0.0875113 0.151574i
\(185\) 1926.46 0.765603
\(186\) 0 0
\(187\) 163.960i 0.0641175i
\(188\) −627.780 −0.243540
\(189\) 0 0
\(190\) 3108.93 1.18708
\(191\) 945.061i 0.358022i −0.983847 0.179011i \(-0.942710\pi\)
0.983847 0.179011i \(-0.0572898\pi\)
\(192\) 0 0
\(193\) 786.769 0.293434 0.146717 0.989178i \(-0.453129\pi\)
0.146717 + 0.989178i \(0.453129\pi\)
\(194\) 2333.48 4041.71i 0.863578 1.49576i
\(195\) 0 0
\(196\) −9.00904 + 3041.92i −0.00328318 + 1.10857i
\(197\) 5047.70i 1.82555i 0.408462 + 0.912775i \(0.366065\pi\)
−0.408462 + 0.912775i \(0.633935\pi\)
\(198\) 0 0
\(199\) 1052.30 + 607.546i 0.374852 + 0.216421i 0.675576 0.737290i \(-0.263895\pi\)
−0.300724 + 0.953711i \(0.597228\pi\)
\(200\) −207.185 + 119.618i −0.0732509 + 0.0422914i
\(201\) 0 0
\(202\) 5485.09 3166.82i 1.91054 1.10305i
\(203\) −2963.90 + 789.471i −1.02475 + 0.272956i
\(204\) 0 0
\(205\) 2429.67 0.827784
\(206\) 858.937 1487.72i 0.290509 0.503177i
\(207\) 0 0
\(208\) −3357.63 + 1938.53i −1.11928 + 0.646215i
\(209\) 356.522 617.514i 0.117996 0.204375i
\(210\) 0 0
\(211\) 312.466 + 541.206i 0.101948 + 0.176579i 0.912487 0.409105i \(-0.134159\pi\)
−0.810539 + 0.585684i \(0.800826\pi\)
\(212\) −2257.72 1303.50i −0.731419 0.422285i
\(213\) 0 0
\(214\) −3245.75 5621.80i −1.03680 1.79579i
\(215\) −1192.72 2065.85i −0.378338 0.655300i
\(216\) 0 0
\(217\) −180.293 180.828i −0.0564014 0.0565687i
\(218\) −1668.41 963.259i −0.518345 0.299267i
\(219\) 0 0
\(220\) 484.036i 0.148335i
\(221\) 1574.80i 0.479332i
\(222\) 0 0
\(223\) −2295.49 1325.30i −0.689316 0.397977i 0.114040 0.993476i \(-0.463621\pi\)
−0.803356 + 0.595499i \(0.796954\pi\)
\(224\) 3396.70 + 3406.78i 1.01318 + 1.01618i
\(225\) 0 0
\(226\) −4111.14 7120.70i −1.21004 2.09585i
\(227\) −408.886 708.211i −0.119554 0.207073i 0.800037 0.599951i \(-0.204813\pi\)
−0.919591 + 0.392877i \(0.871480\pi\)
\(228\) 0 0
\(229\) 608.798 + 351.489i 0.175679 + 0.101428i 0.585261 0.810845i \(-0.300992\pi\)
−0.409582 + 0.912273i \(0.634325\pi\)
\(230\) 1914.06 + 3315.25i 0.548737 + 0.950441i
\(231\) 0 0
\(232\) 295.416 511.675i 0.0835991 0.144798i
\(233\) −3559.17 + 2054.89i −1.00073 + 0.577769i −0.908463 0.417966i \(-0.862743\pi\)
−0.0922626 + 0.995735i \(0.529410\pi\)
\(234\) 0 0
\(235\) 269.408 466.629i 0.0747841 0.129530i
\(236\) 4090.47 1.12825
\(237\) 0 0
\(238\) −1680.77 + 447.693i −0.457764 + 0.121931i
\(239\) 2082.70 1202.45i 0.563677 0.325439i −0.190943 0.981601i \(-0.561155\pi\)
0.754620 + 0.656162i \(0.227821\pi\)
\(240\) 0 0
\(241\) −629.048 + 363.181i −0.168135 + 0.0970729i −0.581706 0.813399i \(-0.697615\pi\)
0.413571 + 0.910472i \(0.364281\pi\)
\(242\) 4551.35 + 2627.72i 1.20897 + 0.698002i
\(243\) 0 0
\(244\) 5874.66i 1.54134i
\(245\) −2257.19 1312.12i −0.588599 0.342156i
\(246\) 0 0
\(247\) −3424.30 + 5931.06i −0.882117 + 1.52787i
\(248\) 49.1875 0.0125944
\(249\) 0 0
\(250\) 6004.35i 1.51899i
\(251\) −529.985 −0.133276 −0.0666382 0.997777i \(-0.521227\pi\)
−0.0666382 + 0.997777i \(0.521227\pi\)
\(252\) 0 0
\(253\) 877.994 0.218178
\(254\) 2147.35i 0.530458i
\(255\) 0 0
\(256\) 3067.50 0.748901
\(257\) −974.429 + 1687.76i −0.236511 + 0.409648i −0.959711 0.280990i \(-0.909337\pi\)
0.723200 + 0.690639i \(0.242670\pi\)
\(258\) 0 0
\(259\) 4525.75 + 1219.86i 1.08578 + 0.292657i
\(260\) 4649.05i 1.10893i
\(261\) 0 0
\(262\) 9112.31 + 5260.99i 2.14870 + 1.24055i
\(263\) 438.975 253.443i 0.102922 0.0594218i −0.447656 0.894206i \(-0.647741\pi\)
0.550577 + 0.834784i \(0.314408\pi\)
\(264\) 0 0
\(265\) 1937.78 1118.78i 0.449195 0.259343i
\(266\) 7303.65 + 1968.60i 1.68352 + 0.453770i
\(267\) 0 0
\(268\) −6370.13 −1.45193
\(269\) 3851.69 6671.33i 0.873018 1.51211i 0.0141598 0.999900i \(-0.495493\pi\)
0.858859 0.512213i \(-0.171174\pi\)
\(270\) 0 0
\(271\) −4585.66 + 2647.53i −1.02789 + 0.593455i −0.916380 0.400308i \(-0.868903\pi\)
−0.111513 + 0.993763i \(0.535570\pi\)
\(272\) −643.662 + 1114.85i −0.143484 + 0.248522i
\(273\) 0 0
\(274\) −2.52250 4.36910i −0.000556167 0.000963310i
\(275\) −416.417 240.418i −0.0913123 0.0527192i
\(276\) 0 0
\(277\) −2108.49 3652.01i −0.457353 0.792158i 0.541467 0.840722i \(-0.317869\pi\)
−0.998820 + 0.0485637i \(0.984536\pi\)
\(278\) 3974.77 + 6884.50i 0.857521 + 1.48527i
\(279\) 0 0
\(280\) 485.976 129.446i 0.103724 0.0276281i
\(281\) 7104.37 + 4101.71i 1.50823 + 0.870774i 0.999954 + 0.00957745i \(0.00304864\pi\)
0.508271 + 0.861197i \(0.330285\pi\)
\(282\) 0 0
\(283\) 1569.02i 0.329571i 0.986329 + 0.164786i \(0.0526932\pi\)
−0.986329 + 0.164786i \(0.947307\pi\)
\(284\) 824.280i 0.172225i
\(285\) 0 0
\(286\) 1756.40 + 1014.06i 0.363140 + 0.209659i
\(287\) 5707.90 + 1538.49i 1.17396 + 0.316426i
\(288\) 0 0
\(289\) 2195.06 + 3801.95i 0.446785 + 0.773854i
\(290\) 2588.80 + 4483.94i 0.524206 + 0.907951i
\(291\) 0 0
\(292\) 7822.22 + 4516.16i 1.56767 + 0.905097i
\(293\) 227.022 + 393.213i 0.0452653 + 0.0784019i 0.887770 0.460287i \(-0.152253\pi\)
−0.842505 + 0.538688i \(0.818920\pi\)
\(294\) 0 0
\(295\) −1755.40 + 3040.45i −0.346452 + 0.600073i
\(296\) −781.927 + 451.446i −0.153542 + 0.0886478i
\(297\) 0 0
\(298\) 4985.97 8635.94i 0.969226 1.67875i
\(299\) −8432.91 −1.63106
\(300\) 0 0
\(301\) −1493.88 5608.43i −0.286065 1.07397i
\(302\) 4966.75 2867.56i 0.946372 0.546388i
\(303\) 0 0
\(304\) 4848.37 2799.21i 0.914714 0.528110i
\(305\) −4366.64 2521.08i −0.819780 0.473300i
\(306\) 0 0
\(307\) 74.2025i 0.0137947i 0.999976 + 0.00689733i \(0.00219550\pi\)
−0.999976 + 0.00689733i \(0.997804\pi\)
\(308\) 306.496 1137.12i 0.0567021 0.210369i
\(309\) 0 0
\(310\) −215.521 + 373.294i −0.0394864 + 0.0683924i
\(311\) −6425.91 −1.17164 −0.585820 0.810441i \(-0.699227\pi\)
−0.585820 + 0.810441i \(0.699227\pi\)
\(312\) 0 0
\(313\) 7714.65i 1.39316i −0.717481 0.696578i \(-0.754705\pi\)
0.717481 0.696578i \(-0.245295\pi\)
\(314\) −3012.24 −0.541372
\(315\) 0 0
\(316\) −7061.41 −1.25707
\(317\) 306.057i 0.0542267i 0.999632 + 0.0271133i \(0.00863150\pi\)
−0.999632 + 0.0271133i \(0.991368\pi\)
\(318\) 0 0
\(319\) 1187.50 0.208424
\(320\) 2346.31 4063.93i 0.409884 0.709939i
\(321\) 0 0
\(322\) 2397.36 + 9000.36i 0.414906 + 1.55767i
\(323\) 2273.98i 0.391727i
\(324\) 0 0
\(325\) 3999.58 + 2309.16i 0.682636 + 0.394120i
\(326\) −10703.9 + 6179.89i −1.81851 + 1.04992i
\(327\) 0 0
\(328\) −986.172 + 569.367i −0.166013 + 0.0958476i
\(329\) 928.381 925.635i 0.155572 0.155112i
\(330\) 0 0
\(331\) −4099.12 −0.680688 −0.340344 0.940301i \(-0.610544\pi\)
−0.340344 + 0.940301i \(0.610544\pi\)
\(332\) −94.9642 + 164.483i −0.0156983 + 0.0271903i
\(333\) 0 0
\(334\) 285.755 164.981i 0.0468138 0.0270280i
\(335\) 2733.70 4734.91i 0.445845 0.772227i
\(336\) 0 0
\(337\) −3390.68 5872.83i −0.548078 0.949298i −0.998406 0.0564355i \(-0.982026\pi\)
0.450329 0.892863i \(-0.351307\pi\)
\(338\) −9055.29 5228.08i −1.45723 0.841331i
\(339\) 0 0
\(340\) 771.826 + 1336.84i 0.123112 + 0.213237i
\(341\) 49.4305 + 85.6161i 0.00784989 + 0.0135964i
\(342\) 0 0
\(343\) −4471.86 4511.77i −0.703959 0.710241i
\(344\) 968.216 + 559.000i 0.151752 + 0.0876141i
\(345\) 0 0
\(346\) 11281.2i 1.75283i
\(347\) 9757.99i 1.50961i −0.655946 0.754807i \(-0.727730\pi\)
0.655946 0.754807i \(-0.272270\pi\)
\(348\) 0 0
\(349\) 2576.08 + 1487.30i 0.395113 + 0.228119i 0.684373 0.729132i \(-0.260076\pi\)
−0.289260 + 0.957251i \(0.593409\pi\)
\(350\) 1327.52 4925.18i 0.202739 0.752176i
\(351\) 0 0
\(352\) −931.265 1613.00i −0.141013 0.244242i
\(353\) −4894.29 8477.16i −0.737951 1.27817i −0.953416 0.301657i \(-0.902460\pi\)
0.215465 0.976511i \(-0.430873\pi\)
\(354\) 0 0
\(355\) −612.687 353.735i −0.0916002 0.0528854i
\(356\) 3012.85 + 5218.41i 0.448542 + 0.776897i
\(357\) 0 0
\(358\) −5908.94 + 10234.6i −0.872338 + 1.51093i
\(359\) −3444.96 + 1988.95i −0.506456 + 0.292403i −0.731376 0.681975i \(-0.761121\pi\)
0.224919 + 0.974377i \(0.427788\pi\)
\(360\) 0 0
\(361\) 1515.14 2624.30i 0.220898 0.382606i
\(362\) −1316.52 −0.191145
\(363\) 0 0
\(364\) −2943.82 + 10921.8i −0.423896 + 1.57268i
\(365\) −6713.72 + 3876.17i −0.962773 + 0.555858i
\(366\) 0 0
\(367\) −3060.78 + 1767.14i −0.435344 + 0.251346i −0.701621 0.712551i \(-0.747540\pi\)
0.266277 + 0.963897i \(0.414207\pi\)
\(368\) 5969.95 + 3446.75i 0.845667 + 0.488246i
\(369\) 0 0
\(370\) 7912.26i 1.11173i
\(371\) 5260.74 1401.26i 0.736183 0.196092i
\(372\) 0 0
\(373\) −2362.93 + 4092.71i −0.328010 + 0.568129i −0.982117 0.188272i \(-0.939711\pi\)
0.654107 + 0.756402i \(0.273045\pi\)
\(374\) 673.408 0.0931046
\(375\) 0 0
\(376\) 252.531i 0.0346365i
\(377\) −11405.6 −1.55815
\(378\) 0 0
\(379\) 5183.61 0.702545 0.351272 0.936273i \(-0.385749\pi\)
0.351272 + 0.936273i \(0.385749\pi\)
\(380\) 6713.16i 0.906257i
\(381\) 0 0
\(382\) −3881.50 −0.519882
\(383\) −3447.20 + 5970.73i −0.459906 + 0.796580i −0.998955 0.0456938i \(-0.985450\pi\)
0.539050 + 0.842274i \(0.318783\pi\)
\(384\) 0 0
\(385\) 713.692 + 715.808i 0.0944756 + 0.0947558i
\(386\) 3231.37i 0.426094i
\(387\) 0 0
\(388\) −8727.32 5038.72i −1.14191 0.659284i
\(389\) 2437.14 1407.08i 0.317655 0.183398i −0.332692 0.943036i \(-0.607957\pi\)
0.650347 + 0.759637i \(0.274624\pi\)
\(390\) 0 0
\(391\) −2424.90 + 1400.02i −0.313638 + 0.181079i
\(392\) 1223.65 + 3.62398i 0.157662 + 0.000466936i
\(393\) 0 0
\(394\) 20731.6 2.65087
\(395\) 3030.36 5248.75i 0.386011 0.668590i
\(396\) 0 0
\(397\) −5248.35 + 3030.14i −0.663494 + 0.383068i −0.793607 0.608431i \(-0.791799\pi\)
0.130113 + 0.991499i \(0.458466\pi\)
\(398\) 2495.28 4321.95i 0.314264 0.544320i
\(399\) 0 0
\(400\) −1887.63 3269.47i −0.235954 0.408684i
\(401\) 10447.9 + 6032.11i 1.30111 + 0.751196i 0.980594 0.196048i \(-0.0628108\pi\)
0.320515 + 0.947244i \(0.396144\pi\)
\(402\) 0 0
\(403\) −474.767 822.321i −0.0586845 0.101645i
\(404\) −6838.15 11844.0i −0.842106 1.45857i
\(405\) 0 0
\(406\) 3242.47 + 12173.1i 0.396357 + 1.48804i
\(407\) −1571.58 907.352i −0.191401 0.110506i
\(408\) 0 0
\(409\) 337.510i 0.0408039i 0.999792 + 0.0204019i \(0.00649459\pi\)
−0.999792 + 0.0204019i \(0.993505\pi\)
\(410\) 9979.00i 1.20202i
\(411\) 0 0
\(412\) −3212.46 1854.71i −0.384142 0.221784i
\(413\) −6049.11 + 6031.23i −0.720720 + 0.718589i
\(414\) 0 0
\(415\) −81.5067 141.174i −0.00964098 0.0166987i
\(416\) 8944.56 + 15492.4i 1.05419 + 1.82591i
\(417\) 0 0
\(418\) −2536.22 1464.28i −0.296771 0.171341i
\(419\) 4094.25 + 7091.45i 0.477368 + 0.826826i 0.999664 0.0259386i \(-0.00825744\pi\)
−0.522295 + 0.852765i \(0.674924\pi\)
\(420\) 0 0
\(421\) 958.165 1659.59i 0.110922 0.192122i −0.805220 0.592976i \(-0.797953\pi\)
0.916142 + 0.400853i \(0.131286\pi\)
\(422\) 2222.81 1283.34i 0.256409 0.148038i
\(423\) 0 0
\(424\) −524.345 + 908.193i −0.0600577 + 0.104023i
\(425\) 1533.45 0.175019
\(426\) 0 0
\(427\) −8661.95 8687.64i −0.981688 0.984600i
\(428\) −12139.2 + 7008.59i −1.37096 + 0.791526i
\(429\) 0 0
\(430\) −8484.72 + 4898.66i −0.951557 + 0.549382i
\(431\) −8604.78 4967.97i −0.961665 0.555218i −0.0649800 0.997887i \(-0.520698\pi\)
−0.896685 + 0.442669i \(0.854032\pi\)
\(432\) 0 0
\(433\) 4551.00i 0.505098i 0.967584 + 0.252549i \(0.0812688\pi\)
−0.967584 + 0.252549i \(0.918731\pi\)
\(434\) −742.686 + 740.490i −0.0821430 + 0.0819001i
\(435\) 0 0
\(436\) −2079.98 + 3602.63i −0.228470 + 0.395721i
\(437\) 12177.0 1.33296
\(438\) 0 0
\(439\) 7418.00i 0.806474i 0.915096 + 0.403237i \(0.132115\pi\)
−0.915096 + 0.403237i \(0.867885\pi\)
\(440\) −194.709 −0.0210963
\(441\) 0 0
\(442\) −6467.91 −0.696035
\(443\) 6327.38i 0.678607i 0.940677 + 0.339303i \(0.110191\pi\)
−0.940677 + 0.339303i \(0.889809\pi\)
\(444\) 0 0
\(445\) −5171.80 −0.550936
\(446\) −5443.21 + 9427.91i −0.577900 + 1.00095i
\(447\) 0 0
\(448\) 8085.38 8061.47i 0.852675 0.850154i
\(449\) 14396.4i 1.51316i −0.653904 0.756578i \(-0.726870\pi\)
0.653904 0.756578i \(-0.273130\pi\)
\(450\) 0 0
\(451\) −1982.09 1144.36i −0.206946 0.119481i
\(452\) −15375.8 + 8877.24i −1.60004 + 0.923783i
\(453\) 0 0
\(454\) −2908.72 + 1679.35i −0.300690 + 0.173603i
\(455\) −6854.83 6875.16i −0.706284 0.708379i
\(456\) 0 0
\(457\) 5147.23 0.526865 0.263432 0.964678i \(-0.415145\pi\)
0.263432 + 0.964678i \(0.415145\pi\)
\(458\) 1443.62 2500.42i 0.147283 0.255102i
\(459\) 0 0
\(460\) 7158.68 4133.06i 0.725598 0.418924i
\(461\) 446.618 773.565i 0.0451217 0.0781530i −0.842583 0.538567i \(-0.818966\pi\)
0.887704 + 0.460414i \(0.152299\pi\)
\(462\) 0 0
\(463\) 5520.47 + 9561.73i 0.554121 + 0.959765i 0.997971 + 0.0636644i \(0.0202787\pi\)
−0.443851 + 0.896101i \(0.646388\pi\)
\(464\) 8074.46 + 4661.79i 0.807861 + 0.466419i
\(465\) 0 0
\(466\) 8439.72 + 14618.0i 0.838975 + 1.45315i
\(467\) 4900.18 + 8487.36i 0.485553 + 0.841003i 0.999862 0.0166023i \(-0.00528493\pi\)
−0.514309 + 0.857605i \(0.671952\pi\)
\(468\) 0 0
\(469\) 9420.34 9392.49i 0.927486 0.924744i
\(470\) −1916.51 1106.50i −0.188089 0.108593i
\(471\) 0 0
\(472\) 1645.44i 0.160460i
\(473\) 2247.05i 0.218434i
\(474\) 0 0
\(475\) −5775.33 3334.39i −0.557875 0.322089i
\(476\) 966.711 + 3629.30i 0.0930864 + 0.349472i
\(477\) 0 0
\(478\) −4938.63 8553.95i −0.472568 0.818512i
\(479\) −69.3349 120.092i −0.00661377 0.0114554i 0.862700 0.505717i \(-0.168772\pi\)
−0.869313 + 0.494261i \(0.835439\pi\)
\(480\) 0 0
\(481\) 15094.6 + 8714.89i 1.43088 + 0.826122i
\(482\) 1491.64 + 2583.59i 0.140959 + 0.244148i
\(483\) 0 0
\(484\) 5674.08 9827.80i 0.532878 0.922971i
\(485\) 7490.56 4324.68i 0.701296 0.404894i
\(486\) 0 0
\(487\) −9148.40 + 15845.5i −0.851239 + 1.47439i 0.0288514 + 0.999584i \(0.490815\pi\)
−0.880091 + 0.474806i \(0.842518\pi\)
\(488\) 2363.15 0.219210
\(489\) 0 0
\(490\) −5389.06 + 9270.61i −0.496843 + 0.854701i
\(491\) −5097.03 + 2942.77i −0.468484 + 0.270479i −0.715605 0.698505i \(-0.753849\pi\)
0.247121 + 0.968985i \(0.420516\pi\)
\(492\) 0 0
\(493\) −3279.71 + 1893.54i −0.299616 + 0.172984i
\(494\) 24359.7 + 14064.1i 2.21861 + 1.28092i
\(495\) 0 0
\(496\) 776.201i 0.0702670i
\(497\) −1215.37 1218.97i −0.109691 0.110017i
\(498\) 0 0
\(499\) −267.363 + 463.086i −0.0239856 + 0.0415442i −0.877769 0.479084i \(-0.840969\pi\)
0.853783 + 0.520628i \(0.174302\pi\)
\(500\) −12965.3 −1.15965
\(501\) 0 0
\(502\) 2176.72i 0.193530i
\(503\) −10504.5 −0.931155 −0.465578 0.885007i \(-0.654153\pi\)
−0.465578 + 0.885007i \(0.654153\pi\)
\(504\) 0 0
\(505\) 11738.2 1.03434
\(506\) 3606.04i 0.316815i
\(507\) 0 0
\(508\) −4636.79 −0.404969
\(509\) −1408.94 + 2440.35i −0.122691 + 0.212508i −0.920828 0.389969i \(-0.872486\pi\)
0.798137 + 0.602476i \(0.205819\pi\)
\(510\) 0 0
\(511\) −18226.6 + 4854.90i −1.57788 + 0.420289i
\(512\) 16230.2i 1.40094i
\(513\) 0 0
\(514\) 6931.87 + 4002.12i 0.594848 + 0.343435i
\(515\) 2757.22 1591.88i 0.235918 0.136207i
\(516\) 0 0
\(517\) −439.558 + 253.779i −0.0373921 + 0.0215884i
\(518\) 5010.12 18587.9i 0.424965 1.57665i
\(519\) 0 0
\(520\) 1870.13 0.157713
\(521\) −5520.76 + 9562.24i −0.464240 + 0.804087i −0.999167 0.0408113i \(-0.987006\pi\)
0.534927 + 0.844898i \(0.320339\pi\)
\(522\) 0 0
\(523\) −4094.57 + 2364.00i −0.342338 + 0.197649i −0.661306 0.750117i \(-0.729997\pi\)
0.318967 + 0.947766i \(0.396664\pi\)
\(524\) 11360.1 19676.3i 0.947080 1.64039i
\(525\) 0 0
\(526\) −1040.92 1802.93i −0.0862860 0.149452i
\(527\) −273.040 157.640i −0.0225689 0.0130302i
\(528\) 0 0
\(529\) 1413.46 + 2448.19i 0.116172 + 0.201216i
\(530\) −4594.97 7958.72i −0.376590 0.652273i
\(531\) 0 0
\(532\) 4250.83 15770.9i 0.346423 1.28525i
\(533\) 19037.5 + 10991.3i 1.54710 + 0.893218i
\(534\) 0 0
\(535\) 12030.8i 0.972218i
\(536\) 2562.45i 0.206495i
\(537\) 0 0
\(538\) −27400.1 15819.5i −2.19573 1.26770i
\(539\) 1223.38 + 2133.53i 0.0977641 + 0.170496i
\(540\) 0 0
\(541\) 11254.7 + 19493.8i 0.894415 + 1.54917i 0.834527 + 0.550967i \(0.185741\pi\)
0.0598879 + 0.998205i \(0.480926\pi\)
\(542\) 10873.8 + 18834.0i 0.861752 + 1.49260i
\(543\) 0 0
\(544\) 5144.05 + 2969.92i 0.405421 + 0.234070i
\(545\) −1785.22 3092.10i −0.140313 0.243029i
\(546\) 0 0
\(547\) −1219.31 + 2111.91i −0.0953088 + 0.165080i −0.909737 0.415184i \(-0.863717\pi\)
0.814429 + 0.580264i \(0.197051\pi\)
\(548\) −9.43426 + 5.44687i −0.000735422 + 0.000424596i
\(549\) 0 0
\(550\) −987.432 + 1710.28i −0.0765532 + 0.132594i
\(551\) 16469.6 1.27337
\(552\) 0 0
\(553\) 10442.6 10411.8i 0.803013 0.800638i
\(554\) −14999.3 + 8659.85i −1.15029 + 0.664119i
\(555\) 0 0
\(556\) 14865.8 8582.77i 1.13390 0.654660i
\(557\) 9826.37 + 5673.25i 0.747498 + 0.431568i 0.824789 0.565440i \(-0.191294\pi\)
−0.0772911 + 0.997009i \(0.524627\pi\)
\(558\) 0 0
\(559\) 21582.3i 1.63298i
\(560\) 2042.71 + 7668.92i 0.154144 + 0.578698i
\(561\) 0 0
\(562\) 16846.3 29178.7i 1.26445 2.19008i
\(563\) −16855.7 −1.26178 −0.630891 0.775871i \(-0.717311\pi\)
−0.630891 + 0.775871i \(0.717311\pi\)
\(564\) 0 0
\(565\) 15238.5i 1.13467i
\(566\) 6444.19 0.478568
\(567\) 0 0
\(568\) 331.576 0.0244940
\(569\) 11917.1i 0.878019i 0.898482 + 0.439009i \(0.144671\pi\)
−0.898482 + 0.439009i \(0.855329\pi\)
\(570\) 0 0
\(571\) 20409.3 1.49580 0.747902 0.663809i \(-0.231061\pi\)
0.747902 + 0.663809i \(0.231061\pi\)
\(572\) 2189.67 3792.62i 0.160061 0.277233i
\(573\) 0 0
\(574\) 6318.80 23443.2i 0.459480 1.70470i
\(575\) 8211.49i 0.595552i
\(576\) 0 0
\(577\) −3374.84 1948.46i −0.243495 0.140582i 0.373287 0.927716i \(-0.378231\pi\)
−0.616782 + 0.787134i \(0.711564\pi\)
\(578\) 15615.1 9015.40i 1.12371 0.648774i
\(579\) 0 0
\(580\) 9682.23 5590.04i 0.693160 0.400196i
\(581\) −102.087 383.263i −0.00728964 0.0273673i
\(582\) 0 0
\(583\) −2107.74 −0.149732
\(584\) 1816.67 3146.57i 0.128724 0.222956i
\(585\) 0 0
\(586\) 1614.98 932.410i 0.113847 0.0657295i
\(587\) 8643.77 14971.5i 0.607780 1.05271i −0.383826 0.923406i \(-0.625394\pi\)
0.991606 0.129300i \(-0.0412730\pi\)
\(588\) 0 0
\(589\) 685.557 + 1187.42i 0.0479591 + 0.0830675i
\(590\) 12487.5 + 7209.68i 0.871362 + 0.503081i
\(591\) 0 0
\(592\) −7124.01 12339.2i −0.494586 0.856649i
\(593\) 985.742 + 1707.36i 0.0682623 + 0.118234i 0.898136 0.439717i \(-0.144921\pi\)
−0.829874 + 0.557951i \(0.811588\pi\)
\(594\) 0 0
\(595\) −3112.52 838.939i −0.214455 0.0578036i
\(596\) −18647.7 10766.3i −1.28161 0.739939i
\(597\) 0 0
\(598\) 34635.1i 2.36845i
\(599\) 13995.3i 0.954646i 0.878728 + 0.477323i \(0.158393\pi\)
−0.878728 + 0.477323i \(0.841607\pi\)
\(600\) 0 0
\(601\) 17296.5 + 9986.12i 1.17394 + 0.677774i 0.954605 0.297875i \(-0.0962780\pi\)
0.219335 + 0.975650i \(0.429611\pi\)
\(602\) −23034.6 + 6135.56i −1.55950 + 0.415393i
\(603\) 0 0
\(604\) −6191.95 10724.8i −0.417131 0.722492i
\(605\) 4870.00 + 8435.09i 0.327262 + 0.566835i
\(606\) 0 0
\(607\) −11256.5 6498.92i −0.752694 0.434568i 0.0739724 0.997260i \(-0.476432\pi\)
−0.826667 + 0.562692i \(0.809766\pi\)
\(608\) −12915.8 22370.8i −0.861522 1.49220i
\(609\) 0 0
\(610\) −10354.4 + 17934.4i −0.687276 + 1.19040i
\(611\) 4221.84 2437.48i 0.279538 0.161391i
\(612\) 0 0
\(613\) −3450.80 + 5976.96i −0.227368 + 0.393812i −0.957027 0.289998i \(-0.906345\pi\)
0.729659 + 0.683811i \(0.239679\pi\)
\(614\) 304.760 0.0200311
\(615\) 0 0
\(616\) −457.420 123.292i −0.0299188 0.00806422i
\(617\) 8207.48 4738.59i 0.535528 0.309187i −0.207737 0.978185i \(-0.566610\pi\)
0.743265 + 0.668998i \(0.233276\pi\)
\(618\) 0 0
\(619\) −13493.9 + 7790.69i −0.876195 + 0.505871i −0.869402 0.494106i \(-0.835496\pi\)
−0.00679306 + 0.999977i \(0.502162\pi\)
\(620\) 806.058 + 465.378i 0.0522130 + 0.0301452i
\(621\) 0 0
\(622\) 26392.1i 1.70133i
\(623\) −12149.8 3274.83i −0.781337 0.210599i
\(624\) 0 0
\(625\) 1372.72 2377.62i 0.0878540 0.152168i
\(626\) −31685.2 −2.02299
\(627\) 0 0
\(628\) 6504.38i 0.413301i
\(629\) 5787.32 0.366861
\(630\) 0 0
\(631\) 7028.73 0.443438 0.221719 0.975111i \(-0.428833\pi\)
0.221719 + 0.975111i \(0.428833\pi\)
\(632\) 2840.53i 0.178782i
\(633\) 0 0
\(634\) 1257.02 0.0787422
\(635\) 1989.85 3446.53i 0.124354 0.215388i
\(636\) 0 0
\(637\) −11750.3 20492.0i −0.730868 1.27460i
\(638\) 4877.23i 0.302651i
\(639\) 0 0
\(640\) −2992.44 1727.69i −0.184823 0.106707i
\(641\) −16662.3 + 9620.01i −1.02671 + 0.592773i −0.916041 0.401084i \(-0.868634\pi\)
−0.110672 + 0.993857i \(0.535300\pi\)
\(642\) 0 0
\(643\) −2402.55 + 1387.11i −0.147352 + 0.0850737i −0.571863 0.820349i \(-0.693779\pi\)
0.424511 + 0.905423i \(0.360446\pi\)
\(644\) 19434.6 5176.65i 1.18918 0.316753i
\(645\) 0 0
\(646\) 9339.57 0.568824
\(647\) 4830.91 8367.38i 0.293544 0.508432i −0.681101 0.732189i \(-0.738499\pi\)
0.974645 + 0.223757i \(0.0718321\pi\)
\(648\) 0 0
\(649\) 2864.06 1653.56i 0.173227 0.100012i
\(650\) 9484.04 16426.8i 0.572299 0.991251i
\(651\) 0 0
\(652\) 13344.3 + 23113.0i 0.801540 + 1.38831i
\(653\) 10293.4 + 5942.91i 0.616865 + 0.356147i 0.775647 0.631167i \(-0.217424\pi\)
−0.158783 + 0.987314i \(0.550757\pi\)
\(654\) 0 0
\(655\) 9750.28 + 16888.0i 0.581641 + 1.00743i
\(656\) −8984.86 15562.2i −0.534756 0.926224i
\(657\) 0 0
\(658\) −3801.71 3812.99i −0.225237 0.225906i
\(659\) −20497.2 11834.1i −1.21162 0.699529i −0.248508 0.968630i \(-0.579940\pi\)
−0.963112 + 0.269100i \(0.913274\pi\)
\(660\) 0 0
\(661\) 9602.52i 0.565045i −0.959261 0.282523i \(-0.908829\pi\)
0.959261 0.282523i \(-0.0911712\pi\)
\(662\) 16835.7i 0.988423i
\(663\) 0 0
\(664\) 66.1650 + 38.2004i 0.00386702 + 0.00223262i
\(665\) 9898.27 + 9927.63i 0.577201 + 0.578913i
\(666\) 0 0
\(667\) 10139.8 + 17562.6i 0.588626 + 1.01953i
\(668\) −356.245 617.034i −0.0206340 0.0357392i
\(669\) 0 0
\(670\) −19447.0 11227.7i −1.12135 0.647409i
\(671\) 2374.82 + 4113.31i 0.136630 + 0.236651i
\(672\) 0 0
\(673\) −3469.40 + 6009.18i −0.198716 + 0.344186i −0.948112 0.317936i \(-0.897010\pi\)
0.749397 + 0.662121i \(0.230344\pi\)
\(674\) −24120.6 + 13926.0i −1.37847 + 0.795860i
\(675\) 0 0
\(676\) −11289.1 + 19553.2i −0.642300 + 1.11250i
\(677\) −8352.99 −0.474197 −0.237098 0.971486i \(-0.576196\pi\)
−0.237098 + 0.971486i \(0.576196\pi\)
\(678\) 0 0
\(679\) 20335.6 5416.65i 1.14935 0.306144i
\(680\) 537.759 310.476i 0.0303267 0.0175091i
\(681\) 0 0
\(682\) 351.638 203.018i 0.0197433 0.0113988i
\(683\) 8631.82 + 4983.58i 0.483583 + 0.279197i 0.721908 0.691989i \(-0.243265\pi\)
−0.238325 + 0.971185i \(0.576598\pi\)
\(684\) 0 0
\(685\) 9.34998i 0.000521524i
\(686\) −18530.5 + 18366.6i −1.03134 + 1.02221i
\(687\) 0 0
\(688\) −8821.27 + 15278.9i −0.488819 + 0.846660i
\(689\) 20244.3 1.11937
\(690\) 0 0
\(691\) 4794.06i 0.263929i −0.991254 0.131964i \(-0.957872\pi\)
0.991254 0.131964i \(-0.0421285\pi\)
\(692\) −24359.6 −1.33817
\(693\) 0 0
\(694\) −40077.4 −2.19210
\(695\) 14733.0i 0.804107i
\(696\) 0 0
\(697\) 7299.00 0.396656
\(698\) 6108.56 10580.3i 0.331250 0.573741i
\(699\) 0 0
\(700\) −10635.0 2866.53i −0.574236 0.154778i
\(701\) 13815.7i 0.744382i 0.928156 + 0.372191i \(0.121393\pi\)
−0.928156 + 0.372191i \(0.878607\pi\)
\(702\) 0 0
\(703\) −21796.4 12584.2i −1.16937 0.675136i
\(704\) −3828.17 + 2210.19i −0.204942 + 0.118324i
\(705\) 0 0
\(706\) −34816.9 + 20101.5i −1.85602 + 1.07157i
\(707\) 27576.0 + 7432.75i 1.46691 + 0.395385i
\(708\) 0 0
\(709\) 134.605 0.00713001 0.00356501 0.999994i \(-0.498865\pi\)
0.00356501 + 0.999994i \(0.498865\pi\)
\(710\) −1452.84 + 2516.39i −0.0767945 + 0.133012i
\(711\) 0 0
\(712\) 2099.16 1211.95i 0.110491 0.0637919i
\(713\) −844.149 + 1462.11i −0.0443389 + 0.0767972i
\(714\) 0 0
\(715\) 1879.37 + 3255.16i 0.0982999 + 0.170260i
\(716\) 22099.7 + 12759.2i 1.15350 + 0.665971i
\(717\) 0 0
\(718\) 8168.88 + 14148.9i 0.424596 + 0.735422i
\(719\) −279.689 484.435i −0.0145071 0.0251271i 0.858681 0.512511i \(-0.171285\pi\)
−0.873188 + 0.487384i \(0.837951\pi\)
\(720\) 0 0
\(721\) 7485.38 1993.83i 0.386644 0.102988i
\(722\) −10778.4 6222.89i −0.555580 0.320764i
\(723\) 0 0
\(724\) 2842.77i 0.145927i
\(725\) 11106.2i 0.568928i
\(726\) 0 0
\(727\) 6529.04 + 3769.54i 0.333079 + 0.192303i 0.657207 0.753710i \(-0.271738\pi\)
−0.324128 + 0.946013i \(0.605071\pi\)
\(728\) 4393.40 + 1184.18i 0.223668 + 0.0602868i
\(729\) 0 0
\(730\) 15920.0 + 27574.2i 0.807157 + 1.39804i
\(731\) −3583.05 6206.03i −0.181291 0.314006i
\(732\) 0 0
\(733\) −29593.0 17085.5i −1.49119 0.860939i −0.491241 0.871024i \(-0.663457\pi\)
−0.999949 + 0.0100844i \(0.996790\pi\)
\(734\) 7257.90 + 12571.0i 0.364978 + 0.632161i
\(735\) 0 0
\(736\) 15903.7 27545.9i 0.796490 1.37956i
\(737\) −4460.23 + 2575.11i −0.222923 + 0.128705i
\(738\) 0 0
\(739\) −5524.56 + 9568.82i −0.274999 + 0.476312i −0.970135 0.242566i \(-0.922011\pi\)
0.695136 + 0.718878i \(0.255344\pi\)
\(740\) −17085.1 −0.848729
\(741\) 0 0
\(742\) −5755.19 21606.6i −0.284743 1.06901i
\(743\) 5588.14 3226.32i 0.275921 0.159303i −0.355655 0.934617i \(-0.615742\pi\)
0.631575 + 0.775315i \(0.282409\pi\)
\(744\) 0 0
\(745\) 16005.1 9240.57i 0.787091 0.454427i
\(746\) 16809.3 + 9704.87i 0.824977 + 0.476301i
\(747\) 0 0
\(748\) 1454.10i 0.0710791i
\(749\) 7618.01 28263.3i 0.371637 1.37880i
\(750\) 0 0
\(751\) 843.892 1461.66i 0.0410041 0.0710211i −0.844795 0.535090i \(-0.820278\pi\)
0.885799 + 0.464069i \(0.153611\pi\)
\(752\) −3985.06 −0.193245
\(753\) 0 0
\(754\) 46844.6i 2.26257i
\(755\) 10629.0 0.512355
\(756\) 0 0
\(757\) 10839.9 0.520453 0.260226 0.965548i \(-0.416203\pi\)
0.260226 + 0.965548i \(0.416203\pi\)
\(758\) 21289.8i 1.02016i
\(759\) 0 0
\(760\) −2700.44 −0.128889
\(761\) −4529.42 + 7845.18i −0.215757 + 0.373702i −0.953507 0.301372i \(-0.902555\pi\)
0.737749 + 0.675075i \(0.235889\pi\)
\(762\) 0 0
\(763\) −2235.99 8394.52i −0.106092 0.398299i
\(764\) 8381.38i 0.396895i
\(765\) 0 0
\(766\) 24522.6 + 14158.2i 1.15671 + 0.667826i
\(767\) −27508.6 + 15882.1i −1.29501 + 0.747677i
\(768\) 0 0
\(769\) −10991.2 + 6345.79i −0.515415 + 0.297575i −0.735057 0.678006i \(-0.762844\pi\)
0.219642 + 0.975581i \(0.429511\pi\)
\(770\) 2939.93 2931.23i 0.137594 0.137187i
\(771\) 0 0
\(772\) −6977.54 −0.325294
\(773\) 10423.9 18054.8i 0.485023 0.840085i −0.514829 0.857293i \(-0.672145\pi\)
0.999852 + 0.0172084i \(0.00547788\pi\)
\(774\) 0 0
\(775\) 800.730 462.302i 0.0371136 0.0214276i
\(776\) −2026.88 + 3510.66i −0.0937639 + 0.162404i
\(777\) 0 0
\(778\) −5779.09 10009.7i −0.266312 0.461265i
\(779\) −27489.8 15871.2i −1.26434 0.729969i
\(780\) 0 0
\(781\) 333.214 + 577.143i 0.0152667 + 0.0264428i
\(782\) 5750.06 + 9959.40i 0.262943 + 0.455431i
\(783\) 0 0
\(784\) −57.1881 + 19309.7i −0.00260514 + 0.879631i
\(785\) −4834.71 2791.32i −0.219819 0.126913i
\(786\) 0 0
\(787\) 5164.85i 0.233935i 0.993136 + 0.116968i \(0.0373173\pi\)
−0.993136 + 0.116968i \(0.962683\pi\)
\(788\) 44766.0i 2.02376i
\(789\) 0 0
\(790\) −21557.3 12446.1i −0.970855 0.560524i
\(791\) 9649.14 35799.0i 0.433734 1.60918i
\(792\) 0 0
\(793\) −22809.6 39507.3i −1.02143 1.76916i
\(794\) 12445.2 + 21555.7i 0.556251 + 0.963455i
\(795\) 0 0
\(796\) −9332.44 5388.09i −0.415552 0.239919i
\(797\) −3686.20 6384.68i −0.163829 0.283760i 0.772410 0.635125i \(-0.219051\pi\)
−0.936239 + 0.351364i \(0.885718\pi\)
\(798\) 0 0
\(799\) 809.332 1401.80i 0.0358349 0.0620679i
\(800\) −15085.7 + 8709.70i −0.666698 + 0.384918i
\(801\) 0 0
\(802\) 24774.7 42911.1i 1.09081 1.88933i
\(803\) 7302.60 0.320925
\(804\) 0 0
\(805\) −4492.45 + 16667.3i −0.196693 + 0.729744i
\(806\) −3377.39 + 1949.94i −0.147597 + 0.0852154i
\(807\) 0 0
\(808\) −4764.39 + 2750.72i −0.207439 + 0.119765i
\(809\) −15808.7 9127.15i −0.687026 0.396655i 0.115471 0.993311i \(-0.463162\pi\)
−0.802497 + 0.596656i \(0.796496\pi\)
\(810\) 0 0
\(811\) 32302.9i 1.39865i −0.714802 0.699327i \(-0.753483\pi\)
0.714802 0.699327i \(-0.246517\pi\)
\(812\) 26285.6 7001.51i 1.13602 0.302592i
\(813\) 0 0
\(814\) −3726.62 + 6454.70i −0.160464 + 0.277933i
\(815\) −22906.6 −0.984518
\(816\) 0 0
\(817\) 31164.5i 1.33453i
\(818\) 1386.20 0.0592510
\(819\) 0 0
\(820\) −21547.8 −0.917661
\(821\) 17372.0i 0.738475i −0.929335 0.369238i \(-0.879619\pi\)
0.929335 0.369238i \(-0.120381\pi\)
\(822\) 0 0
\(823\) −12896.9 −0.546241 −0.273120 0.961980i \(-0.588056\pi\)
−0.273120 + 0.961980i \(0.588056\pi\)
\(824\) −746.079 + 1292.25i −0.0315423 + 0.0546329i
\(825\) 0 0
\(826\) 24771.1 + 24844.6i 1.04346 + 1.04655i
\(827\) 34437.8i 1.44803i 0.689785 + 0.724014i \(0.257705\pi\)
−0.689785 + 0.724014i \(0.742295\pi\)
\(828\) 0 0
\(829\) −37770.2 21806.6i −1.58240 0.913601i −0.994508 0.104664i \(-0.966623\pi\)
−0.587896 0.808937i \(-0.700043\pi\)
\(830\) −579.820 + 334.759i −0.0242480 + 0.0139996i
\(831\) 0 0
\(832\) 36768.6 21228.3i 1.53212 0.884568i
\(833\) −6780.86 3941.75i −0.282044 0.163954i
\(834\) 0 0
\(835\) 611.522 0.0253444
\(836\) −3161.85 + 5476.49i −0.130807 + 0.226565i
\(837\) 0 0
\(838\) 29125.6 16815.7i 1.20063 0.693183i
\(839\) −15073.9 + 26108.8i −0.620274 + 1.07435i 0.369160 + 0.929366i \(0.379645\pi\)
−0.989434 + 0.144981i \(0.953688\pi\)
\(840\) 0 0
\(841\) 1519.71 + 2632.21i 0.0623112 + 0.107926i
\(842\) −6816.17 3935.32i −0.278980 0.161069i
\(843\) 0 0
\(844\) −2771.14 4799.75i −0.113017 0.195751i
\(845\) −9689.27 16782.3i −0.394463 0.683230i
\(846\) 0 0
\(847\) 6099.67 + 22899.9i 0.247446 + 0.928983i
\(848\) −14331.7 8274.40i −0.580368 0.335076i
\(849\) 0 0
\(850\) 6298.09i 0.254144i
\(851\) 30990.6i 1.24835i
\(852\) 0 0
\(853\) 23967.5 + 13837.6i 0.962053 + 0.555441i 0.896804 0.442428i \(-0.145883\pi\)
0.0652484 + 0.997869i \(0.479216\pi\)
\(854\) −35681.4 + 35575.8i −1.42973 + 1.42550i
\(855\) 0 0
\(856\) 2819.28 + 4883.14i 0.112571 + 0.194979i
\(857\) −8243.26 14277.8i −0.328570 0.569100i 0.653658 0.756790i \(-0.273233\pi\)
−0.982228 + 0.187690i \(0.939900\pi\)
\(858\) 0 0
\(859\) 17391.0 + 10040.7i 0.690771 + 0.398817i 0.803901 0.594764i \(-0.202754\pi\)
−0.113130 + 0.993580i \(0.536088\pi\)
\(860\) 10577.7 + 18321.2i 0.419416 + 0.726450i
\(861\) 0 0
\(862\) −20404.2 + 35341.0i −0.806228 + 1.39643i
\(863\) 23674.1 13668.3i 0.933808 0.539134i 0.0457940 0.998951i \(-0.485418\pi\)
0.888014 + 0.459817i \(0.152085\pi\)
\(864\) 0 0
\(865\) 10453.8 18106.5i 0.410913 0.711721i
\(866\) 18691.6 0.733449
\(867\) 0 0
\(868\) 1598.95 + 1603.69i 0.0625252 + 0.0627107i
\(869\) −4944.25 + 2854.56i −0.193006 + 0.111432i
\(870\) 0 0
\(871\) 42839.3 24733.3i 1.66654 0.962177i
\(872\) 1449.20 + 836.694i 0.0562798 + 0.0324932i
\(873\) 0 0
\(874\) 50012.6i 1.93559i
\(875\) 19173.5 19116.7i 0.740778 0.738588i
\(876\) 0 0
\(877\) 21668.1 37530.3i 0.834300 1.44505i −0.0602984 0.998180i \(-0.519205\pi\)
0.894599 0.446870i \(-0.147461\pi\)
\(878\) 30466.8 1.17108
\(879\) 0 0
\(880\) 3072.59i 0.117701i
\(881\) −48.3703 −0.00184976 −0.000924878 1.00000i \(-0.500294\pi\)
−0.000924878 1.00000i \(0.500294\pi\)
\(882\) 0 0
\(883\) 36776.7 1.40162 0.700812 0.713346i \(-0.252821\pi\)
0.700812 + 0.713346i \(0.252821\pi\)
\(884\) 13966.3i 0.531376i
\(885\) 0 0
\(886\) 25987.4 0.985400
\(887\) −13975.2 + 24205.7i −0.529019 + 0.916288i 0.470408 + 0.882449i \(0.344107\pi\)
−0.999427 + 0.0338392i \(0.989227\pi\)
\(888\) 0 0
\(889\) 6857.04 6836.76i 0.258693 0.257927i
\(890\) 21241.3i 0.800011i
\(891\) 0 0
\(892\) 20357.8 + 11753.6i 0.764159 + 0.441188i
\(893\) −6096.28 + 3519.69i −0.228448 + 0.131895i
\(894\) 0 0
\(895\) −18967.9 + 10951.1i −0.708410 + 0.409001i
\(896\) −5936.00 5953.61i −0.221326 0.221982i
\(897\) 0 0
\(898\) −59127.9 −2.19724
\(899\) −1141.73 + 1977.53i −0.0423567 + 0.0733640i
\(900\) 0 0
\(901\) 5821.30 3360.93i 0.215245 0.124272i
\(902\) −4700.04 + 8140.71i −0.173497 + 0.300506i
\(903\) 0 0
\(904\) 3570.97 + 6185.09i 0.131381 + 0.227559i
\(905\) −2113.03 1219.96i −0.0776129 0.0448098i
\(906\) 0 0
\(907\) −10805.4 18715.5i −0.395576 0.685158i 0.597598 0.801796i \(-0.296122\pi\)
−0.993175 + 0.116637i \(0.962788\pi\)
\(908\) 3626.25 + 6280.85i 0.132535 + 0.229557i
\(909\) 0 0
\(910\) −28237.2 + 28153.7i −1.02863 + 1.02559i
\(911\) 5927.13 + 3422.03i 0.215560 + 0.124453i 0.603892 0.797066i \(-0.293616\pi\)
−0.388333 + 0.921519i \(0.626949\pi\)
\(912\) 0 0
\(913\) 153.556i 0.00556624i
\(914\) 21140.4i 0.765057i
\(915\) 0 0
\(916\) −5399.19 3117.22i −0.194753 0.112441i
\(917\) 12212.2 + 45848.0i 0.439785 + 1.65107i
\(918\) 0 0
\(919\) 14558.6 + 25216.3i 0.522573 + 0.905124i 0.999655 + 0.0262648i \(0.00836130\pi\)
−0.477082 + 0.878859i \(0.658305\pi\)
\(920\) −1662.57 2879.66i −0.0595797 0.103195i
\(921\) 0 0
\(922\) −3177.14 1834.32i −0.113485 0.0655209i
\(923\) −3200.43 5543.31i −0.114132 0.197682i
\(924\) 0 0
\(925\) −8486.06 + 14698.3i −0.301643 + 0.522461i
\(926\) 39271.4 22673.3i 1.39367 0.804635i
\(927\) 0 0
\(928\) 21510.0 37256.4i 0.760883 1.31789i
\(929\) 22477.8 0.793834 0.396917 0.917854i \(-0.370080\pi\)
0.396917 + 0.917854i \(0.370080\pi\)
\(930\) 0 0
\(931\) 16967.2 + 29590.1i 0.597292 + 1.04165i
\(932\) 31564.9 18224.0i 1.10938 0.640501i
\(933\) 0 0
\(934\) 34858.8 20125.7i 1.22121 0.705068i
\(935\) 1080.83 + 624.019i 0.0378043 + 0.0218263i
\(936\) 0 0
\(937\) 25912.1i 0.903426i 0.892163 + 0.451713i \(0.149187\pi\)
−0.892163 + 0.451713i \(0.850813\pi\)
\(938\) −38576.3 38690.7i −1.34281 1.34680i
\(939\) 0 0
\(940\) −2389.28 + 4138.35i −0.0829038 + 0.143594i
\(941\) 39812.7 1.37923 0.689615 0.724176i \(-0.257780\pi\)
0.689615 + 0.724176i \(0.257780\pi\)
\(942\) 0 0
\(943\) 39085.6i 1.34974i
\(944\) 25965.7 0.895246
\(945\) 0 0
\(946\) 9228.94 0.317187
\(947\) 37664.1i 1.29242i 0.763161 + 0.646209i \(0.223646\pi\)
−0.763161 + 0.646209i \(0.776354\pi\)
\(948\) 0 0
\(949\) −70139.6 −2.39919
\(950\) −13694.8 + 23720.1i −0.467703 + 0.810086i
\(951\) 0 0
\(952\) 1459.93 388.870i 0.0497022 0.0132388i
\(953\) 18055.8i 0.613730i 0.951753 + 0.306865i \(0.0992801\pi\)
−0.951753 + 0.306865i \(0.900720\pi\)
\(954\) 0 0
\(955\) −6229.88 3596.82i −0.211093 0.121875i
\(956\) −18470.7 + 10664.0i −0.624879 + 0.360774i
\(957\) 0 0
\(958\) −493.233 + 284.768i −0.0166343 + 0.00960381i
\(959\) 5.92049 21.9654i 0.000199356 0.000739625i
\(960\) 0 0
\(961\) 29600.9 0.993619
\(962\) 35793.3 61995.8i 1.19961 2.07778i
\(963\) 0 0
\(964\) 5578.78 3220.91i 0.186391 0.107613i
\(965\) 2994.37 5186.41i 0.0998884 0.173012i
\(966\) 0 0
\(967\) −15995.7 27705.3i −0.531940 0.921348i −0.999305 0.0372829i \(-0.988130\pi\)
0.467364 0.884065i \(-0.345204\pi\)
\(968\) −3953.34 2282.46i −0.131266 0.0757862i
\(969\) 0 0
\(970\) −17762.1 30764.8i −0.587944 1.01835i
\(971\) 13431.5 + 23264.0i 0.443910 + 0.768874i 0.997976 0.0635987i \(-0.0202578\pi\)
−0.554066 + 0.832473i \(0.686924\pi\)
\(972\) 0 0
\(973\) −9329.07 + 34611.5i −0.307376 + 1.14038i
\(974\) 65079.7 + 37573.8i 2.14095 + 1.23608i
\(975\) 0 0
\(976\) 37291.5i 1.22303i
\(977\) 29282.8i 0.958894i 0.877571 + 0.479447i \(0.159163\pi\)
−0.877571 + 0.479447i \(0.840837\pi\)
\(978\) 0 0
\(979\) 4219.07 + 2435.88i 0.137734 + 0.0795210i
\(980\) 20018.2 + 11636.7i 0.652507 + 0.379306i
\(981\) 0 0
\(982\) 12086.4 + 20934.2i 0.392761 + 0.680283i
\(983\) −996.957 1726.78i −0.0323479 0.0560282i 0.849398 0.527752i \(-0.176965\pi\)
−0.881746 + 0.471724i \(0.843632\pi\)
\(984\) 0 0
\(985\) 33274.6 + 19211.1i 1.07636 + 0.621438i
\(986\) 7777.05 + 13470.2i 0.251188 + 0.435071i
\(987\) 0 0
\(988\) 30368.8 52600.3i 0.977894 1.69376i
\(989\) −33232.8 + 19187.0i −1.06849 + 0.616896i
\(990\) 0 0
\(991\) −8752.81 + 15160.3i −0.280567 + 0.485957i −0.971525 0.236939i \(-0.923856\pi\)
0.690957 + 0.722896i \(0.257189\pi\)
\(992\) 3581.47 0.114629
\(993\) 0 0
\(994\) −5006.49 + 4991.68i −0.159755 + 0.159282i
\(995\) 8009.93 4624.53i 0.255208 0.147344i
\(996\) 0 0
\(997\) −26709.1 + 15420.5i −0.848431 + 0.489842i −0.860121 0.510090i \(-0.829612\pi\)
0.0116900 + 0.999932i \(0.496279\pi\)
\(998\) 1901.96 + 1098.10i 0.0603261 + 0.0348293i
\(999\) 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.i.a.143.4 44
3.2 odd 2 63.4.i.a.38.19 yes 44
7.5 odd 6 189.4.s.a.89.4 44
9.4 even 3 63.4.s.a.59.19 yes 44
9.5 odd 6 189.4.s.a.17.4 44
21.5 even 6 63.4.s.a.47.19 yes 44
63.5 even 6 inner 189.4.i.a.152.19 44
63.40 odd 6 63.4.i.a.5.4 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.i.a.5.4 44 63.40 odd 6
63.4.i.a.38.19 yes 44 3.2 odd 2
63.4.s.a.47.19 yes 44 21.5 even 6
63.4.s.a.59.19 yes 44 9.4 even 3
189.4.i.a.143.4 44 1.1 even 1 trivial
189.4.i.a.152.19 44 63.5 even 6 inner
189.4.s.a.17.4 44 9.5 odd 6
189.4.s.a.89.4 44 7.5 odd 6