Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(25,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.t (of order \(6\), degree \(2\), 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: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 103.26 | ||
Character | \(\chi\) | \(=\) | 117.103 |
Dual form | 117.4.t.a.25.26 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.55219 | − | 0.896159i | 0.548783 | − | 0.316840i | −0.199848 | − | 0.979827i | \(-0.564045\pi\) |
0.748631 | + | 0.662987i | \(0.230712\pi\) | |||||||
\(3\) | −5.10957 | − | 0.944628i | −0.983337 | − | 0.181794i | ||||
\(4\) | −2.39380 | + | 4.14618i | −0.299225 | + | 0.518273i | ||||
\(5\) | −1.81395 | − | 1.04728i | −0.162244 | − | 0.0936719i | 0.416679 | − | 0.909054i | \(-0.363194\pi\) |
−0.578924 | + | 0.815382i | \(0.696527\pi\) | |||||||
\(6\) | −8.77757 | + | 3.11274i | −0.597238 | + | 0.211795i | ||||
\(7\) | 22.1814 | − | 12.8064i | 1.19768 | − | 0.691482i | 0.237643 | − | 0.971352i | \(-0.423625\pi\) |
0.960038 | + | 0.279871i | \(0.0902917\pi\) | |||||||
\(8\) | 22.9194i | 1.01291i | ||||||||
\(9\) | 25.2154 | + | 9.65328i | 0.933902 | + | 0.357529i | ||||
\(10\) | −3.75413 | −0.118716 | ||||||||
\(11\) | 32.5884 | − | 18.8149i | 0.893253 | − | 0.515720i | 0.0182476 | − | 0.999833i | \(-0.494191\pi\) |
0.875005 | + | 0.484114i | \(0.160858\pi\) | |||||||
\(12\) | 16.1479 | − | 18.9240i | 0.388458 | − | 0.455240i | ||||
\(13\) | 11.4875 | − | 45.4427i | 0.245081 | − | 0.969503i | ||||
\(14\) | 22.9532 | − | 39.7560i | 0.438178 | − | 0.758946i | ||||
\(15\) | 8.27920 | + | 7.06467i | 0.142512 | + | 0.121606i | ||||
\(16\) | 1.38905 | + | 2.40590i | 0.0217038 | + | 0.0375922i | ||||
\(17\) | 86.9156 | 1.24001 | 0.620004 | − | 0.784599i | \(-0.287131\pi\) | ||||
0.620004 | + | 0.784599i | \(0.287131\pi\) | |||||||
\(18\) | 47.7899 | − | 7.61321i | 0.625789 | − | 0.0996917i | ||||
\(19\) | 132.035i | 1.59425i | 0.603812 | + | 0.797127i | \(0.293648\pi\) | ||||
−0.603812 | + | 0.797127i | \(0.706352\pi\) | |||||||
\(20\) | 8.68446 | − | 5.01397i | 0.0970952 | − | 0.0560579i | ||||
\(21\) | −125.434 | + | 44.4821i | −1.30343 | + | 0.462228i | ||||
\(22\) | 33.7223 | − | 58.4088i | 0.326801 | − | 0.566036i | ||||
\(23\) | 35.1515 | − | 60.8841i | 0.318678 | − | 0.551966i | −0.661535 | − | 0.749915i | \(-0.730095\pi\) |
0.980212 | + | 0.197949i | \(0.0634279\pi\) | |||||||
\(24\) | 21.6503 | − | 117.108i | 0.184140 | − | 0.996027i | ||||
\(25\) | −60.3064 | − | 104.454i | −0.482451 | − | 0.835630i | ||||
\(26\) | −22.8931 | − | 80.8304i | −0.172681 | − | 0.609698i | ||||
\(27\) | −119.721 | − | 73.1432i | −0.853344 | − | 0.521349i | ||||
\(28\) | 122.624i | 0.827634i | ||||||||
\(29\) | 116.674 | + | 202.084i | 0.747094 | + | 1.29400i | 0.949210 | + | 0.314643i | \(0.101885\pi\) |
−0.202116 | + | 0.979362i | \(0.564782\pi\) | |||||||
\(30\) | 19.1820 | + | 3.54625i | 0.116738 | + | 0.0215818i | ||||
\(31\) | 57.7500 | + | 33.3420i | 0.334587 | + | 0.193174i | 0.657876 | − | 0.753126i | \(-0.271455\pi\) |
−0.323289 | + | 0.946300i | \(0.604788\pi\) | |||||||
\(32\) | −154.478 | − | 89.1881i | −0.853380 | − | 0.492699i | ||||
\(33\) | −184.286 | + | 65.3522i | −0.972123 | + | 0.344738i | ||||
\(34\) | 134.910 | − | 77.8902i | 0.680495 | − | 0.392884i | ||||
\(35\) | −53.6478 | −0.259089 | ||||||||
\(36\) | −100.385 | + | 81.4395i | −0.464744 | + | 0.377035i | ||||
\(37\) | − | 196.349i | − | 0.872420i | −0.899845 | − | 0.436210i | \(-0.856321\pi\) | ||
0.899845 | − | 0.436210i | \(-0.143679\pi\) | |||||||
\(38\) | 118.324 | + | 204.943i | 0.505123 | + | 0.874899i | ||||
\(39\) | −101.623 | + | 221.341i | −0.417247 | + | 0.908793i | ||||
\(40\) | 24.0031 | − | 41.5747i | 0.0948807 | − | 0.164338i | ||||
\(41\) | 258.552 | + | 149.275i | 0.984853 | + | 0.568605i | 0.903732 | − | 0.428099i | \(-0.140817\pi\) |
0.0811214 | + | 0.996704i | \(0.474150\pi\) | |||||||
\(42\) | −154.835 | + | 181.454i | −0.568848 | + | 0.666642i | ||||
\(43\) | −65.3625 | − | 113.211i | −0.231807 | − | 0.401501i | 0.726533 | − | 0.687132i | \(-0.241130\pi\) |
−0.958340 | + | 0.285630i | \(0.907797\pi\) | |||||||
\(44\) | 180.157i | 0.617265i | ||||||||
\(45\) | −35.6296 | − | 43.9182i | −0.118030 | − | 0.145487i | ||||
\(46\) | − | 126.005i | − | 0.403879i | ||||||
\(47\) | −182.692 | + | 105.477i | −0.566987 | + | 0.327350i | −0.755945 | − | 0.654635i | \(-0.772822\pi\) |
0.188958 | + | 0.981985i | \(0.439489\pi\) | |||||||
\(48\) | −4.82475 | − | 13.6052i | −0.0145082 | − | 0.0409114i | ||||
\(49\) | 156.509 | − | 271.081i | 0.456293 | − | 0.790323i | ||||
\(50\) | −187.214 | − | 108.088i | −0.529522 | − | 0.305720i | ||||
\(51\) | −444.101 | − | 82.1029i | −1.21935 | − | 0.225426i | ||||
\(52\) | 160.915 | + | 156.410i | 0.429132 | + | 0.417118i | ||||
\(53\) | 34.4933 | 0.0893966 | 0.0446983 | − | 0.999001i | \(-0.485767\pi\) | ||||
0.0446983 | + | 0.999001i | \(0.485767\pi\) | |||||||
\(54\) | −251.378 | − | 6.24350i | −0.633484 | − | 0.0157339i | ||||
\(55\) | −78.8183 | −0.193234 | ||||||||
\(56\) | 293.516 | + | 508.384i | 0.700405 | + | 1.21314i | ||||
\(57\) | 124.724 | − | 674.640i | 0.289825 | − | 1.56769i | ||||
\(58\) | 362.199 | + | 209.116i | 0.819985 | + | 0.473418i | ||||
\(59\) | 379.780 | + | 219.266i | 0.838019 | + | 0.483830i | 0.856590 | − | 0.515997i | \(-0.172579\pi\) |
−0.0185717 | + | 0.999828i | \(0.505912\pi\) | |||||||
\(60\) | −49.1102 | + | 17.4157i | −0.105668 | + | 0.0374725i | ||||
\(61\) | −289.638 | − | 501.667i | −0.607940 | − | 1.05298i | −0.991579 | − | 0.129500i | \(-0.958663\pi\) |
0.383640 | − | 0.923483i | \(-0.374670\pi\) | |||||||
\(62\) | 119.519 | 0.244821 | ||||||||
\(63\) | 682.935 | − | 108.795i | 1.36574 | − | 0.217570i | ||||
\(64\) | −341.932 | −0.667835 | ||||||||
\(65\) | −68.4291 | + | 70.4000i | −0.130578 | + | 0.134339i | ||||
\(66\) | −227.481 | + | 266.589i | −0.424257 | + | 0.497194i | ||||
\(67\) | −452.159 | − | 261.054i | −0.824477 | − | 0.476012i | 0.0274808 | − | 0.999622i | \(-0.491251\pi\) |
−0.851958 | + | 0.523610i | \(0.824585\pi\) | |||||||
\(68\) | −208.059 | + | 360.368i | −0.371041 | + | 0.642663i | ||||
\(69\) | −237.122 | + | 277.886i | −0.413711 | + | 0.484835i | ||||
\(70\) | −83.2717 | + | 48.0769i | −0.142184 | + | 0.0820899i | ||||
\(71\) | − | 760.015i | − | 1.27038i | −0.772355 | − | 0.635192i | \(-0.780921\pi\) | ||
0.772355 | − | 0.635192i | \(-0.219079\pi\) | |||||||
\(72\) | −221.248 | + | 577.922i | −0.362143 | + | 0.945954i | ||||
\(73\) | 724.442i | 1.16150i | 0.814082 | + | 0.580750i | \(0.197241\pi\) | ||||
−0.814082 | + | 0.580750i | \(0.802759\pi\) | |||||||
\(74\) | −175.960 | − | 304.771i | −0.276417 | − | 0.478769i | ||||
\(75\) | 209.470 | + | 590.681i | 0.322500 | + | 0.909412i | ||||
\(76\) | −547.440 | − | 316.065i | −0.826259 | − | 0.477041i | ||||
\(77\) | 481.904 | − | 834.682i | 0.713221 | − | 1.23534i | ||||
\(78\) | 40.6189 | + | 434.634i | 0.0589640 | + | 0.630930i | ||||
\(79\) | −341.980 | − | 592.327i | −0.487035 | − | 0.843570i | 0.512854 | − | 0.858476i | \(-0.328588\pi\) |
−0.999889 | + | 0.0149064i | \(0.995255\pi\) | |||||||
\(80\) | − | 5.81890i | − | 0.00813216i | ||||||
\(81\) | 542.628 | + | 486.822i | 0.744346 | + | 0.667794i | ||||
\(82\) | 535.096 | 0.720627 | ||||||||
\(83\) | −1097.62 | + | 633.711i | −1.45156 | + | 0.838058i | −0.998570 | − | 0.0534572i | \(-0.982976\pi\) |
−0.452990 | + | 0.891516i | \(0.649643\pi\) | |||||||
\(84\) | 115.834 | − | 626.556i | 0.150459 | − | 0.813843i | ||||
\(85\) | −157.660 | − | 91.0253i | −0.201184 | − | 0.116154i | ||||
\(86\) | −202.910 | − | 117.150i | −0.254423 | − | 0.146891i | ||||
\(87\) | −405.257 | − | 1142.78i | −0.499403 | − | 1.40826i | ||||
\(88\) | 431.228 | + | 746.908i | 0.522375 | + | 0.904780i | ||||
\(89\) | 1419.23i | 1.69032i | 0.534515 | + | 0.845159i | \(0.320494\pi\) | ||||
−0.534515 | + | 0.845159i | \(0.679506\pi\) | |||||||
\(90\) | −94.6617 | − | 36.2396i | −0.110869 | − | 0.0424444i | ||||
\(91\) | −327.150 | − | 1155.09i | −0.376864 | − | 1.33062i | ||||
\(92\) | 168.291 | + | 291.489i | 0.190713 | + | 0.330324i | ||||
\(93\) | −263.582 | − | 224.915i | −0.293894 | − | 0.250781i | ||||
\(94\) | −189.049 | + | 327.442i | −0.207435 | + | 0.359288i | ||||
\(95\) | 138.278 | − | 239.504i | 0.149337 | − | 0.258659i | ||||
\(96\) | 705.068 | + | 601.637i | 0.749591 | + | 0.639629i | ||||
\(97\) | 1224.12 | − | 706.747i | 1.28135 | − | 0.739786i | 0.304253 | − | 0.952591i | \(-0.401593\pi\) |
0.977095 | + | 0.212805i | \(0.0682599\pi\) | |||||||
\(98\) | − | 561.026i | − | 0.578288i | ||||||
\(99\) | 1003.35 | − | 159.840i | 1.01860 | − | 0.162268i | ||||
\(100\) | 577.446 | 0.577446 | ||||||||
\(101\) | 167.754 | + | 290.558i | 0.165269 | + | 0.286254i | 0.936751 | − | 0.349997i | \(-0.113818\pi\) |
−0.771482 | + | 0.636251i | \(0.780484\pi\) | |||||||
\(102\) | −762.908 | + | 270.546i | −0.740580 | + | 0.262628i | ||||
\(103\) | 866.357 | − | 1500.57i | 0.828784 | − | 1.43550i | −0.0702092 | − | 0.997532i | \(-0.522367\pi\) |
0.898993 | − | 0.437963i | \(-0.144300\pi\) | |||||||
\(104\) | 1041.52 | + | 263.287i | 0.982014 | + | 0.248244i | ||||
\(105\) | 274.117 | + | 50.6772i | 0.254772 | + | 0.0471008i | ||||
\(106\) | 53.5402 | − | 30.9115i | 0.0490593 | − | 0.0283244i | ||||
\(107\) | −78.4966 | −0.0709210 | −0.0354605 | − | 0.999371i | \(-0.511290\pi\) | ||||
−0.0354605 | + | 0.999371i | \(0.511290\pi\) | |||||||
\(108\) | 589.853 | − | 321.294i | 0.525543 | − | 0.286264i | ||||
\(109\) | 1254.99i | 1.10281i | 0.834237 | + | 0.551406i | \(0.185908\pi\) | ||||
−0.834237 | + | 0.551406i | \(0.814092\pi\) | |||||||
\(110\) | −122.341 | + | 70.6337i | −0.106043 | + | 0.0612241i | ||||
\(111\) | −185.476 | + | 1003.26i | −0.158600 | + | 0.857882i | ||||
\(112\) | 61.6219 | + | 35.5774i | 0.0519886 | + | 0.0300156i | ||||
\(113\) | 414.683 | − | 718.253i | 0.345222 | − | 0.597943i | −0.640172 | − | 0.768232i | \(-0.721137\pi\) |
0.985394 | + | 0.170289i | \(0.0544702\pi\) | |||||||
\(114\) | −410.989 | − | 1158.94i | −0.337655 | − | 0.952149i | ||||
\(115\) | −127.526 | + | 73.6271i | −0.103407 | + | 0.0597023i | ||||
\(116\) | −1117.17 | −0.894197 | ||||||||
\(117\) | 728.332 | − | 1034.96i | 0.575507 | − | 0.817797i | ||||
\(118\) | 785.988 | 0.613187 | ||||||||
\(119\) | 1927.91 | − | 1113.08i | 1.48513 | − | 0.857443i | ||||
\(120\) | −161.918 | + | 189.754i | −0.123175 | + | 0.144351i | ||||
\(121\) | 42.5035 | − | 73.6181i | 0.0319335 | − | 0.0553104i | ||||
\(122\) | −899.147 | − | 519.123i | −0.667254 | − | 0.385239i | ||||
\(123\) | −1180.08 | − | 1006.97i | −0.865073 | − | 0.738171i | ||||
\(124\) | −276.484 | + | 159.628i | −0.200234 | + | 0.115605i | ||||
\(125\) | 514.452i | 0.368112i | ||||||||
\(126\) | 962.548 | − | 780.889i | 0.680560 | − | 0.552120i | ||||
\(127\) | −1649.60 | −1.15259 | −0.576293 | − | 0.817243i | \(-0.695501\pi\) | ||||
−0.576293 | + | 0.817243i | \(0.695501\pi\) | |||||||
\(128\) | 705.083 | − | 407.080i | 0.486884 | − | 0.281103i | ||||
\(129\) | 227.032 | + | 640.204i | 0.154954 | + | 0.436952i | ||||
\(130\) | −43.1255 | + | 170.598i | −0.0290951 | + | 0.115095i | ||||
\(131\) | 25.4799 | − | 44.1325i | 0.0169938 | − | 0.0294341i | −0.857403 | − | 0.514645i | \(-0.827924\pi\) |
0.874397 | + | 0.485211i | \(0.161257\pi\) | |||||||
\(132\) | 170.181 | − | 920.523i | 0.112215 | − | 0.606979i | ||||
\(133\) | 1690.89 | + | 2928.71i | 1.10240 | + | 1.90941i | ||||
\(134\) | −935.783 | −0.603279 | ||||||||
\(135\) | 140.566 | + | 258.060i | 0.0896145 | + | 0.164520i | ||||
\(136\) | 1992.06i | 1.25601i | ||||||||
\(137\) | −122.257 | + | 70.5850i | −0.0762416 | + | 0.0440181i | −0.537636 | − | 0.843177i | \(-0.680683\pi\) |
0.461395 | + | 0.887195i | \(0.347349\pi\) | |||||||
\(138\) | −119.028 | + | 643.832i | −0.0734227 | + | 0.397149i | ||||
\(139\) | −828.509 | + | 1435.02i | −0.505563 | + | 0.875660i | 0.494417 | + | 0.869225i | \(0.335382\pi\) |
−0.999979 | + | 0.00643526i | \(0.997952\pi\) | |||||||
\(140\) | 128.422 | − | 222.434i | 0.0775260 | − | 0.134279i | ||||
\(141\) | 1033.11 | − | 366.368i | 0.617049 | − | 0.218821i | ||||
\(142\) | −681.094 | − | 1179.69i | −0.402508 | − | 0.697165i | ||||
\(143\) | −480.642 | − | 1697.04i | −0.281072 | − | 0.992404i | ||||
\(144\) | 11.8005 | + | 74.0744i | 0.00682898 | + | 0.0428671i | ||||
\(145\) | − | 488.761i | − | 0.279927i | ||||||
\(146\) | 649.215 | + | 1124.47i | 0.368010 | + | 0.637411i | ||||
\(147\) | −1055.76 | + | 1237.26i | −0.592366 | + | 0.694203i | ||||
\(148\) | 814.098 | + | 470.019i | 0.452151 | + | 0.261050i | ||||
\(149\) | 98.9880 | + | 57.1507i | 0.0544256 | + | 0.0314226i | 0.526966 | − | 0.849886i | \(-0.323330\pi\) |
−0.472540 | + | 0.881309i | \(0.656663\pi\) | |||||||
\(150\) | 854.481 | + | 729.132i | 0.465120 | + | 0.396889i | ||||
\(151\) | −2121.94 | + | 1225.10i | −1.14358 | + | 0.660247i | −0.947315 | − | 0.320304i | \(-0.896215\pi\) |
−0.196266 | + | 0.980551i | \(0.562882\pi\) | |||||||
\(152\) | −3026.16 | −1.61483 | ||||||||
\(153\) | 2191.61 | + | 839.021i | 1.15805 | + | 0.443339i | ||||
\(154\) | − | 1727.45i | − | 0.903908i | ||||||
\(155\) | −69.8370 | − | 120.961i | −0.0361899 | − | 0.0626828i | ||||
\(156\) | −674.456 | − | 951.192i | −0.346152 | − | 0.488181i | ||||
\(157\) | −1516.09 | + | 2625.94i | −0.770681 | + | 1.33486i | 0.166509 | + | 0.986040i | \(0.446751\pi\) |
−0.937190 | + | 0.348819i | \(0.886583\pi\) | |||||||
\(158\) | −1061.64 | − | 612.937i | −0.534553 | − | 0.308624i | ||||
\(159\) | −176.246 | − | 32.5833i | −0.0879069 | − | 0.0162517i | ||||
\(160\) | 186.810 | + | 323.565i | 0.0923041 | + | 0.159875i | ||||
\(161\) | − | 1800.66i | − | 0.881439i | ||||||
\(162\) | 1278.53 | + | 269.360i | 0.620068 | + | 0.130635i | ||||
\(163\) | − | 114.426i | − | 0.0549847i | −0.999622 | − | 0.0274923i | \(-0.991248\pi\) | ||
0.999622 | − | 0.0274923i | \(-0.00875219\pi\) | |||||||
\(164\) | −1237.84 | + | 714.668i | −0.589385 | + | 0.340282i | ||||
\(165\) | 402.727 | + | 74.4539i | 0.190014 | + | 0.0351287i | ||||
\(166\) | −1135.81 | + | 1967.28i | −0.531061 | + | 0.919824i | ||||
\(167\) | 203.998 | + | 117.778i | 0.0945259 | + | 0.0545746i | 0.546518 | − | 0.837447i | \(-0.315953\pi\) |
−0.451992 | + | 0.892022i | \(0.649286\pi\) | |||||||
\(168\) | −1019.50 | − | 2874.89i | −0.468193 | − | 1.32025i | ||||
\(169\) | −1933.07 | − | 1044.05i | −0.879870 | − | 0.475214i | ||||
\(170\) | −326.292 | −0.147209 | ||||||||
\(171\) | −1274.57 | + | 3329.30i | −0.569992 | + | 1.48888i | ||||
\(172\) | 625.859 | 0.277450 | ||||||||
\(173\) | −340.393 | − | 589.577i | −0.149593 | − | 0.259103i | 0.781484 | − | 0.623925i | \(-0.214463\pi\) |
−0.931077 | + | 0.364823i | \(0.881130\pi\) | |||||||
\(174\) | −1653.15 | − | 1410.64i | −0.720257 | − | 0.614598i | ||||
\(175\) | −2675.36 | − | 1544.62i | −1.15565 | − | 0.667212i | ||||
\(176\) | 90.5336 | + | 52.2696i | 0.0387740 | + | 0.0223862i | ||||
\(177\) | −1733.38 | − | 1479.10i | −0.736097 | − | 0.628115i | ||||
\(178\) | 1271.86 | + | 2202.92i | 0.535560 | + | 0.927618i | ||||
\(179\) | −2452.79 | −1.02419 | −0.512096 | − | 0.858928i | \(-0.671131\pi\) | ||||
−0.512096 | + | 0.858928i | \(0.671131\pi\) | |||||||
\(180\) | 267.383 | − | 42.5956i | 0.110720 | − | 0.0176383i | ||||
\(181\) | −219.252 | −0.0900382 | −0.0450191 | − | 0.998986i | \(-0.514335\pi\) | ||||
−0.0450191 | + | 0.998986i | \(0.514335\pi\) | |||||||
\(182\) | −1542.95 | − | 1499.75i | −0.628411 | − | 0.610818i | ||||
\(183\) | 1006.03 | + | 2836.90i | 0.406384 | + | 1.14596i | ||||
\(184\) | 1395.43 | + | 805.652i | 0.559089 | + | 0.322790i | ||||
\(185\) | −205.633 | + | 356.166i | −0.0817212 | + | 0.141545i | ||||
\(186\) | −610.689 | − | 112.901i | −0.240741 | − | 0.0445069i | ||||
\(187\) | 2832.44 | − | 1635.31i | 1.10764 | − | 0.639496i | ||||
\(188\) | − | 1009.97i | − | 0.391805i | ||||||
\(189\) | −3592.27 | − | 89.2217i | −1.38254 | − | 0.0343382i | ||||
\(190\) | − | 495.675i | − | 0.189263i | ||||||
\(191\) | −936.557 | − | 1622.16i | −0.354800 | − | 0.614532i | 0.632283 | − | 0.774737i | \(-0.282118\pi\) |
−0.987084 | + | 0.160205i | \(0.948785\pi\) | |||||||
\(192\) | 1747.12 | + | 322.998i | 0.656707 | + | 0.121408i | ||||
\(193\) | 1524.26 | + | 880.035i | 0.568492 | + | 0.328219i | 0.756547 | − | 0.653939i | \(-0.226885\pi\) |
−0.188055 | + | 0.982159i | \(0.560218\pi\) | |||||||
\(194\) | 1266.71 | − | 2194.01i | 0.468788 | − | 0.811964i | ||||
\(195\) | 416.145 | − | 295.074i | 0.152824 | − | 0.108362i | ||||
\(196\) | 749.301 | + | 1297.83i | 0.273069 | + | 0.472969i | ||||
\(197\) | 2858.25i | 1.03371i | 0.856072 | + | 0.516857i | \(0.172898\pi\) | ||||
−0.856072 | + | 0.516857i | \(0.827102\pi\) | |||||||
\(198\) | 1414.16 | − | 1147.27i | 0.507574 | − | 0.411781i | ||||
\(199\) | −2484.71 | −0.885108 | −0.442554 | − | 0.896742i | \(-0.645928\pi\) | ||||
−0.442554 | + | 0.896742i | \(0.645928\pi\) | |||||||
\(200\) | 2394.02 | − | 1382.19i | 0.846414 | − | 0.488677i | ||||
\(201\) | 2063.74 | + | 1760.99i | 0.724203 | + | 0.617965i | ||||
\(202\) | 520.773 | + | 300.668i | 0.181393 | + | 0.104727i | ||||
\(203\) | 5175.96 | + | 2988.34i | 1.78956 | + | 1.03320i | ||||
\(204\) | 1403.50 | − | 1644.79i | 0.481691 | − | 0.564501i | ||||
\(205\) | −312.666 | − | 541.554i | −0.106525 | − | 0.184506i | ||||
\(206\) | − | 3105.57i | − | 1.05037i | ||||||
\(207\) | 1474.09 | − | 1195.89i | 0.494958 | − | 0.401546i | ||||
\(208\) | 125.287 | − | 35.4842i | 0.0417649 | − | 0.0118288i | ||||
\(209\) | 2484.22 | + | 4302.80i | 0.822188 | + | 1.42407i | ||||
\(210\) | 470.897 | − | 166.992i | 0.154738 | − | 0.0548739i | ||||
\(211\) | −135.778 | + | 235.175i | −0.0443003 | + | 0.0767304i | −0.887325 | − | 0.461144i | \(-0.847439\pi\) |
0.843025 | + | 0.537874i | \(0.180773\pi\) | |||||||
\(212\) | −82.5700 | + | 143.015i | −0.0267497 | + | 0.0463318i | ||||
\(213\) | −717.932 | + | 3883.35i | −0.230948 | + | 1.24921i | ||||
\(214\) | −121.842 | + | 70.3454i | −0.0389202 | + | 0.0224706i | ||||
\(215\) | 273.812i | 0.0868551i | ||||||||
\(216\) | 1676.40 | − | 2743.93i | 0.528077 | − | 0.864356i | ||||
\(217\) | 1707.96 | 0.534305 | ||||||||
\(218\) | 1124.67 | + | 1947.99i | 0.349415 | + | 0.605204i | ||||
\(219\) | 684.328 | − | 3701.58i | 0.211153 | − | 1.14215i | ||||
\(220\) | 188.675 | − | 326.795i | 0.0578203 | − | 0.100148i | ||||
\(221\) | 998.443 | − | 3949.68i | 0.303903 | − | 1.20219i | ||||
\(222\) | 611.182 | + | 1723.46i | 0.184774 | + | 0.521042i | ||||
\(223\) | −1970.35 | + | 1137.58i | −0.591679 | + | 0.341606i | −0.765761 | − | 0.643125i | \(-0.777638\pi\) |
0.174082 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(224\) | −4568.72 | −1.36277 | ||||||||
\(225\) | −512.326 | − | 3215.99i | −0.151800 | − | 0.952887i | ||||
\(226\) | − | 1486.49i | − | 0.437521i | ||||||
\(227\) | −3153.37 | + | 1820.60i | −0.922010 | + | 0.532323i | −0.884276 | − | 0.466965i | \(-0.845347\pi\) |
−0.0377345 | + | 0.999288i | \(0.512014\pi\) | |||||||
\(228\) | 2498.62 | + | 2132.08i | 0.725767 | + | 0.619300i | ||||
\(229\) | −2915.57 | − | 1683.31i | −0.841338 | − | 0.485747i | 0.0163807 | − | 0.999866i | \(-0.494786\pi\) |
−0.857719 | + | 0.514119i | \(0.828119\pi\) | |||||||
\(230\) | −131.963 | + | 228.567i | −0.0378321 | + | 0.0655271i | ||||
\(231\) | −3250.78 | + | 3809.64i | −0.925913 | + | 1.08509i | ||||
\(232\) | −4631.66 | + | 2674.09i | −1.31070 | + | 0.756736i | ||||
\(233\) | 2786.25 | 0.783405 | 0.391702 | − | 0.920092i | \(-0.371886\pi\) | ||||
0.391702 | + | 0.920092i | \(0.371886\pi\) | |||||||
\(234\) | 203.022 | − | 2259.16i | 0.0567178 | − | 0.631136i | ||||
\(235\) | 441.859 | 0.122654 | ||||||||
\(236\) | −1818.23 | + | 1049.76i | −0.501512 | + | 0.289548i | ||||
\(237\) | 1187.84 | + | 3349.58i | 0.325564 | + | 0.918053i | ||||
\(238\) | 1994.99 | − | 3455.42i | 0.543344 | − | 0.941100i | ||||
\(239\) | −1873.82 | − | 1081.85i | −0.507143 | − | 0.292799i | 0.224515 | − | 0.974471i | \(-0.427920\pi\) |
−0.731659 | + | 0.681671i | \(0.761253\pi\) | |||||||
\(240\) | −5.49669 | + | 29.7321i | −0.00147838 | + | 0.00799665i | ||||
\(241\) | 2691.77 | − | 1554.10i | 0.719470 | − | 0.415386i | −0.0950875 | − | 0.995469i | \(-0.530313\pi\) |
0.814558 | + | 0.580083i | \(0.196980\pi\) | |||||||
\(242\) | − | 152.359i | − | 0.0404712i | ||||||
\(243\) | −2312.73 | − | 3000.03i | −0.610542 | − | 0.791984i | ||||
\(244\) | 2773.34 | 0.727643 | ||||||||
\(245\) | −567.797 | + | 327.818i | −0.148062 | + | 0.0854837i | ||||
\(246\) | −2734.11 | − | 505.466i | −0.708619 | − | 0.131006i | ||||
\(247\) | 6000.01 | + | 1516.75i | 1.54563 | + | 0.390722i | ||||
\(248\) | −764.179 | + | 1323.60i | −0.195667 | + | 0.338905i | ||||
\(249\) | 6206.99 | − | 2201.15i | 1.57973 | − | 0.560209i | ||||
\(250\) | 461.031 | + | 798.529i | 0.116633 | + | 0.202014i | ||||
\(251\) | 2756.79 | 0.693256 | 0.346628 | − | 0.938003i | \(-0.387327\pi\) | ||||
0.346628 | + | 0.938003i | \(0.387327\pi\) | |||||||
\(252\) | −1183.72 | + | 3092.01i | −0.295903 | + | 0.772929i | ||||
\(253\) | − | 2645.49i | − | 0.657393i | ||||||
\(254\) | −2560.50 | + | 1478.31i | −0.632520 | + | 0.365185i | ||||
\(255\) | 719.591 | + | 614.030i | 0.176716 | + | 0.150792i | ||||
\(256\) | 2097.34 | − | 3632.70i | 0.512047 | − | 0.886891i | ||||
\(257\) | 2375.80 | − | 4115.00i | 0.576646 | − | 0.998781i | −0.419214 | − | 0.907887i | \(-0.637694\pi\) |
0.995861 | − | 0.0908934i | \(-0.0289722\pi\) | |||||||
\(258\) | 926.121 | + | 790.263i | 0.223480 | + | 0.190696i | ||||
\(259\) | −2514.52 | − | 4355.28i | −0.603262 | − | 1.04488i | ||||
\(260\) | −128.086 | − | 452.243i | −0.0305521 | − | 0.107873i | ||||
\(261\) | 991.186 | + | 6221.91i | 0.235069 | + | 1.47558i | ||||
\(262\) | − | 91.3361i | − | 0.0215373i | ||||||
\(263\) | 2690.52 | + | 4660.12i | 0.630817 | + | 1.09261i | 0.987385 | + | 0.158337i | \(0.0506133\pi\) |
−0.356569 | + | 0.934269i | \(0.616053\pi\) | |||||||
\(264\) | −1497.84 | − | 4223.73i | −0.349187 | − | 0.984668i | ||||
\(265\) | −62.5690 | − | 36.1242i | −0.0145041 | − | 0.00837394i | ||||
\(266\) | 5249.17 | + | 3030.61i | 1.20995 | + | 0.698567i | ||||
\(267\) | 1340.65 | − | 7251.66i | 0.307289 | − | 1.66215i | ||||
\(268\) | 2164.75 | − | 1249.82i | 0.493408 | − | 0.284869i | ||||
\(269\) | −3491.60 | −0.791400 | −0.395700 | − | 0.918380i | \(-0.629498\pi\) | ||||
−0.395700 | + | 0.918380i | \(0.629498\pi\) | |||||||
\(270\) | 449.447 | + | 274.589i | 0.101305 | + | 0.0618924i | ||||
\(271\) | 1310.13i | 0.293671i | 0.989161 | + | 0.146836i | \(0.0469089\pi\) | ||||
−0.989161 | + | 0.146836i | \(0.953091\pi\) | |||||||
\(272\) | 120.730 | + | 209.110i | 0.0269129 | + | 0.0466146i | ||||
\(273\) | 580.459 | + | 6211.07i | 0.128685 | + | 1.37696i | ||||
\(274\) | −126.511 | + | 219.123i | −0.0278934 | + | 0.0483127i | ||||
\(275\) | −3930.58 | − | 2269.32i | −0.861902 | − | 0.497619i | ||||
\(276\) | −584.546 | − | 1648.35i | −0.127484 | − | 0.359490i | ||||
\(277\) | −1157.76 | − | 2005.30i | −0.251130 | − | 0.434971i | 0.712707 | − | 0.701462i | \(-0.247469\pi\) |
−0.963837 | + | 0.266491i | \(0.914136\pi\) | |||||||
\(278\) | 2969.90i | 0.640730i | ||||||||
\(279\) | 1134.33 | + | 1398.21i | 0.243406 | + | 0.300030i | ||||
\(280\) | − | 1229.58i | − | 0.262433i | ||||||
\(281\) | −524.677 | + | 302.922i | −0.111386 | + | 0.0643090i | −0.554658 | − | 0.832078i | \(-0.687151\pi\) |
0.443272 | + | 0.896387i | \(0.353818\pi\) | |||||||
\(282\) | 1275.27 | − | 1494.51i | 0.269295 | − | 0.315591i | ||||
\(283\) | 557.491 | − | 965.603i | 0.117100 | − | 0.202824i | −0.801517 | − | 0.597972i | \(-0.795973\pi\) |
0.918617 | + | 0.395148i | \(0.129307\pi\) | |||||||
\(284\) | 3151.16 | + | 1819.32i | 0.658405 | + | 0.380130i | ||||
\(285\) | −932.781 | + | 1093.14i | −0.193871 | + | 0.227200i | ||||
\(286\) | −2266.87 | − | 2203.40i | −0.468681 | − | 0.455559i | ||||
\(287\) | 7646.70 | 1.57272 | ||||||||
\(288\) | −3034.27 | − | 3740.13i | −0.620819 | − | 0.765241i | ||||
\(289\) | 2641.33 | 0.537620 | ||||||||
\(290\) | −438.007 | − | 758.651i | −0.0886920 | − | 0.153619i | ||||
\(291\) | −6922.34 | + | 2454.83i | −1.39448 | + | 0.494518i | ||||
\(292\) | −3003.67 | − | 1734.17i | −0.601974 | − | 0.347550i | ||||
\(293\) | −5434.62 | − | 3137.68i | −1.08360 | − | 0.625615i | −0.151733 | − | 0.988422i | \(-0.548485\pi\) |
−0.931865 | + | 0.362806i | \(0.881819\pi\) | |||||||
\(294\) | −529.961 | + | 2866.60i | −0.105129 | + | 0.568652i | ||||
\(295\) | −459.267 | − | 795.474i | −0.0906426 | − | 0.156998i | ||||
\(296\) | 4500.20 | 0.883679 | ||||||||
\(297\) | −5277.70 | − | 131.083i | −1.03112 | − | 0.0256101i | ||||
\(298\) | 204.864 | 0.0398238 | ||||||||
\(299\) | −2362.94 | − | 2296.78i | −0.457030 | − | 0.444235i | ||||
\(300\) | −2950.50 | − | 545.471i | −0.567824 | − | 0.104976i | ||||
\(301\) | −2899.66 | − | 1674.12i | −0.555261 | − | 0.320580i | ||||
\(302\) | −2195.77 | + | 3803.18i | −0.418385 | + | 0.724664i | ||||
\(303\) | −582.681 | − | 1643.09i | −0.110476 | − | 0.311529i | ||||
\(304\) | −317.662 | + | 183.402i | −0.0599315 | + | 0.0346014i | ||||
\(305\) | 1213.33i | 0.227787i | ||||||||
\(306\) | 4153.69 | − | 661.707i | 0.775983 | − | 0.123619i | ||||
\(307\) | − | 1362.75i | − | 0.253342i | −0.991945 | − | 0.126671i | \(-0.959571\pi\) | ||
0.991945 | − | 0.126671i | \(-0.0404293\pi\) | |||||||
\(308\) | 2307.16 | + | 3996.12i | 0.426827 | + | 0.739286i | ||||
\(309\) | −5844.20 | + | 6848.90i | −1.07594 | + | 1.26091i | ||||
\(310\) | −216.801 | − | 125.170i | −0.0397208 | − | 0.0229328i | ||||
\(311\) | 994.094 | − | 1721.82i | 0.181254 | − | 0.313941i | −0.761054 | − | 0.648689i | \(-0.775318\pi\) |
0.942308 | + | 0.334748i | \(0.108651\pi\) | |||||||
\(312\) | −5073.01 | − | 2329.13i | −0.920521 | − | 0.422632i | ||||
\(313\) | −140.018 | − | 242.518i | −0.0252853 | − | 0.0437954i | 0.853106 | − | 0.521738i | \(-0.174716\pi\) |
−0.878391 | + | 0.477942i | \(0.841383\pi\) | |||||||
\(314\) | 5434.62i | 0.976730i | ||||||||
\(315\) | −1352.75 | − | 517.877i | −0.241964 | − | 0.0926320i | ||||
\(316\) | 3274.53 | 0.582932 | ||||||||
\(317\) | 8467.60 | − | 4888.77i | 1.50028 | − | 0.866185i | 0.500277 | − | 0.865865i | \(-0.333231\pi\) |
1.00000 | 0.000320173i | \(-0.000101914\pi\) | ||||||||
\(318\) | −302.767 | + | 107.369i | −0.0533910 | + | 0.0189337i | ||||
\(319\) | 7604.41 | + | 4390.41i | 1.33469 | + | 0.770582i | ||||
\(320\) | 620.246 | + | 358.099i | 0.108353 | + | 0.0625573i | ||||
\(321\) | 401.084 | + | 74.1501i | 0.0697393 | + | 0.0128930i | ||||
\(322\) | −1613.67 | − | 2794.97i | −0.279275 | − | 0.483719i | ||||
\(323\) | 11475.9i | 1.97689i | ||||||||
\(324\) | −3317.40 | + | 1084.48i | −0.568826 | + | 0.185954i | ||||
\(325\) | −5439.43 | + | 1540.57i | −0.928385 | + | 0.262940i | ||||
\(326\) | −102.543 | − | 177.611i | −0.0174213 | − | 0.0301747i | ||||
\(327\) | 1185.50 | − | 6412.47i | 0.200484 | − | 1.08443i | ||||
\(328\) | −3421.30 | + | 5925.86i | −0.575943 | + | 0.997563i | ||||
\(329\) | −2701.57 | + | 4679.26i | −0.452713 | + | 0.784122i | ||||
\(330\) | 691.832 | − | 245.341i | 0.115406 | − | 0.0409259i | ||||
\(331\) | 4729.32 | − | 2730.48i | 0.785338 | − | 0.453415i | −0.0529805 | − | 0.998596i | \(-0.516872\pi\) |
0.838319 | + | 0.545180i | \(0.183539\pi\) | |||||||
\(332\) | − | 6067.91i | − | 1.00307i | ||||||
\(333\) | 1895.41 | − | 4951.00i | 0.311915 | − | 0.814755i | ||||
\(334\) | 422.192 | 0.0691656 | ||||||||
\(335\) | 546.795 | + | 947.076i | 0.0891779 | + | 0.154461i | ||||
\(336\) | −281.254 | − | 239.995i | −0.0456656 | − | 0.0389667i | ||||
\(337\) | 1424.22 | − | 2466.82i | 0.230214 | − | 0.398742i | −0.727657 | − | 0.685941i | \(-0.759391\pi\) |
0.957871 | + | 0.287199i | \(0.0927241\pi\) | |||||||
\(338\) | −3936.13 | + | 111.783i | −0.633424 | + | 0.0179887i | ||||
\(339\) | −2797.33 | + | 3278.24i | −0.448172 | + | 0.525220i | ||||
\(340\) | 754.815 | − | 435.793i | 0.120399 | − | 0.0695123i | ||||
\(341\) | 2509.31 | 0.398494 | ||||||||
\(342\) | 1005.21 | + | 6309.93i | 0.158934 | + | 0.997666i | ||||
\(343\) | 767.943i | 0.120889i | ||||||||
\(344\) | 2594.74 | − | 1498.07i | 0.406683 | − | 0.234798i | ||||
\(345\) | 721.152 | − | 255.738i | 0.112538 | − | 0.0399086i | ||||
\(346\) | −1056.71 | − | 610.092i | −0.164188 | − | 0.0947940i | ||||
\(347\) | −3662.05 | + | 6342.86i | −0.566539 | + | 0.981275i | 0.430365 | + | 0.902655i | \(0.358385\pi\) |
−0.996905 | + | 0.0786202i | \(0.974949\pi\) | |||||||
\(348\) | 5708.27 | + | 1055.31i | 0.879297 | + | 0.162559i | ||||
\(349\) | −1075.74 | + | 621.080i | −0.164995 | + | 0.0952597i | −0.580224 | − | 0.814457i | \(-0.697035\pi\) |
0.415229 | + | 0.909717i | \(0.363701\pi\) | |||||||
\(350\) | −5536.89 | −0.845598 | ||||||||
\(351\) | −4699.12 | + | 4600.20i | −0.714588 | + | 0.699546i | ||||
\(352\) | −6712.27 | −1.01638 | ||||||||
\(353\) | 2307.15 | − | 1332.04i | 0.347868 | − | 0.200842i | −0.315878 | − | 0.948800i | \(-0.602299\pi\) |
0.663746 | + | 0.747958i | \(0.268966\pi\) | |||||||
\(354\) | −4016.06 | − | 742.466i | −0.602969 | − | 0.111474i | ||||
\(355\) | −795.951 | + | 1378.63i | −0.118999 | + | 0.206113i | ||||
\(356\) | −5884.40 | − | 3397.36i | −0.876046 | − | 0.505786i | ||||
\(357\) | −10902.2 | + | 3866.19i | −1.61626 | + | 0.573167i | ||||
\(358\) | −3807.21 | + | 2198.09i | −0.562059 | + | 0.324505i | ||||
\(359\) | − | 12452.4i | − | 1.83068i | −0.402683 | − | 0.915340i | \(-0.631922\pi\) | ||
0.402683 | − | 0.915340i | \(-0.368078\pi\) | |||||||
\(360\) | 1006.58 | − | 816.611i | 0.147365 | − | 0.119553i | ||||
\(361\) | −10574.1 | −1.54165 | ||||||||
\(362\) | −340.322 | + | 196.485i | −0.0494114 | + | 0.0285277i | ||||
\(363\) | −286.716 | + | 336.007i | −0.0414564 | + | 0.0485834i | ||||
\(364\) | 5572.36 | + | 1408.64i | 0.802393 | + | 0.202838i | ||||
\(365\) | 758.696 | − | 1314.10i | 0.108800 | − | 0.188447i | ||||
\(366\) | 4103.87 | + | 3501.85i | 0.586101 | + | 0.500122i | ||||
\(367\) | 2875.27 | + | 4980.11i | 0.408959 | + | 0.708337i | 0.994773 | − | 0.102108i | \(-0.0325587\pi\) |
−0.585815 | + | 0.810445i | \(0.699225\pi\) | |||||||
\(368\) | 195.308 | 0.0276661 | ||||||||
\(369\) | 5078.48 | + | 6259.89i | 0.716464 | + | 0.883135i | ||||
\(370\) | 737.118i | 0.103570i | ||||||||
\(371\) | 765.108 | − | 441.735i | 0.107069 | − | 0.0618161i | ||||
\(372\) | 1563.50 | − | 554.456i | 0.217913 | − | 0.0772774i | ||||
\(373\) | 542.068 | − | 938.890i | 0.0752473 | − | 0.130332i | −0.825947 | − | 0.563748i | \(-0.809359\pi\) |
0.901194 | + | 0.433416i | \(0.142692\pi\) | |||||||
\(374\) | 2931.00 | − | 5076.64i | 0.405236 | − | 0.701889i | ||||
\(375\) | 485.966 | − | 2628.63i | 0.0669205 | − | 0.361978i | ||||
\(376\) | −2417.48 | − | 4187.20i | −0.331575 | − | 0.574304i | ||||
\(377\) | 10523.5 | − | 2980.51i | 1.43764 | − | 0.407173i | ||||
\(378\) | −5655.85 | + | 3080.76i | −0.769592 | + | 0.419199i | ||||
\(379\) | − | 3910.29i | − | 0.529969i | −0.964253 | − | 0.264984i | \(-0.914633\pi\) | ||
0.964253 | − | 0.264984i | \(-0.0853668\pi\) | |||||||
\(380\) | 662.018 | + | 1146.65i | 0.0893706 | + | 0.154794i | ||||
\(381\) | 8428.75 | + | 1558.26i | 1.13338 | + | 0.209533i | ||||
\(382\) | −2907.43 | − | 1678.61i | −0.389417 | − | 0.224830i | ||||
\(383\) | −3513.74 | − | 2028.66i | −0.468782 | − | 0.270652i | 0.246948 | − | 0.969029i | \(-0.420572\pi\) |
−0.715730 | + | 0.698377i | \(0.753906\pi\) | |||||||
\(384\) | −3987.21 | + | 1413.96i | −0.529874 | + | 0.187906i | ||||
\(385\) | −1748.30 | + | 1009.38i | −0.231432 | + | 0.133618i | ||||
\(386\) | 3154.60 | 0.415972 | ||||||||
\(387\) | −555.280 | − | 3485.62i | −0.0729366 | − | 0.457840i | ||||
\(388\) | 6767.24i | 0.885450i | ||||||||
\(389\) | −2137.24 | − | 3701.81i | −0.278567 | − | 0.482491i | 0.692462 | − | 0.721454i | \(-0.256526\pi\) |
−0.971029 | + | 0.238963i | \(0.923193\pi\) | |||||||
\(390\) | 381.504 | − | 830.942i | 0.0495339 | − | 0.107888i | ||||
\(391\) | 3055.21 | − | 5291.78i | 0.395163 | − | 0.684442i | ||||
\(392\) | 6213.02 | + | 3587.09i | 0.800523 | + | 0.462182i | ||||
\(393\) | −171.880 | + | 201.429i | −0.0220616 | + | 0.0258543i | ||||
\(394\) | 2561.44 | + | 4436.55i | 0.327522 | + | 0.567285i | ||||
\(395\) | 1432.60i | 0.182486i | ||||||||
\(396\) | −1739.10 | + | 4542.72i | −0.220690 | + | 0.576465i | ||||
\(397\) | 6909.83i | 0.873537i | 0.899574 | + | 0.436769i | \(0.143877\pi\) | ||||
−0.899574 | + | 0.436769i | \(0.856123\pi\) | |||||||
\(398\) | −3856.75 | + | 2226.69i | −0.485732 | + | 0.280438i | ||||
\(399\) | −5873.18 | − | 16561.7i | −0.736909 | − | 2.07800i | ||||
\(400\) | 167.537 | − | 290.182i | 0.0209421 | − | 0.0362728i | ||||
\(401\) | 4664.79 | + | 2693.22i | 0.580919 | + | 0.335394i | 0.761498 | − | 0.648167i | \(-0.224464\pi\) |
−0.180580 | + | 0.983560i | \(0.557797\pi\) | |||||||
\(402\) | 4781.45 | + | 883.967i | 0.593226 | + | 0.109672i | ||||
\(403\) | 2178.55 | − | 2241.30i | 0.269284 | − | 0.277040i | ||||
\(404\) | −1606.28 | −0.197810 | ||||||||
\(405\) | −474.459 | − | 1451.35i | −0.0582125 | − | 0.178070i | ||||
\(406\) | 10712.1 | 1.30944 | ||||||||
\(407\) | −3694.29 | − | 6398.69i | −0.449924 | − | 0.779291i | ||||
\(408\) | 1881.75 | − | 10178.5i | 0.228335 | − | 1.23508i | ||||
\(409\) | 3929.36 | + | 2268.62i | 0.475047 | + | 0.274269i | 0.718350 | − | 0.695682i | \(-0.244898\pi\) |
−0.243303 | + | 0.969950i | \(0.578231\pi\) | |||||||
\(410\) | −970.636 | − | 560.397i | −0.116918 | − | 0.0675025i | ||||
\(411\) | 691.355 | − | 245.171i | 0.0829734 | − | 0.0294244i | ||||
\(412\) | 4147.77 | + | 7184.15i | 0.495986 | + | 0.859072i | ||||
\(413\) | 11232.0 | 1.33824 | ||||||||
\(414\) | 1216.36 | − | 3177.26i | 0.144398 | − | 0.377184i | ||||
\(415\) | 2654.70 | 0.314010 | ||||||||
\(416\) | −5827.52 | + | 5995.36i | −0.686821 | + | 0.706603i | ||||
\(417\) | 5588.88 | − | 6549.70i | 0.656328 | − | 0.769161i | ||||
\(418\) | 7711.98 | + | 4452.52i | 0.902405 | + | 0.521004i | ||||
\(419\) | −8075.22 | + | 13986.7i | −0.941528 | + | 1.63078i | −0.178971 | + | 0.983854i | \(0.557277\pi\) |
−0.762557 | + | 0.646921i | \(0.776056\pi\) | |||||||
\(420\) | −866.298 | + | 1015.23i | −0.100645 | + | 0.117948i | ||||
\(421\) | 10636.6 | − | 6141.04i | 1.23135 | − | 0.710917i | 0.264035 | − | 0.964513i | \(-0.414947\pi\) |
0.967310 | + | 0.253596i | \(0.0816133\pi\) | |||||||
\(422\) | 486.716i | 0.0561444i | ||||||||
\(423\) | −5624.85 | + | 896.071i | −0.646547 | + | 0.102999i | ||||
\(424\) | 790.567i | 0.0905503i | ||||||||
\(425\) | −5241.57 | − | 9078.66i | −0.598243 | − | 1.03619i | ||||
\(426\) | 2365.73 | + | 6671.08i | 0.269061 | + | 0.758721i | ||||
\(427\) | −12849.1 | − | 7418.44i | −1.45624 | − | 0.840758i | ||||
\(428\) | 187.905 | − | 325.461i | 0.0212213 | − | 0.0367565i | ||||
\(429\) | 852.799 | + | 9125.18i | 0.0959755 | + | 1.02696i | ||||
\(430\) | 245.379 | + | 425.009i | 0.0275192 | + | 0.0476646i | ||||
\(431\) | − | 294.723i | − | 0.0329381i | −0.999864 | − | 0.0164690i | \(-0.994758\pi\) | ||
0.999864 | − | 0.0164690i | \(-0.00524250\pi\) | |||||||
\(432\) | 9.67742 | − | 389.635i | 0.00107779 | − | 0.0433943i | ||||
\(433\) | 10453.5 | 1.16019 | 0.580095 | − | 0.814549i | \(-0.303016\pi\) | ||||
0.580095 | + | 0.814549i | \(0.303016\pi\) | |||||||
\(434\) | 2651.09 | − | 1530.61i | 0.293217 | − | 0.169289i | ||||
\(435\) | −461.697 | + | 2497.36i | −0.0508889 | + | 0.275262i | ||||
\(436\) | −5203.43 | − | 3004.20i | −0.571557 | − | 0.329989i | ||||
\(437\) | 8038.81 | + | 4641.21i | 0.879974 | + | 0.508053i | ||||
\(438\) | −2255.00 | − | 6358.84i | −0.246000 | − | 0.693692i | ||||
\(439\) | −6709.76 | − | 11621.6i | −0.729475 | − | 1.26349i | −0.957105 | − | 0.289740i | \(-0.906431\pi\) |
0.227631 | − | 0.973748i | \(-0.426902\pi\) | |||||||
\(440\) | − | 1806.47i | − | 0.195727i | ||||||
\(441\) | 6563.24 | − | 5324.58i | 0.708697 | − | 0.574947i | ||||
\(442\) | −1989.76 | − | 7025.42i | −0.214125 | − | 0.756030i | ||||
\(443\) | −7673.42 | − | 13290.7i | −0.822968 | − | 1.42542i | −0.903462 | − | 0.428668i | \(-0.858983\pi\) |
0.0804936 | − | 0.996755i | \(-0.474350\pi\) | |||||||
\(444\) | −3715.69 | − | 3170.62i | −0.397160 | − | 0.338898i | ||||
\(445\) | 1486.34 | − | 2574.41i | 0.158335 | − | 0.274245i | ||||
\(446\) | −2038.91 | + | 3531.49i | −0.216469 | + | 0.374935i | ||||
\(447\) | −451.800 | − | 385.522i | −0.0478062 | − | 0.0407932i | ||||
\(448\) | −7584.51 | + | 4378.92i | −0.799853 | + | 0.461796i | ||||
\(449\) | 4351.64i | 0.457386i | 0.973499 | + | 0.228693i | \(0.0734453\pi\) | ||||
−0.973499 | + | 0.228693i | \(0.926555\pi\) | |||||||
\(450\) | −3677.27 | − | 4532.71i | −0.385218 | − | 0.474831i | ||||
\(451\) | 11234.4 | 1.17296 | ||||||||
\(452\) | 1985.34 | + | 3438.71i | 0.206598 | + | 0.357839i | ||||
\(453\) | 11999.4 | − | 4255.29i | 1.24455 | − | 0.441349i | ||||
\(454\) | −3263.09 | + | 5651.83i | −0.337322 | + | 0.584259i | ||||
\(455\) | −616.279 | + | 2437.90i | −0.0634980 | + | 0.251188i | ||||
\(456\) | 15462.4 | + | 2858.59i | 1.58792 | + | 0.293566i | ||||
\(457\) | −14985.3 | + | 8651.76i | −1.53388 | + | 0.885585i | −0.534701 | + | 0.845041i | \(0.679576\pi\) |
−0.999178 | + | 0.0405437i | \(0.987091\pi\) | |||||||
\(458\) | −6034.04 | −0.615616 | ||||||||
\(459\) | −10405.6 | − | 6357.29i | −1.05815 | − | 0.646477i | ||||
\(460\) | − | 704.994i | − | 0.0714576i | ||||||
\(461\) | −2492.68 | + | 1439.15i | −0.251835 | + | 0.145397i | −0.620604 | − | 0.784124i | \(-0.713113\pi\) |
0.368769 | + | 0.929521i | \(0.379779\pi\) | |||||||
\(462\) | −1631.80 | + | 8826.52i | −0.164325 | + | 0.888846i | ||||
\(463\) | −3902.43 | − | 2253.07i | −0.391709 | − | 0.226153i | 0.291192 | − | 0.956665i | \(-0.405948\pi\) |
−0.682900 | + | 0.730512i | \(0.739282\pi\) | |||||||
\(464\) | −324.130 | + | 561.409i | −0.0324296 | + | 0.0561698i | ||||
\(465\) | 242.573 | + | 684.029i | 0.0241915 | + | 0.0682174i | ||||
\(466\) | 4324.80 | − | 2496.92i | 0.429919 | − | 0.248214i | ||||
\(467\) | 2242.57 | 0.222214 | 0.111107 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111107 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(468\) | 2547.66 | + | 5497.29i | 0.251636 | + | 0.542975i | ||||
\(469\) | −13372.7 | −1.31661 | ||||||||
\(470\) | 685.849 | − | 395.975i | 0.0673104 | − | 0.0388617i | ||||
\(471\) | 10227.1 | − | 11985.3i | 1.00051 | − | 1.17251i | ||||
\(472\) | −5025.45 | + | 8704.33i | −0.490074 | + | 0.848833i | ||||
\(473\) | −4260.12 | − | 2459.58i | −0.414124 | − | 0.239095i | ||||
\(474\) | 4845.51 | + | 4134.70i | 0.469540 | + | 0.400660i | ||||
\(475\) | 13791.5 | − | 7962.53i | 1.33221 | − | 0.769150i | ||||
\(476\) | 10657.9i | 1.02627i | ||||||||
\(477\) | 869.761 | + | 332.973i | 0.0834876 | + | 0.0319619i | ||||
\(478\) | −3878.04 | −0.371082 | ||||||||
\(479\) | 2684.72 | − | 1550.03i | 0.256092 | − | 0.147855i | −0.366458 | − | 0.930434i | \(-0.619430\pi\) |
0.622551 | + | 0.782580i | \(0.286096\pi\) | |||||||
\(480\) | −648.872 | − | 1829.74i | −0.0617017 | − | 0.173992i | ||||
\(481\) | −8922.61 | − | 2255.55i | −0.845813 | − | 0.213814i | ||||
\(482\) | 2785.43 | − | 4824.51i | 0.263222 | − | 0.455914i | ||||
\(483\) | −1700.95 | + | 9200.58i | −0.160240 | + | 0.866751i | ||||
\(484\) | 203.490 | + | 352.454i | 0.0191106 | + | 0.0331005i | ||||
\(485\) | −2960.66 | −0.277189 | ||||||||
\(486\) | −6278.31 | − | 2584.05i | −0.585987 | − | 0.241183i | ||||
\(487\) | 16039.2i | 1.49241i | 0.665716 | + | 0.746205i | \(0.268126\pi\) | ||||
−0.665716 | + | 0.746205i | \(0.731874\pi\) | |||||||
\(488\) | 11497.9 | − | 6638.33i | 1.06657 | − | 0.615785i | ||||
\(489\) | −108.090 | + | 584.665i | −0.00999587 | + | 0.0540685i | ||||
\(490\) | −587.553 | + | 1017.67i | −0.0541693 | + | 0.0938240i | ||||
\(491\) | −549.688 | + | 952.088i | −0.0505236 | + | 0.0875094i | −0.890181 | − | 0.455607i | \(-0.849422\pi\) |
0.839658 | + | 0.543116i | \(0.182756\pi\) | |||||||
\(492\) | 6999.93 | − | 2482.35i | 0.641425 | − | 0.227465i | ||||
\(493\) | 10140.8 | + | 17564.3i | 0.926403 | + | 1.60458i | ||||
\(494\) | 10672.4 | − | 3022.68i | 0.972013 | − | 0.275297i | ||||
\(495\) | −1987.43 | − | 760.855i | −0.180461 | − | 0.0690866i | ||||
\(496\) | 185.254i | 0.0167705i | ||||||||
\(497\) | −9733.07 | − | 16858.2i | −0.878447 | − | 1.52151i | ||||
\(498\) | 7661.86 | − | 8979.05i | 0.689430 | − | 0.807953i | ||||
\(499\) | 1189.15 | + | 686.558i | 0.106681 | + | 0.0615923i | 0.552391 | − | 0.833585i | \(-0.313715\pi\) |
−0.445710 | + | 0.895177i | \(0.647049\pi\) | |||||||
\(500\) | −2133.01 | − | 1231.50i | −0.190783 | − | 0.110148i | ||||
\(501\) | −931.084 | − | 794.498i | −0.0830295 | − | 0.0708494i | ||||
\(502\) | 4279.07 | − | 2470.52i | 0.380447 | − | 0.219651i | ||||
\(503\) | −20268.8 | −1.79670 | −0.898350 | − | 0.439280i | \(-0.855234\pi\) | ||||
−0.898350 | + | 0.439280i | \(0.855234\pi\) | |||||||
\(504\) | 2493.53 | + | 15652.5i | 0.220378 | + | 1.38337i | ||||
\(505\) | − | 702.744i | − | 0.0619241i | ||||||
\(506\) | −2370.78 | − | 4106.31i | −0.208288 | − | 0.360766i | ||||
\(507\) | 8890.94 | + | 7160.66i | 0.778818 | + | 0.627250i | ||||
\(508\) | 3948.82 | − | 6839.55i | 0.344883 | − | 0.597354i | ||||
\(509\) | −8141.24 | − | 4700.35i | −0.708948 | − | 0.409311i | 0.101724 | − | 0.994813i | \(-0.467564\pi\) |
−0.810671 | + | 0.585502i | \(0.800898\pi\) | |||||||
\(510\) | 1667.21 | + | 308.225i | 0.144756 | + | 0.0267616i | ||||
\(511\) | 9277.50 | + | 16069.1i | 0.803156 | + | 1.39111i | ||||
\(512\) | − | 1004.92i | − | 0.0867418i | ||||||
\(513\) | 9657.44 | − | 15807.3i | 0.831162 | − | 1.36045i | ||||
\(514\) | − | 8516.36i | − | 0.730818i | ||||||
\(515\) | −3143.05 | + | 1814.64i | −0.268931 | + | 0.155267i | ||||
\(516\) | −3197.87 | − | 591.204i | −0.272826 | − | 0.0504386i | ||||
\(517\) | −3969.10 | + | 6874.68i | −0.337642 | + | 0.584813i | ||||
\(518\) | −7806.05 | − | 4506.82i | −0.662120 | − | 0.382275i | ||||
\(519\) | 1182.33 | + | 3334.03i | 0.0999970 | + | 0.281980i | ||||
\(520\) | −1613.53 | − | 1568.36i | −0.136073 | − | 0.132263i | ||||
\(521\) | 5247.88 | 0.441293 | 0.220647 | − | 0.975354i | \(-0.429183\pi\) | ||||
0.220647 | + | 0.975354i | \(0.429183\pi\) | |||||||
\(522\) | 7114.33 | + | 8769.34i | 0.596525 | + | 0.735295i | ||||
\(523\) | 8209.70 | 0.686396 | 0.343198 | − | 0.939263i | \(-0.388490\pi\) | ||||
0.343198 | + | 0.939263i | \(0.388490\pi\) | |||||||
\(524\) | 121.988 | + | 211.289i | 0.0101699 | + | 0.0176149i | ||||
\(525\) | 12210.8 | + | 10419.5i | 1.01509 | + | 0.866183i | ||||
\(526\) | 8352.42 | + | 4822.27i | 0.692362 | + | 0.399736i | ||||
\(527\) | 5019.38 | + | 2897.94i | 0.414891 | + | 0.239537i | ||||
\(528\) | −413.212 | − | 352.596i | −0.0340583 | − | 0.0290620i | ||||
\(529\) | 3612.25 | + | 6256.60i | 0.296889 | + | 0.514227i | ||||
\(530\) | −129.492 | −0.0106128 | ||||||||
\(531\) | 7459.64 | + | 9194.99i | 0.609644 | + | 0.751466i | ||||
\(532\) | −16190.6 | −1.31946 | ||||||||
\(533\) | 9753.56 | − | 10034.5i | 0.792633 | − | 0.815463i | ||||
\(534\) | −4417.70 | − | 12457.4i | −0.358001 | − | 1.00952i | ||||
\(535\) | 142.389 | + | 82.2082i | 0.0115065 | + | 0.00664331i | ||||
\(536\) | 5983.21 | − | 10363.2i | 0.482155 | − | 0.835117i | ||||
\(537\) | 12532.7 | + | 2316.98i | 1.00713 | + | 0.186192i | ||||
\(538\) | −5419.64 | + | 3129.03i | −0.434307 | + | 0.250747i | ||||
\(539\) | − | 11778.8i | − | 0.941278i | ||||||
\(540\) | −1406.45 | − | 34.9321i | −0.112081 | − | 0.00278378i | ||||
\(541\) | − | 3850.42i | − | 0.305993i | −0.988227 | − | 0.152997i | \(-0.951108\pi\) | ||
0.988227 | − | 0.152997i | \(-0.0488924\pi\) | |||||||
\(542\) | 1174.09 | + | 2033.58i | 0.0930468 | + | 0.161162i | ||||
\(543\) | 1120.29 | + | 207.112i | 0.0885378 | + | 0.0163684i | ||||
\(544\) | −13426.6 | − | 7751.84i | −1.05820 | − | 0.610951i | ||||
\(545\) | 1314.33 | − | 2276.49i | 0.103302 | − | 0.178925i | ||||
\(546\) | 6467.08 | + | 9120.59i | 0.506897 | + | 0.714881i | ||||
\(547\) | −3496.38 | − | 6055.91i | −0.273299 | − | 0.473368i | 0.696406 | − | 0.717648i | \(-0.254782\pi\) |
−0.969705 | + | 0.244281i | \(0.921448\pi\) | |||||||
\(548\) | − | 675.865i | − | 0.0526853i | ||||||
\(549\) | −2460.58 | − | 15445.7i | −0.191285 | − | 1.20074i | ||||
\(550\) | −8134.69 | −0.630662 | ||||||||
\(551\) | −26682.2 | + | 15404.9i | −2.06297 | + | 1.19106i | ||||
\(552\) | −6369.00 | − | 5434.69i | −0.491092 | − | 0.419051i | ||||
\(553\) | −15171.2 | − | 8759.08i | −1.16663 | − | 0.673552i | ||||
\(554\) | −3594.13 | − | 2075.07i | −0.275632 | − | 0.159136i | ||||
\(555\) | 1387.14 | − | 1625.61i | 0.106091 | − | 0.124330i | ||||
\(556\) | −3966.57 | − | 6870.30i | −0.302554 | − | 0.524039i | ||||
\(557\) | 9193.79i | 0.699378i | 0.936866 | + | 0.349689i | \(0.113713\pi\) | ||||
−0.936866 | + | 0.349689i | \(0.886287\pi\) | |||||||
\(558\) | 3013.71 | + | 1153.75i | 0.228639 | + | 0.0875305i | ||||
\(559\) | −5895.47 | + | 1669.74i | −0.446068 | + | 0.126337i | ||||
\(560\) | −74.5192 | − | 129.071i | −0.00562324 | − | 0.00973973i | ||||
\(561\) | −16017.3 | + | 5680.13i | −1.20544 | + | 0.427478i | ||||
\(562\) | −542.933 | + | 940.387i | −0.0407513 | + | 0.0705833i | ||||
\(563\) | −12479.7 | + | 21615.4i | −0.934201 | + | 1.61808i | −0.158149 | + | 0.987415i | \(0.550553\pi\) |
−0.776052 | + | 0.630669i | \(0.782781\pi\) | |||||||
\(564\) | −954.043 | + | 5160.49i | −0.0712277 | + | 0.385276i | ||||
\(565\) | −1504.43 | + | 868.582i | −0.112021 | + | 0.0646752i | ||||
\(566\) | − | 1998.40i | − | 0.148408i | ||||||
\(567\) | 18270.7 | + | 3849.25i | 1.35326 | + | 0.285103i | ||||
\(568\) | 17419.1 | 1.28678 | ||||||||
\(569\) | −5744.75 | − | 9950.20i | −0.423256 | − | 0.733100i | 0.573000 | − | 0.819555i | \(-0.305779\pi\) |
−0.996256 | + | 0.0864550i | \(0.972446\pi\) | |||||||
\(570\) | −468.228 | + | 2532.68i | −0.0344069 | + | 0.186110i | ||||
\(571\) | −4289.28 | + | 7429.25i | −0.314362 | + | 0.544491i | −0.979302 | − | 0.202406i | \(-0.935124\pi\) |
0.664940 | + | 0.746897i | \(0.268457\pi\) | |||||||
\(572\) | 8186.81 | + | 2069.55i | 0.598440 | + | 0.151280i | ||||
\(573\) | 3253.06 | + | 9173.25i | 0.237170 | + | 0.668793i | ||||
\(574\) | 11869.2 | − | 6852.66i | 0.863082 | − | 0.498301i | ||||
\(575\) | −8479.43 | −0.614986 | ||||||||
\(576\) | −8621.92 | − | 3300.76i | −0.623692 | − | 0.238770i | ||||
\(577\) | 8496.12i | 0.612995i | 0.951871 | + | 0.306497i | \(0.0991571\pi\) | ||||
−0.951871 | + | 0.306497i | \(0.900843\pi\) | |||||||
\(578\) | 4099.85 | − | 2367.05i | 0.295037 | − | 0.170339i | ||||
\(579\) | −6957.03 | − | 5936.46i | −0.499351 | − | 0.426098i | ||||
\(580\) | 2026.49 | + | 1170.00i | 0.145078 | + | 0.0837611i | ||||
\(581\) | −16231.1 | + | 28113.2i | −1.15900 | + | 2.00745i | ||||
\(582\) | −8544.89 | + | 10013.9i | −0.608586 | + | 0.713211i | ||||
\(583\) | 1124.08 | − | 648.989i | 0.0798537 | − | 0.0461036i | ||||
\(584\) | −16603.8 | −1.17649 | ||||||||
\(585\) | −2405.05 | + | 1114.60i | −0.169977 | + | 0.0787741i | ||||
\(586\) | −11247.4 | −0.792879 | ||||||||
\(587\) | 17341.7 | − | 10012.2i | 1.21937 | − | 0.704001i | 0.254584 | − | 0.967051i | \(-0.418062\pi\) |
0.964782 | + | 0.263049i | \(0.0847282\pi\) | |||||||
\(588\) | −2602.64 | − | 7339.14i | −0.182536 | − | 0.514730i | ||||
\(589\) | −4402.29 | + | 7625.00i | −0.307968 | + | 0.533417i | ||||
\(590\) | −1425.74 | − | 823.152i | −0.0994861 | − | 0.0574384i | ||||
\(591\) | 2699.98 | − | 14604.4i | 0.187923 | − | 1.01649i | ||||
\(592\) | 472.395 | − | 272.737i | 0.0327961 | − | 0.0189349i | ||||
\(593\) | 19765.3i | 1.36874i | 0.729134 | + | 0.684371i | \(0.239923\pi\) | ||||
−0.729134 | + | 0.684371i | \(0.760077\pi\) | |||||||
\(594\) | −8309.47 | + | 4526.19i | −0.573976 | + | 0.312646i | ||||
\(595\) | −4662.83 | −0.321273 | ||||||||
\(596\) | −473.915 | + | 273.615i | −0.0325710 | + | 0.0188049i | ||||
\(597\) | 12695.8 | + | 2347.13i | 0.870359 | + | 0.160907i | ||||
\(598\) | −5726.01 | − | 1447.48i | −0.391562 | − | 0.0989833i | ||||
\(599\) | 6205.69 | − | 10748.6i | 0.423302 | − | 0.733180i | −0.572959 | − | 0.819584i | \(-0.694204\pi\) |
0.996260 | + | 0.0864045i | \(0.0275378\pi\) | |||||||
\(600\) | −13538.1 | + | 4800.93i | −0.921148 | + | 0.326662i | ||||
\(601\) | 8504.08 | + | 14729.5i | 0.577186 | + | 0.999716i | 0.995800 | + | 0.0915515i | \(0.0291826\pi\) |
−0.418614 | + | 0.908164i | \(0.637484\pi\) | |||||||
\(602\) | −6001.11 | −0.406290 | ||||||||
\(603\) | −8881.32 | − | 10947.4i | −0.599793 | − | 0.739323i | ||||
\(604\) | − | 11730.6i | − | 0.790250i | ||||||
\(605\) | −154.198 | + | 89.0263i | −0.0103621 | + | 0.00598254i | ||||
\(606\) | −2376.90 | − | 2028.22i | −0.159332 | − | 0.135958i | ||||
\(607\) | 998.103 | − | 1728.77i | 0.0667409 | − | 0.115599i | −0.830724 | − | 0.556685i | \(-0.812073\pi\) |
0.897465 | + | 0.441086i | \(0.145407\pi\) | |||||||
\(608\) | 11775.9 | − | 20396.5i | 0.785488 | − | 1.36051i | ||||
\(609\) | −23624.0 | − | 20158.5i | −1.57191 | − | 1.34132i | ||||
\(610\) | 1087.34 | + | 1883.32i | 0.0721721 | + | 0.125006i | ||||
\(611\) | 2694.50 | + | 9513.69i | 0.178409 | + | 0.629923i | ||||
\(612\) | −8725.01 | + | 7078.36i | −0.576287 | + | 0.467526i | ||||
\(613\) | − | 14597.6i | − | 0.961814i | −0.876772 | − | 0.480907i | \(-0.840308\pi\) | ||
0.876772 | − | 0.480907i | \(-0.159692\pi\) | |||||||
\(614\) | −1221.24 | − | 2115.24i | −0.0802689 | − | 0.139030i | ||||
\(615\) | 1086.02 | + | 3062.46i | 0.0712075 | + | 0.200797i | ||||
\(616\) | 19130.4 | + | 11045.0i | 1.25128 | + | 0.722426i | ||||
\(617\) | −6061.63 | − | 3499.68i | −0.395514 | − | 0.228350i | 0.289033 | − | 0.957319i | \(-0.406666\pi\) |
−0.684546 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(618\) | −2933.61 | + | 15868.1i | −0.190950 | + | 1.03286i | ||||
\(619\) | −22686.0 | + | 13097.8i | −1.47307 | + | 0.850476i | −0.999541 | − | 0.0303034i | \(-0.990353\pi\) |
−0.473527 | + | 0.880779i | \(0.657019\pi\) | |||||||
\(620\) | 668.703 | 0.0433157 | ||||||||
\(621\) | −8661.62 | + | 4718.00i | −0.559708 | + | 0.304874i | ||||
\(622\) | − | 3563.46i | − | 0.229714i | ||||||
\(623\) | 18175.3 | + | 31480.5i | 1.16882 | + | 2.02446i | ||||
\(624\) | −673.682 | + | 62.9594i | −0.0432194 | + | 0.00403909i | ||||
\(625\) | −6999.52 | + | 12123.5i | −0.447969 | + | 0.775906i | ||||
\(626\) | −434.670 | − | 250.957i | −0.0277522 | − | 0.0160228i | ||||
\(627\) | −8628.76 | − | 24332.1i | −0.549600 | − | 1.54981i | ||||
\(628\) | −7258.42 | − | 12571.9i | −0.461214 | − | 0.798846i | ||||
\(629\) | − | 17065.8i | − | 1.08181i | ||||||
\(630\) | −2563.82 | + | 408.432i | −0.162135 | + | 0.0258291i | ||||
\(631\) | 16432.2i | 1.03670i | 0.855169 | + | 0.518350i | \(0.173453\pi\) | ||||
−0.855169 | + | 0.518350i | \(0.826547\pi\) | |||||||
\(632\) | 13575.8 | − | 7837.99i | 0.854456 | − | 0.493321i | ||||
\(633\) | 915.921 | − | 1073.38i | 0.0575112 | − | 0.0673983i | ||||
\(634\) | 8762.23 | − | 15176.6i | 0.548884 | − | 0.950695i | ||||
\(635\) | 2992.29 | + | 1727.60i | 0.187001 | + | 0.107965i | ||||
\(636\) | 556.994 | − | 652.749i | 0.0347268 | − | 0.0406968i | ||||
\(637\) | −10520.8 | − | 10226.2i | −0.654391 | − | 0.636071i | ||||
\(638\) | 15738.0 | 0.976605 | ||||||||
\(639\) | 7336.64 | − | 19164.1i | 0.454199 | − | 1.18641i | ||||
\(640\) | −1705.31 | −0.105326 | ||||||||
\(641\) | −8487.81 | − | 14701.3i | −0.523008 | − | 0.905877i | −0.999641 | − | 0.0267749i | \(-0.991476\pi\) |
0.476633 | − | 0.879102i | \(-0.341857\pi\) | |||||||
\(642\) | 689.009 | − | 244.339i | 0.0423567 | − | 0.0150207i | ||||
\(643\) | 6518.57 | + | 3763.50i | 0.399794 | + | 0.230821i | 0.686395 | − | 0.727229i | \(-0.259192\pi\) |
−0.286601 | + | 0.958050i | \(0.592525\pi\) | |||||||
\(644\) | 7465.85 | + | 4310.41i | 0.456826 | + | 0.263749i | ||||
\(645\) | 258.651 | − | 1399.06i | 0.0157897 | − | 0.0854078i | ||||
\(646\) | 10284.2 | + | 17812.8i | 0.626357 | + | 1.08488i | ||||
\(647\) | 18077.9 | 1.09848 | 0.549240 | − | 0.835664i | \(-0.314917\pi\) | ||||
0.549240 | + | 0.835664i | \(0.314917\pi\) | |||||||
\(648\) | −11157.7 | + | 12436.7i | −0.676412 | + | 0.753952i | ||||
\(649\) | 16501.9 | 0.998083 | ||||||||
\(650\) | −7062.44 | + | 7265.85i | −0.426172 | + | 0.438447i | ||||
\(651\) | −8726.96 | − | 1613.39i | −0.525402 | − | 0.0971333i | ||||
\(652\) | 474.430 | + | 273.912i | 0.0284971 | + | 0.0164528i | ||||
\(653\) | −12017.8 | + | 20815.4i | −0.720201 | + | 1.24743i | 0.240718 | + | 0.970595i | \(0.422617\pi\) |
−0.960919 | + | 0.276830i | \(0.910716\pi\) | |||||||
\(654\) | −3906.46 | − | 11015.8i | −0.233570 | − | 0.658641i | ||||
\(655\) | −92.4384 | + | 53.3693i | −0.00551430 | + | 0.00318368i | ||||
\(656\) | 829.399i | 0.0493637i | ||||||||
\(657\) | −6993.24 | + | 18267.1i | −0.415270 | + | 1.08473i | ||||
\(658\) | 9684.15i | 0.573750i | ||||||||
\(659\) | 15876.0 | + | 27498.0i | 0.938454 | + | 1.62545i | 0.768356 | + | 0.640023i | \(0.221075\pi\) |
0.170098 | + | 0.985427i | \(0.445592\pi\) | |||||||
\(660\) | −1272.75 | + | 1491.55i | −0.0750631 | + | 0.0879676i | ||||
\(661\) | 18503.2 | + | 10682.8i | 1.08879 | + | 0.628612i | 0.933254 | − | 0.359218i | \(-0.116957\pi\) |
0.155535 | + | 0.987830i | \(0.450290\pi\) | |||||||
\(662\) | 4893.88 | − | 8476.44i | 0.287320 | − | 0.497653i | ||||
\(663\) | −8832.59 | + | 19238.0i | −0.517390 | + | 1.12691i | ||||
\(664\) | −14524.3 | − | 25156.8i | −0.848874 | − | 1.47029i | ||||
\(665\) | − | 7083.37i | − | 0.413054i | ||||||
\(666\) | −1494.84 | − | 9383.49i | −0.0869730 | − | 0.545950i | ||||
\(667\) | 16405.0 | 0.952329 | ||||||||
\(668\) | −976.660 | + | 563.875i | −0.0565690 | + | 0.0326601i | ||||
\(669\) | 11142.2 | − | 3951.31i | 0.643922 | − | 0.228350i | ||||
\(670\) | 1697.46 | + | 980.030i | 0.0978786 | + | 0.0565102i | ||||
\(671\) | −18877.7 | − | 10899.0i | −1.08609 | − | 0.627053i | ||||
\(672\) | 23344.2 | + | 4315.74i | 1.34006 | + | 0.247743i | ||||
\(673\) | −10902.7 | − | 18884.1i | −0.624472 | − | 1.08162i | −0.988643 | − | 0.150285i | \(-0.951981\pi\) |
0.364171 | − | 0.931332i | \(-0.381353\pi\) | |||||||
\(674\) | − | 5105.30i | − | 0.291764i | ||||||
\(675\) | −420.152 | + | 16916.3i | −0.0239580 | + | 0.964605i | ||||
\(676\) | 8956.20 | − | 5515.65i | 0.509570 | − | 0.313817i | ||||
\(677\) | −3147.68 | − | 5451.93i | −0.178693 | − | 0.309505i | 0.762740 | − | 0.646705i | \(-0.223853\pi\) |
−0.941433 | + | 0.337200i | \(0.890520\pi\) | |||||||
\(678\) | −1404.18 | + | 7595.31i | −0.0795385 | + | 0.430230i | ||||
\(679\) | 18101.8 | − | 31353.2i | 1.02310 | − | 1.77206i | ||||
\(680\) | 2086.25 | − | 3613.49i | 0.117653 | − | 0.203781i | ||||
\(681\) | 17832.1 | − | 6323.71i | 1.00342 | − | 0.355837i | ||||
\(682\) | 3894.93 | − | 2248.74i | 0.218687 | − | 0.126259i | ||||
\(683\) | − | 6430.64i | − | 0.360266i | −0.983642 | − | 0.180133i | \(-0.942347\pi\) | ||
0.983642 | − | 0.180133i | \(-0.0576528\pi\) | |||||||
\(684\) | −10752.8 | − | 13254.3i | −0.601089 | − | 0.740921i | ||||
\(685\) | 295.690 | 0.0164930 | ||||||||
\(686\) | 688.198 | + | 1191.99i | 0.0383025 | + | 0.0663419i | ||||
\(687\) | 13307.2 | + | 11355.1i | 0.739013 | + | 0.630603i | ||||
\(688\) | 181.583 | − | 314.511i | 0.0100622 | − | 0.0174282i | ||||
\(689\) | 396.241 | − | 1567.47i | 0.0219094 | − | 0.0866702i | ||||
\(690\) | 890.185 | − | 1043.22i | 0.0491141 | − | 0.0575576i | ||||
\(691\) | −4054.50 | + | 2340.87i | −0.223214 | + | 0.128872i | −0.607437 | − | 0.794368i | \(-0.707802\pi\) |
0.384224 | + | 0.923240i | \(0.374469\pi\) | |||||||
\(692\) | 3259.33 | 0.179048 | ||||||||
\(693\) | 20208.8 | − | 16394.8i | 1.10775 | − | 0.898685i | ||||
\(694\) | 13127.1i | 0.718009i | ||||||||
\(695\) | 3005.74 | − | 1735.37i | 0.164049 | − | 0.0947140i | ||||
\(696\) | 26191.8 | − | 9288.25i | 1.42643 | − | 0.505848i | ||||
\(697\) | 22472.2 | + | 12974.3i | 1.22123 | + | 0.705075i | ||||
\(698\) | −1113.17 | + | 1928.07i | −0.0603641 | + | 0.104554i | ||||
\(699\) | −14236.5 | − | 2631.97i | −0.770351 | − | 0.142418i | ||||
\(700\) | 12808.5 | − | 7395.01i | 0.691596 | − | 0.399293i | ||||
\(701\) | 15104.6 | 0.813827 | 0.406914 | − | 0.913467i | \(-0.366605\pi\) | ||||
0.406914 | + | 0.913467i | \(0.366605\pi\) | |||||||
\(702\) | −3171.42 | + | 11351.6i | −0.170509 | + | 0.610309i | ||||
\(703\) | 25924.8 | 1.39086 | ||||||||
\(704\) | −11143.0 | + | 6433.42i | −0.596545 | + | 0.344416i | ||||
\(705\) | −2257.71 | − | 417.392i | −0.120610 | − | 0.0222977i | ||||
\(706\) | 2387.43 | − | 4135.15i | 0.127269 | − | 0.220437i | ||||
\(707\) | 7442.02 | + | 4296.65i | 0.395878 | + | 0.228561i | ||||
\(708\) | 10282.0 | − | 3646.25i | 0.545793 | − | 0.193552i | ||||
\(709\) | −6007.39 | + | 3468.37i | −0.318212 | + | 0.183720i | −0.650595 | − | 0.759425i | \(-0.725481\pi\) |
0.332383 | + | 0.943144i | \(0.392147\pi\) | |||||||
\(710\) | 2853.19i | 0.150815i | ||||||||
\(711\) | −2905.25 | − | 18237.0i | −0.153243 | − | 0.961941i | ||||
\(712\) | −32528.0 | −1.71213 | ||||||||
\(713\) | 4059.99 | − | 2344.04i | 0.213251 | − | 0.123120i | ||||
\(714\) | −13457.6 | + | 15771.2i | −0.705376 | + | 0.826641i | ||||
\(715\) | −905.424 | + | 3581.71i | −0.0473580 | + | 0.187341i | ||||
\(716\) | 5871.50 | − | 10169.7i | 0.306464 | − | 0.530811i | ||||
\(717\) | 8552.46 | + | 7297.85i | 0.445464 | + | 0.380116i | ||||
\(718\) | −11159.3 | − | 19328.6i | −0.580032 | − | 1.00465i | ||||
\(719\) | 25335.7 | 1.31414 | 0.657068 | − | 0.753831i | \(-0.271796\pi\) | ||||
0.657068 | + | 0.753831i | \(0.271796\pi\) | |||||||
\(720\) | 56.1715 | − | 146.726i | 0.00290748 | − | 0.00759464i | ||||
\(721\) | − | 44379.7i | − | 2.29235i | ||||||
\(722\) | −16413.1 | + | 9476.11i | −0.846029 | + | 0.488455i | ||||
\(723\) | −15221.8 | + | 5398.03i | −0.782996 | + | 0.277669i | ||||
\(724\) | 524.847 | − | 909.061i | 0.0269417 | − | 0.0466643i | ||||
\(725\) | 14072.3 | − | 24374.0i | 0.720873 | − | 1.24859i | ||||
\(726\) | −143.923 | + | 778.490i | −0.00735741 | + | 0.0397968i | ||||
\(727\) | 4248.18 | + | 7358.07i | 0.216721 | + | 0.375372i | 0.953804 | − | 0.300431i | \(-0.0971303\pi\) |
−0.737082 | + | 0.675803i | \(0.763797\pi\) | |||||||
\(728\) | 26474.1 | − | 7498.08i | 1.34780 | − | 0.381727i | ||||
\(729\) | 8983.14 | + | 17513.5i | 0.456391 | + | 0.889779i | ||||
\(730\) | − | 2719.65i | − | 0.137889i | ||||||
\(731\) | −5681.03 | − | 9839.83i | −0.287442 | − | 0.497865i | ||||
\(732\) | −14170.6 | − | 2619.77i | −0.715518 | − | 0.132281i | ||||
\(733\) | −2584.41 | − | 1492.11i | −0.130228 | − | 0.0751873i | 0.433471 | − | 0.901168i | \(-0.357289\pi\) |
−0.563699 | + | 0.825980i | \(0.690622\pi\) | |||||||
\(734\) | 8925.94 | + | 5153.39i | 0.448859 | + | 0.259149i | ||||
\(735\) | 3210.86 | − | 1138.65i | 0.161135 | − | 0.0571425i | ||||
\(736\) | −10860.3 | + | 6270.19i | −0.543907 | + | 0.314025i | ||||
\(737\) | −19646.8 | −0.981955 | ||||||||
\(738\) | 13492.6 | + | 5165.43i | 0.672995 | + | 0.257645i | ||||
\(739\) | 13882.8i | 0.691052i | 0.938409 | + | 0.345526i | \(0.112300\pi\) | ||||
−0.938409 | + | 0.345526i | \(0.887700\pi\) | |||||||
\(740\) | −984.487 | − | 1705.18i | −0.0489060 | − | 0.0847077i | ||||
\(741\) | −29224.7 | − | 13417.7i | −1.44885 | − | 0.665198i | ||||
\(742\) | 791.730 | − | 1371.32i | 0.0391716 | − | 0.0678472i | ||||
\(743\) | 20316.3 | + | 11729.6i | 1.00314 | + | 0.579164i | 0.909176 | − | 0.416411i | \(-0.136712\pi\) |
0.0939655 | + | 0.995575i | \(0.470046\pi\) | |||||||
\(744\) | 5154.93 | − | 6041.14i | 0.254017 | − | 0.297687i | ||||
\(745\) | −119.706 | − | 207.337i | −0.00588683 | − | 0.0101963i | ||||
\(746\) | − | 1943.12i | − | 0.0953653i | ||||||
\(747\) | −33794.3 | + | 5383.62i | −1.65524 | + | 0.263690i | ||||
\(748\) | 15658.4i | 0.765413i | ||||||||
\(749\) | −1741.16 | + | 1005.26i | −0.0849408 | + | 0.0490406i | ||||
\(750\) | −1601.36 | − | 4515.64i | −0.0779643 | − | 0.219850i | ||||
\(751\) | 6002.11 | − | 10396.0i | 0.291638 | − | 0.505132i | −0.682559 | − | 0.730830i | \(-0.739133\pi\) |
0.974197 | + | 0.225698i | \(0.0724664\pi\) | |||||||
\(752\) | −507.536 | − | 293.026i | −0.0246116 | − | 0.0142095i | ||||
\(753\) | −14086.0 | − | 2604.14i | −0.681704 | − | 0.126030i | ||||
\(754\) | 13663.6 | − | 14057.1i | 0.659943 | − | 0.678951i | ||||
\(755\) | 5132.11 | 0.247386 | ||||||||
\(756\) | 8969.11 | − | 14680.6i | 0.431486 | − | 0.706256i | ||||
\(757\) | −5735.67 | −0.275385 | −0.137693 | − | 0.990475i | \(-0.543969\pi\) | ||||
−0.137693 | + | 0.990475i | \(0.543969\pi\) | |||||||
\(758\) | −3504.24 | − | 6069.52i | −0.167915 | − | 0.290838i | ||||
\(759\) | −2499.00 | + | 13517.3i | −0.119510 | + | 0.646439i | ||||
\(760\) | 5489.30 | + | 3169.25i | 0.261997 | + | 0.151264i | ||||
\(761\) | 5758.79 | + | 3324.84i | 0.274318 | + | 0.158378i | 0.630848 | − | 0.775906i | \(-0.282707\pi\) |
−0.356530 | + | 0.934284i | \(0.616040\pi\) | |||||||
\(762\) | 14479.5 | − | 5134.78i | 0.688368 | − | 0.244112i | ||||
\(763\) | 16072.0 | + | 27837.4i | 0.762574 | + | 1.32082i | ||||
\(764\) | 8967.72 | 0.424661 | ||||||||
\(765\) | −3096.77 | − | 3817.18i | −0.146358 | − | 0.180406i | ||||
\(766\) | −7271.99 | −0.343013 | ||||||||
\(767\) | 14326.7 | − | 14739.4i | 0.674457 | − | 0.693883i | ||||
\(768\) | −14148.1 | + | 16580.3i | −0.664745 | + | 0.779025i | ||||
\(769\) | 14466.5 | + | 8352.23i | 0.678381 | + | 0.391663i | 0.799245 | − | 0.601006i | \(-0.205233\pi\) |
−0.120864 | + | 0.992669i | \(0.538567\pi\) | |||||||
\(770\) | −1809.13 | + | 3133.50i | −0.0846707 | + | 0.146654i | ||||
\(771\) | −16026.4 | + | 18781.6i | −0.748610 | + | 0.877307i | ||||
\(772\) | −7297.57 | + | 4213.25i | −0.340214 | + | 0.196423i | ||||
\(773\) | 27948.9i | 1.30045i | 0.759740 | + | 0.650227i | \(0.225326\pi\) | ||||
−0.759740 | + | 0.650227i | \(0.774674\pi\) | |||||||
\(774\) | −3985.57 | − | 4912.74i | −0.185088 | − | 0.228146i | ||||
\(775\) | − | 8042.93i | − | 0.372788i | ||||||
\(776\) | 16198.2 | + | 28056.2i | 0.749334 | + | 1.29788i | ||||
\(777\) | 8734.00 | + | 24628.9i | 0.403257 | + | 1.13714i | ||||
\(778\) | −6634.82 | − | 3830.61i | −0.305745 | − | 0.176522i | ||||
\(779\) | −19709.5 | + | 34137.8i | −0.906501 | + | 1.57011i | ||||
\(780\) | 227.261 | + | 2431.76i | 0.0104324 | + | 0.111629i | ||||
\(781\) | −14299.6 | − | 24767.7i | −0.655162 | − | 1.13477i | ||||
\(782\) | − | 10951.8i | − | 0.500813i | ||||||
\(783\) | 812.859 | − | 32727.6i | 0.0370999 | − | 1.49373i | ||||
\(784\) | 869.591 | 0.0396133 | ||||||||
\(785\) | 5500.21 | − | 3175.55i | 0.250077 | − | 0.144382i | ||||
\(786\) | −86.2786 | + | 466.688i | −0.00391534 | + | 0.0211784i | ||||
\(787\) | −21103.6 | − | 12184.2i | −0.955862 | − | 0.551867i | −0.0609648 | − | 0.998140i | \(-0.519418\pi\) |
−0.894897 | + | 0.446273i | \(0.852751\pi\) | |||||||
\(788\) | −11850.8 | − | 6842.08i | −0.535746 | − | 0.309313i | ||||
\(789\) | −9345.33 | − | 26352.8i | −0.421676 | − | 1.18908i | ||||
\(790\) | 1283.84 | + | 2223.67i | 0.0578188 | + | 0.100145i | ||||
\(791\) | − | 21242.4i | − | 0.954859i | ||||||
\(792\) | 3663.44 | + | 22996.3i | 0.164362 | + | 1.03174i | ||||
\(793\) | −26124.3 | + | 7399.02i | −1.16986 | + | 0.331333i | ||||
\(794\) | 6192.30 | + | 10725.4i | 0.276771 | + | 0.479382i | ||||
\(795\) | 285.577 | + | 243.684i | 0.0127401 | + | 0.0108712i | ||||
\(796\) | 5947.90 | − | 10302.1i | 0.264846 | − | 0.458727i | ||||
\(797\) | −743.175 | + | 1287.22i | −0.0330296 | + | 0.0572090i | −0.882068 | − | 0.471123i | \(-0.843849\pi\) |
0.849038 | + | 0.528332i | \(0.177182\pi\) | |||||||
\(798\) | −23958.2 | − | 20443.6i | −1.06280 | − | 0.906888i | ||||
\(799\) | −15878.8 | + | 9167.63i | −0.703068 | + | 0.405917i | ||||
\(800\) | 21514.5i | 0.950814i | ||||||||
\(801\) | −13700.2 | + | 35786.5i | −0.604338 | + | 1.57859i | ||||
\(802\) | 9654.19 | 0.425064 | ||||||||
\(803\) | 13630.3 | + | 23608.4i | 0.599008 | + | 1.03751i | ||||
\(804\) | −12241.6 | + | 4341.16i | −0.536974 | + | 0.190424i | ||||
\(805\) | −1885.80 | + | 3266.30i | −0.0825660 | + | 0.143009i | ||||
\(806\) | 1372.97 | − | 5431.25i | 0.0600010 | − | 0.237354i | ||||
\(807\) | 17840.6 | + | 3298.26i | 0.778213 | + | 0.143872i | ||||
\(808\) | −6659.43 | + | 3844.83i | −0.289948 | + | 0.167402i | ||||
\(809\) | −35576.9 | −1.54613 | −0.773064 | − | 0.634328i | \(-0.781277\pi\) | ||||
−0.773064 | + | 0.634328i | \(0.781277\pi\) | |||||||
\(810\) | −2037.10 | − | 1827.59i | −0.0883657 | − | 0.0792778i | ||||
\(811\) | − | 31468.0i | − | 1.36250i | −0.732049 | − | 0.681252i | \(-0.761436\pi\) | ||
0.732049 | − | 0.681252i | \(-0.238564\pi\) | |||||||
\(812\) | −24780.4 | + | 14307.0i | −1.07096 | + | 0.618321i | ||||
\(813\) | 1237.59 | − | 6694.21i | 0.0533876 | − | 0.288778i | ||||
\(814\) | −11468.5 | − | 6621.33i | −0.493821 | − | 0.285108i | ||||
\(815\) | −119.836 | + | 207.562i | −0.00515052 | + | 0.00892096i | ||||
\(816\) | −419.346 | − | 1182.51i | −0.0179902 | − | 0.0507304i | ||||
\(817\) | 14947.8 | − | 8630.12i | 0.640095 | − | 0.369559i | ||||
\(818\) | 8132.16 | 0.347597 | ||||||||
\(819\) | 2901.25 | − | 32284.2i | 0.123783 | − | 1.37741i | ||||
\(820\) | 2993.84 | 0.127499 | ||||||||
\(821\) | −33470.8 | + | 19324.4i | −1.42283 | + | 0.821469i | −0.996540 | − | 0.0831194i | \(-0.973512\pi\) |
−0.426286 | + | 0.904588i | \(0.640178\pi\) | |||||||
\(822\) | 853.404 | − | 1000.12i | 0.0362115 | − | 0.0424369i | ||||
\(823\) | 20690.5 | − | 35837.1i | 0.876339 | − | 1.51786i | 0.0210099 | − | 0.999779i | \(-0.493312\pi\) |
0.855329 | − | 0.518085i | \(-0.173355\pi\) | |||||||
\(824\) | 34392.3 | + | 19856.4i | 1.45402 | + | 0.839479i | ||||
\(825\) | 17939.9 | + | 15308.2i | 0.757075 | + | 0.646015i | ||||
\(826\) | 17434.3 | − | 10065.7i | 0.734402 | − | 0.424007i | ||||
\(827\) | − | 9106.80i | − | 0.382920i | −0.981500 | − | 0.191460i | \(-0.938678\pi\) | ||
0.981500 | − | 0.191460i | \(-0.0613222\pi\) | |||||||
\(828\) | 1429.70 | + | 8974.56i | 0.0600066 | + | 0.376676i | ||||
\(829\) | −8360.15 | −0.350253 | −0.175127 | − | 0.984546i | \(-0.556033\pi\) | ||||
−0.175127 | + | 0.984546i | \(0.556033\pi\) | |||||||
\(830\) | 4120.61 | − | 2379.03i | 0.172323 | − | 0.0994909i | ||||
\(831\) | 4021.39 | + | 11339.9i | 0.167871 | + | 0.473376i | ||||
\(832\) | −3927.94 | + | 15538.3i | −0.163674 | + | 0.647468i | ||||
\(833\) | 13603.0 | − | 23561.2i | 0.565807 | − | 0.980007i | ||||
\(834\) | 2805.45 | − | 15174.9i | 0.116481 | − | 0.630053i | ||||
\(835\) | −246.694 | − | 427.287i | −0.0102242 | − | 0.0177088i | ||||
\(836\) | −23786.9 | −0.984077 | ||||||||
\(837\) | −4475.14 | − | 8215.75i | −0.184807 | − | 0.339280i | ||||
\(838\) | 28946.7i | 1.19326i | ||||||||
\(839\) | −19475.3 | + | 11244.1i | −0.801384 | + | 0.462679i | −0.843955 | − | 0.536414i | \(-0.819778\pi\) |
0.0425710 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(840\) | −1161.49 | + | 6282.61i | −0.0477087 | + | 0.258060i | ||||
\(841\) | −15030.9 | + | 26034.3i | −0.616299 | + | 1.06746i | ||||
\(842\) | 11006.7 | − | 19064.2i | 0.450494 | − | 0.780278i | ||||
\(843\) | 2967.02 | − | 1052.18i | 0.121221 | − | 0.0429880i | ||||
\(844\) | −650.052 | − | 1125.92i | −0.0265115 | − | 0.0459193i | ||||
\(845\) | 2413.09 | + | 3918.32i | 0.0982399 | + | 0.159520i | ||||
\(846\) | −7927.83 | + | 6431.63i | −0.322180 | + | 0.261376i | ||||
\(847\) | − | 2177.27i | − | 0.0883256i | ||||||
\(848\) | 47.9128 | + | 82.9873i | 0.00194025 | + | 0.00336061i | ||||
\(849\) | −3760.68 | + | 4407.19i | −0.152021 | + | 0.178156i | ||||
\(850\) | −16271.8 | − | 9394.55i | −0.656611 | − | 0.379095i | ||||
\(851\) | −11954.5 | − | 6901.94i | −0.481546 | − | 0.278021i | ||||
\(852\) | −14382.5 | − | 12272.6i | −0.578329 | − | 0.493490i | ||||
\(853\) | 38256.6 | − | 22087.4i | 1.53562 | − | 0.886588i | 0.536528 | − | 0.843883i | \(-0.319736\pi\) |
0.999088 | − | 0.0427051i | \(-0.0135976\pi\) | |||||||
\(854\) | −26592.4 | −1.06554 | ||||||||
\(855\) | 5798.72 | − | 4704.34i | 0.231944 | − | 0.188170i | ||||
\(856\) | − | 1799.10i | − | 0.0718363i | ||||||
\(857\) | 214.752 | + | 371.962i | 0.00855986 | + | 0.0148261i | 0.870274 | − | 0.492569i | \(-0.163942\pi\) |
−0.861714 | + | 0.507395i | \(0.830609\pi\) | |||||||
\(858\) | 9501.31 | + | 13399.8i | 0.378053 | + | 0.533171i | ||||
\(859\) | −1296.12 | + | 2244.95i | −0.0514821 | + | 0.0891697i | −0.890618 | − | 0.454752i | \(-0.849728\pi\) |
0.839136 | + | 0.543922i | \(0.183061\pi\) | |||||||
\(860\) | −1135.28 | − | 655.452i | −0.0450146 | − | 0.0259892i | ||||
\(861\) | −39071.4 | − | 7223.29i | −1.54651 | − | 0.285911i | ||||
\(862\) | −264.119 | − | 457.467i | −0.0104361 | − | 0.0180759i | ||||
\(863\) | 22257.5i | 0.877932i | 0.898504 | + | 0.438966i | \(0.144655\pi\) | ||||
−0.898504 | + | 0.438966i | \(0.855345\pi\) | |||||||
\(864\) | 11970.8 | + | 21976.7i | 0.471359 | + | 0.865351i | ||||
\(865\) | 1425.95i | 0.0560506i | ||||||||
\(866\) | 16225.8 | − | 9367.97i | 0.636692 | − | 0.367594i | ||||
\(867\) | −13496.0 | − | 2495.07i | −0.528661 | − | 0.0977359i | ||||
\(868\) | −4088.53 | + | 7081.53i | −0.159877 | + | 0.276916i | ||||
\(869\) | −22289.2 | − | 12868.7i | −0.870091 | − | 0.502347i | ||||
\(870\) | 1521.38 | + | 4290.13i | 0.0592871 | + | 0.167183i | ||||
\(871\) | −17057.2 | + | 17548.4i | −0.663559 | + | 0.682671i | ||||
\(872\) | −28763.7 | −1.11704 | ||||||||
\(873\) | 37689.1 | − | 6004.09i | 1.46115 | − | 0.232769i | ||||
\(874\) | 16637.0 | 0.643886 | ||||||||
\(875\) | 6588.29 | + | 11411.3i | 0.254543 | + | 0.440881i | ||||
\(876\) | 13709.3 | + | 11698.2i | 0.528761 | + | 0.451194i | ||||
\(877\) | −29361.3 | − | 16951.8i | −1.13051 | − | 0.652703i | −0.186450 | − | 0.982464i | \(-0.559698\pi\) |
−0.944064 | + | 0.329762i | \(0.893032\pi\) | |||||||
\(878\) | −20829.7 | − | 12026.0i | −0.800646 | − | 0.462253i | ||||
\(879\) | 24804.6 | + | 21165.9i | 0.951808 | + | 0.812182i | ||||
\(880\) | −109.482 | − | 189.629i | −0.00419391 | − | 0.00726407i | ||||
\(881\) | −9325.22 | −0.356611 | −0.178306 | − | 0.983975i | \(-0.557062\pi\) | ||||
−0.178306 | + | 0.983975i | \(0.557062\pi\) | |||||||
\(882\) | 5415.74 | − | 14146.5i | 0.206755 | − | 0.540064i | ||||
\(883\) | 6288.88 | 0.239680 | 0.119840 | − | 0.992793i | \(-0.461762\pi\) | ||||
0.119840 | + | 0.992793i | \(0.461762\pi\) | |||||||
\(884\) | 13986.0 | + | 13594.5i | 0.532128 | + | 0.517230i | ||||
\(885\) | 1595.23 | + | 4498.36i | 0.0605910 | + | 0.170860i | ||||
\(886\) | −23821.2 | − | 13753.2i | −0.903262 | − | 0.521498i | ||||
\(887\) | 9553.63 | − | 16547.4i | 0.361645 | − | 0.626388i | −0.626586 | − | 0.779352i | \(-0.715548\pi\) |
0.988232 | + | 0.152964i | \(0.0488818\pi\) | |||||||
\(888\) | −22994.1 | − | 4251.02i | −0.868954 | − | 0.160647i | ||||
\(889\) | −36590.4 | + | 21125.5i | −1.38043 | + | 0.796993i | ||||
\(890\) | − | 5327.98i | − | 0.200668i | ||||||
\(891\) | 26842.9 | + | 5655.24i | 1.00928 | + | 0.212635i | ||||
\(892\) | − | 10892.6i | − | 0.408868i | ||||||
\(893\) | −13926.7 | − | 24121.7i | −0.521879 | − | 0.903921i | ||||
\(894\) | −1046.77 | − | 193.521i | −0.0391602 | − | 0.00723971i | ||||
\(895\) | 4449.24 | + | 2568.77i | 0.166170 | + | 0.0959380i | ||||
\(896\) | 10426.5 | − | 18059.2i | 0.388755 | − | 0.673343i | ||||
\(897\) | 9903.97 | + | 13967.7i | 0.368656 | + | 0.519918i | ||||
\(898\) | 3899.76 | + | 6754.58i | 0.144918 | + | 0.251006i | ||||
\(899\) | 15560.5i | 0.577277i | ||||||||
\(900\) | 14560.5 | + | 5574.25i | 0.539278 | + | 0.206454i | ||||
\(901\) | 2998.01 | 0.110852 | ||||||||
\(902\) | 17437.9 | − | 10067.8i | 0.643702 | − | 0.371642i | ||||
\(903\) | 13234.6 | + | 11293.1i | 0.487729 | + | 0.416181i | ||||
\(904\) | 16461.9 | + | 9504.31i | 0.605659 | + | 0.349678i | ||||
\(905\) | 397.713 | + | 229.619i | 0.0146082 | + | 0.00843404i | ||||
\(906\) | 14812.0 | − | 17358.4i | 0.543153 | − | 0.636529i | ||||
\(907\) | −14574.0 | − | 25243.0i | −0.533542 | − | 0.924122i | −0.999232 | − | 0.0391743i | \(-0.987527\pi\) |
0.465690 | − | 0.884948i | \(-0.345806\pi\) | |||||||
\(908\) | − | 17432.6i | − | 0.637137i | ||||||
\(909\) | 1425.13 | + | 8945.91i | 0.0520008 | + | 0.326421i | ||||
\(910\) | 1228.16 | + | 4336.37i | 0.0447397 | + | 0.157966i | ||||
\(911\) | 14954.3 | + | 25901.7i | 0.543863 | + | 0.941998i | 0.998678 | + | 0.0514120i | \(0.0163722\pi\) |
−0.454815 | + | 0.890586i | \(0.650295\pi\) | |||||||
\(912\) | 1796.36 | − | 637.034i | 0.0652231 | − | 0.0231297i | ||||
\(913\) | −23846.5 | + | 41303.3i | −0.864406 | + | 1.49720i | ||||
\(914\) | −15506.7 | + | 26858.4i | −0.561177 | + | 0.971988i | ||||
\(915\) | 1146.15 | − | 6199.60i | 0.0414103 | − | 0.223992i | ||||
\(916\) | 13958.6 | − | 8059.00i | 0.503499 | − | 0.290695i | ||||
\(917\) | − | 1305.22i | − | 0.0470036i | ||||||
\(918\) | −21848.6 | − | 542.657i | −0.785526 | − | 0.0195102i | ||||
\(919\) | 50551.8 | 1.81452 | 0.907262 | − | 0.420565i | \(-0.138168\pi\) | ||||
0.907262 | + | 0.420565i | \(0.138168\pi\) | |||||||
\(920\) | −1687.49 | − | 2922.82i | −0.0604727 | − | 0.104742i | ||||
\(921\) | −1287.29 | + | 6963.04i | −0.0460560 | + | 0.249121i | ||||
\(922\) | −2579.41 | + | 4467.67i | −0.0921350 | + | 0.159582i | ||||
\(923\) | −34537.1 | − | 8730.67i | −1.23164 | − | 0.311347i | ||||
\(924\) | −8013.75 | − | 22597.9i | −0.285317 | − | 0.804562i | ||||
\(925\) | −20509.4 | + | 11841.1i | −0.729020 | + | 0.420900i | ||||
\(926\) | −8076.42 | −0.286617 | ||||||||
\(927\) | 36331.0 | − | 29474.3i | 1.28723 | − | 1.04430i | ||||
\(928\) | − | 41623.6i | − | 1.47237i | ||||||
\(929\) | 45556.8 | − | 26302.3i | 1.60890 | − | 0.928901i | 0.619288 | − | 0.785164i | \(-0.287421\pi\) |
0.989616 | − | 0.143737i | \(-0.0459119\pi\) | |||||||
\(930\) | 989.519 | + | 844.360i | 0.0348899 | + | 0.0297717i | ||||
\(931\) | 35792.1 | + | 20664.6i | 1.25998 | + | 0.727448i | ||||
\(932\) | −6669.73 | + | 11552.3i | −0.234414 | + | 0.406017i | ||||
\(933\) | −6705.87 | + | 7858.71i | −0.235306 | + | 0.275759i | ||||
\(934\) | 3480.91 | − | 2009.70i | 0.121947 | − | 0.0704063i | ||||
\(935\) | −6850.54 | −0.239611 | ||||||||
\(936\) | 23720.7 | + | 16693.0i | 0.828351 | + | 0.582934i | ||||
\(937\) | −56244.7 | −1.96098 | −0.980488 | − | 0.196577i | \(-0.937018\pi\) | ||||
−0.980488 | + | 0.196577i | \(0.937018\pi\) | |||||||
\(938\) | −20756.9 | + | 11984.0i | −0.722535 | + | 0.417156i | ||||
\(939\) | 486.342 | + | 1371.43i | 0.0169022 | + | 0.0476623i | ||||
\(940\) | −1057.72 | + | 1832.03i | −0.0367011 | + | 0.0635682i | ||||
\(941\) | 9218.11 | + | 5322.08i | 0.319343 | + | 0.184373i | 0.651100 | − | 0.758992i | \(-0.274308\pi\) |
−0.331757 | + | 0.943365i | \(0.607641\pi\) | |||||||
\(942\) | 5133.69 | − | 27768.5i | 0.177563 | − | 0.960454i | ||||
\(943\) | 18176.9 | − | 10494.5i | 0.627702 | − | 0.362404i | ||||
\(944\) | 1218.28i | 0.0420039i | ||||||||
\(945\) | 6422.76 | + | 3923.97i | 0.221092 | + | 0.135076i | ||||
\(946\) | −8816.71 | −0.303019 | ||||||||
\(947\) | −6080.41 | + | 3510.53i | −0.208645 | + | 0.120461i | −0.600681 | − | 0.799488i | \(-0.705104\pi\) |
0.392037 | + | 0.919950i | \(0.371771\pi\) | |||||||
\(948\) | −16731.4 | − | 3093.21i | −0.573219 | − | 0.105973i | ||||
\(949\) | 32920.6 | + | 8322.02i | 1.12608 | + | 0.284662i | ||||
\(950\) | 14271.4 | − | 24718.8i | 0.487395 | − | 0.844192i | ||||
\(951\) | −47883.8 | + | 16980.8i | −1.63274 | + | 0.579011i | ||||
\(952\) | 25511.1 | + | 44186.5i | 0.868508 | + | 1.50430i | ||||
\(953\) | 22731.5 | 0.772660 | 0.386330 | − | 0.922361i | \(-0.373743\pi\) | ||||
0.386330 | + | 0.922361i | \(0.373743\pi\) | |||||||
\(954\) | 1648.43 | − | 262.605i | 0.0559434 | − | 0.00891210i | ||||
\(955\) | 3923.36i | 0.132939i | ||||||||
\(956\) | 8971.10 | − | 5179.47i | 0.303500 | − | 0.175226i | ||||
\(957\) | −34707.9 | − | 29616.4i | −1.17236 | − | 1.00038i | ||||
\(958\) | 2778.14 | − | 4811.88i | 0.0936927 | − | 0.162280i | ||||
\(959\) | −1807.88 | + | 3131.34i | −0.0608754 | + | 0.105439i | ||||
\(960\) | −2830.92 | − | 2415.63i | −0.0951745 | − | 0.0812127i | ||||
\(961\) | −12672.1 | − | 21948.8i | −0.425368 | − | 0.736758i | ||||
\(962\) | −15870.9 | + | 4495.02i | −0.531912 | + | 0.150650i | ||||
\(963\) | −1979.32 | − | 757.750i | −0.0662333 | − | 0.0253563i | ||||
\(964\) | 14880.8i | 0.497176i | ||||||||
\(965\) | −1843.29 | − | 3192.67i | −0.0614898 | − | 0.106503i | ||||
\(966\) | 5604.97 | + | 15805.4i | 0.186684 | + | 0.526429i | ||||
\(967\) | 1387.68 | + | 801.178i | 0.0461477 | + | 0.0266434i | 0.522896 | − | 0.852396i | \(-0.324851\pi\) |
−0.476749 | + | 0.879040i | \(0.658185\pi\) | |||||||
\(968\) | 1687.29 | + | 974.155i | 0.0560242 | + | 0.0323456i | ||||
\(969\) | 10840.4 | − | 58636.8i | 0.359386 | − | 1.94395i | ||||
\(970\) | −4595.51 | + | 2653.22i | −0.152116 | + | 0.0878244i | ||||
\(971\) | −57819.7 | −1.91094 | −0.955469 | − | 0.295090i | \(-0.904650\pi\) | ||||
−0.955469 | + | 0.295090i | \(0.904650\pi\) | |||||||
\(972\) | 17974.9 | − | 2407.53i | 0.593153 | − | 0.0794461i | ||||
\(973\) | 42440.9i | 1.39835i | ||||||||
\(974\) | 14373.6 | + | 24895.8i | 0.472855 | + | 0.819009i | ||||
\(975\) | 29248.4 | − | 2733.42i | 0.960716 | − | 0.0897843i | ||||
\(976\) | 804.640 | − | 1393.68i | 0.0263893 | − | 0.0457075i | ||||
\(977\) | 18852.3 | + | 10884.4i | 0.617339 | + | 0.356421i | 0.775832 | − | 0.630939i | \(-0.217330\pi\) |
−0.158493 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(978\) | 356.177 | + | 1004.38i | 0.0116455 | + | 0.0328389i | ||||
\(979\) | 26702.8 | + | 46250.5i | 0.871730 | + | 1.50988i | ||||
\(980\) | − | 3138.92i | − | 0.102315i | ||||||
\(981\) | −12114.8 | + | 31645.1i | −0.394287 | + | 1.02992i | ||||
\(982\) | 1970.43i | 0.0640315i | ||||||||
\(983\) | −2121.90 | + | 1225.08i | −0.0688484 | + | 0.0397496i | −0.534029 | − | 0.845466i | \(-0.679323\pi\) |
0.465181 | + | 0.885216i | \(0.345989\pi\) | |||||||
\(984\) | 23079.1 | − | 27046.7i | 0.747697 | − | 0.876238i | ||||
\(985\) | 2993.40 | − | 5184.71i | 0.0968300 | − | 0.167714i | ||||
\(986\) | 31480.8 | + | 18175.4i | 1.01679 | + | 0.587043i | ||||
\(987\) | 18224.0 | − | 21357.0i | 0.587718 | − | 0.688756i | ||||
\(988\) | −20651.5 | + | 21246.3i | −0.664993 | + | 0.684146i | ||||
\(989\) | −9190.36 | −0.295487 | ||||||||
\(990\) | −3766.72 | + | 600.060i | −0.120923 | + | 0.0192638i | ||||
\(991\) | 41816.5 | 1.34041 | 0.670204 | − | 0.742177i | \(-0.266207\pi\) | ||||
0.670204 | + | 0.742177i | \(0.266207\pi\) | |||||||
\(992\) | −5947.41 | − | 10301.2i | −0.190353 | − | 0.329702i | ||||
\(993\) | −26744.1 | + | 9484.10i | −0.854680 | + | 0.303090i | ||||
\(994\) | −30215.2 | − | 17444.8i | −0.964153 | − | 0.556654i | ||||
\(995\) | 4507.14 | + | 2602.20i | 0.143604 | + | 0.0829097i | ||||
\(996\) | −5731.92 | + | 31004.4i | −0.182352 | + | 0.986358i | ||||
\(997\) | 4266.40 | + | 7389.61i | 0.135525 | + | 0.234736i | 0.925798 | − | 0.378019i | \(-0.123395\pi\) |
−0.790273 | + | 0.612755i | \(0.790061\pi\) | |||||||
\(998\) | 2461.06 | 0.0780596 | ||||||||
\(999\) | −14361.6 | + | 23507.0i | −0.454835 | + | 0.744474i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 117.4.t.a.103.26 | yes | 80 | |
3.2 | odd | 2 | 351.4.t.a.64.15 | 80 | |||
9.2 | odd | 6 | 351.4.t.a.181.26 | 80 | |||
9.7 | even | 3 | inner | 117.4.t.a.25.15 | ✓ | 80 | |
13.12 | even | 2 | inner | 117.4.t.a.103.15 | yes | 80 | |
39.38 | odd | 2 | 351.4.t.a.64.26 | 80 | |||
117.25 | even | 6 | inner | 117.4.t.a.25.26 | yes | 80 | |
117.38 | odd | 6 | 351.4.t.a.181.15 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.t.a.25.15 | ✓ | 80 | 9.7 | even | 3 | inner | |
117.4.t.a.25.26 | yes | 80 | 117.25 | even | 6 | inner | |
117.4.t.a.103.15 | yes | 80 | 13.12 | even | 2 | inner | |
117.4.t.a.103.26 | yes | 80 | 1.1 | even | 1 | trivial | |
351.4.t.a.64.15 | 80 | 3.2 | odd | 2 | |||
351.4.t.a.64.26 | 80 | 39.38 | odd | 2 | |||
351.4.t.a.181.15 | 80 | 117.38 | odd | 6 | |||
351.4.t.a.181.26 | 80 | 9.2 | odd | 6 |