Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [425,3,Mod(24,425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(425, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([8, 11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("425.24");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.t (of order \(16\), degree \(8\), 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: | \(11.5804112353\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 299.1 | ||
Root | \(0.382683 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 425.299 |
Dual form | 425.3.t.a.199.1 |
$q$-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 \(\left(\mathbb{Z}/425\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{16}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79690 | − | 1.15851i | −1.39845 | − | 0.579256i | −0.449100 | − | 0.893481i | \(-0.648255\pi\) |
−0.949348 | + | 0.314225i | \(0.898255\pi\) | |||||||
\(3\) | −0.451406 | + | 0.675577i | −0.150469 | + | 0.225192i | −0.899045 | − | 0.437857i | \(-0.855738\pi\) |
0.748576 | + | 0.663049i | \(0.230738\pi\) | |||||||
\(4\) | 3.65205 | + | 3.65205i | 0.913014 | + | 0.913014i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.04520 | − | 1.36656i | 0.340867 | − | 0.227760i | ||||
\(7\) | 1.53233 | − | 7.70353i | 0.218904 | − | 1.10050i | −0.702436 | − | 0.711746i | \(-0.747904\pi\) |
0.921340 | − | 0.388757i | \(-0.127096\pi\) | |||||||
\(8\) | −1.34942 | − | 3.25778i | −0.168677 | − | 0.407223i | ||||
\(9\) | 3.19151 | + | 7.70500i | 0.354613 | + | 0.856111i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.48649 | + | 6.71450i | 0.407863 | + | 0.610410i | 0.977360 | − | 0.211584i | \(-0.0678621\pi\) |
−0.569497 | + | 0.821993i | \(0.692862\pi\) | |||||||
\(12\) | −4.11580 | + | 0.818684i | −0.342983 | + | 0.0682236i | ||||
\(13\) | 0.798835 | + | 0.798835i | 0.0614489 | + | 0.0614489i | 0.737163 | − | 0.675715i | \(-0.236165\pi\) |
−0.675715 | + | 0.737163i | \(0.736165\pi\) | |||||||
\(14\) | −13.2104 | + | 19.7707i | −0.943599 | + | 1.41220i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 9.98414i | − | 0.624009i | ||||||
\(17\) | −15.7060 | − | 6.50562i | −0.923880 | − | 0.382683i | ||||
\(18\) | − | 25.2475i | − | 1.40264i | ||||||
\(19\) | −1.07647 | + | 2.59882i | −0.0566561 | + | 0.136780i | −0.949673 | − | 0.313244i | \(-0.898584\pi\) |
0.893017 | + | 0.450023i | \(0.148584\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.51262 | + | 4.51262i | 0.214887 | + | 0.214887i | ||||
\(22\) | −4.76941 | − | 23.9774i | −0.216791 | − | 1.08988i | ||||
\(23\) | 4.76696 | + | 7.13426i | 0.207259 | + | 0.310185i | 0.920507 | − | 0.390727i | \(-0.127776\pi\) |
−0.713247 | + | 0.700912i | \(0.752776\pi\) | |||||||
\(24\) | 2.81002 | + | 0.558947i | 0.117084 | + | 0.0232895i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.30880 | − | 3.15972i | −0.0503384 | − | 0.121528i | ||||
\(27\) | −13.8181 | − | 2.74858i | −0.511780 | − | 0.101799i | ||||
\(28\) | 33.7298 | − | 22.5376i | 1.20464 | − | 0.804913i | ||||
\(29\) | 0.599020 | + | 3.01148i | 0.0206559 | + | 0.103844i | 0.989738 | − | 0.142895i | \(-0.0456410\pi\) |
−0.969082 | + | 0.246739i | \(0.920641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.13254 | + | 10.6746i | −0.230082 | + | 0.344342i | −0.928490 | − | 0.371358i | \(-0.878892\pi\) |
0.698408 | + | 0.715700i | \(0.253892\pi\) | |||||||
\(32\) | −16.9644 | + | 40.9557i | −0.530138 | + | 1.27987i | ||||
\(33\) | −6.56139 | −0.198830 | ||||||||
\(34\) | 36.3911 | + | 36.3911i | 1.07033 | + | 1.07033i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −16.4835 | + | 39.7946i | −0.457875 | + | 1.10541i | ||||
\(37\) | −13.1509 | + | 19.6817i | −0.355429 | + | 0.531938i | −0.965498 | − | 0.260411i | \(-0.916142\pi\) |
0.610068 | + | 0.792349i | \(0.291142\pi\) | |||||||
\(38\) | 6.02153 | − | 6.02153i | 0.158461 | − | 0.158461i | ||||
\(39\) | −0.900273 | + | 0.179075i | −0.0230839 | + | 0.00459168i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.4206 | + | 4.26082i | 0.522453 | + | 0.103922i | 0.449270 | − | 0.893396i | \(-0.351684\pi\) |
0.0731833 | + | 0.997319i | \(0.476684\pi\) | |||||||
\(42\) | −7.39341 | − | 17.8493i | −0.176034 | − | 0.424982i | ||||
\(43\) | −21.4671 | + | 8.89197i | −0.499235 | + | 0.206790i | −0.618069 | − | 0.786124i | \(-0.712085\pi\) |
0.118833 | + | 0.992914i | \(0.462085\pi\) | |||||||
\(44\) | −8.13684 | + | 40.9066i | −0.184928 | + | 0.929696i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.06757 | − | 25.4764i | −0.110164 | − | 0.553834i | ||||
\(47\) | 55.6597 | + | 55.6597i | 1.18425 | + | 1.18425i | 0.978632 | + | 0.205617i | \(0.0659202\pi\) |
0.205617 | + | 0.978632i | \(0.434080\pi\) | |||||||
\(48\) | 6.74505 | + | 4.50690i | 0.140522 | + | 0.0938937i | ||||
\(49\) | −11.7262 | − | 4.85715i | −0.239310 | − | 0.0991254i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.4848 | − | 7.67390i | 0.225192 | − | 0.150469i | ||||
\(52\) | 5.83478i | 0.112207i | ||||||||
\(53\) | 55.5080 | + | 22.9922i | 1.04732 | + | 0.433815i | 0.838935 | − | 0.544232i | \(-0.183179\pi\) |
0.208386 | + | 0.978047i | \(0.433179\pi\) | |||||||
\(54\) | 35.4634 | + | 23.6959i | 0.656730 | + | 0.438813i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −27.1642 | + | 5.40329i | −0.485074 | + | 0.0964873i | ||||
\(57\) | −1.26978 | − | 1.90036i | −0.0222768 | − | 0.0333396i | ||||
\(58\) | 1.81344 | − | 9.11677i | 0.0312662 | − | 0.157186i | ||||
\(59\) | 25.3733 | − | 10.5100i | 0.430057 | − | 0.178135i | −0.157146 | − | 0.987575i | \(-0.550229\pi\) |
0.587202 | + | 0.809440i | \(0.300229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.11302 | − | 35.7596i | 0.116607 | − | 0.586223i | −0.877659 | − | 0.479286i | \(-0.840896\pi\) |
0.994266 | − | 0.106937i | \(-0.0341043\pi\) | |||||||
\(62\) | 32.3156 | − | 21.5926i | 0.521220 | − | 0.348268i | ||||
\(63\) | 64.2461 | − | 12.7793i | 1.01978 | − | 0.202847i | ||||
\(64\) | 66.6561 | − | 66.6561i | 1.04150 | − | 1.04150i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 18.3515 | + | 7.60145i | 0.278054 | + | 0.115174i | ||||
\(67\) | 117.219 | 1.74953 | 0.874767 | − | 0.484544i | \(-0.161015\pi\) | ||||
0.874767 | + | 0.484544i | \(0.161015\pi\) | |||||||
\(68\) | −33.6001 | − | 81.1179i | −0.494119 | − | 1.19291i | ||||
\(69\) | −6.97157 | −0.101037 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 88.1108 | + | 58.8738i | 1.24100 | + | 0.829208i | 0.990312 | − | 0.138861i | \(-0.0443440\pi\) |
0.250685 | + | 0.968069i | \(0.419344\pi\) | |||||||
\(72\) | 20.7945 | − | 20.7945i | 0.288813 | − | 0.288813i | ||||
\(73\) | 11.9073 | + | 59.8620i | 0.163114 | + | 0.820028i | 0.972527 | + | 0.232789i | \(0.0747851\pi\) |
−0.809414 | + | 0.587239i | \(0.800215\pi\) | |||||||
\(74\) | 59.5832 | − | 39.8122i | 0.805178 | − | 0.538003i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.4223 | + | 5.55971i | −0.176610 | + | 0.0731541i | ||||
\(77\) | 58.6001 | − | 24.2730i | 0.761041 | − | 0.315233i | ||||
\(78\) | 2.72543 | + | 0.542122i | 0.0349414 | + | 0.00695029i | ||||
\(79\) | −52.9382 | − | 79.2276i | −0.670103 | − | 1.00288i | −0.998301 | − | 0.0582714i | \(-0.981441\pi\) |
0.328197 | − | 0.944609i | \(-0.393559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −44.9799 | + | 44.9799i | −0.555308 | + | 0.555308i | ||||
\(82\) | −54.9749 | − | 36.7331i | −0.670426 | − | 0.447964i | ||||
\(83\) | −45.4770 | + | 109.791i | −0.547916 | + | 1.32279i | 0.371110 | + | 0.928589i | \(0.378977\pi\) |
−0.919026 | + | 0.394197i | \(0.871023\pi\) | |||||||
\(84\) | 32.9607i | 0.392389i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 70.3428 | 0.817939 | ||||||||
\(87\) | −2.30489 | − | 0.954715i | −0.0264929 | − | 0.0109737i | ||||
\(88\) | 15.8202 | − | 23.6767i | 0.179776 | − | 0.269053i | ||||
\(89\) | 61.4534 | + | 61.4534i | 0.690488 | + | 0.690488i | 0.962339 | − | 0.271851i | \(-0.0876359\pi\) |
−0.271851 | + | 0.962339i | \(0.587636\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.37792 | − | 4.92977i | 0.0810761 | − | 0.0541733i | ||||
\(92\) | −8.64551 | + | 43.4639i | −0.0939729 | + | 0.472434i | ||||
\(93\) | −3.99184 | − | 9.63715i | −0.0429230 | − | 0.103625i | ||||
\(94\) | −91.1920 | − | 220.157i | −0.970128 | − | 2.34210i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −20.0109 | − | 29.9484i | −0.208447 | − | 0.311963i | ||||
\(97\) | −24.1185 | + | 4.79748i | −0.248645 | + | 0.0494585i | −0.317839 | − | 0.948145i | \(-0.602957\pi\) |
0.0691943 | + | 0.997603i | \(0.477957\pi\) | |||||||
\(98\) | 27.1699 | + | 27.1699i | 0.277244 | + | 0.277244i | ||||
\(99\) | −37.4165 | + | 55.9978i | −0.377945 | + | 0.565635i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.70266i | 0.0762640i | 0.999273 | + | 0.0381320i | \(0.0121407\pi\) | ||||
−0.999273 | + | 0.0381320i | \(0.987859\pi\) | |||||||
\(102\) | −41.0121 | + | 8.15782i | −0.402080 | + | 0.0799786i | ||||
\(103\) | − | 41.5688i | − | 0.403581i | −0.979429 | − | 0.201790i | \(-0.935324\pi\) | ||
0.979429 | − | 0.201790i | \(-0.0646760\pi\) | |||||||
\(104\) | 1.52447 | − | 3.68039i | 0.0146584 | − | 0.0353884i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −128.614 | − | 128.614i | −1.21333 | − | 1.21333i | ||||
\(107\) | 17.2484 | + | 86.7136i | 0.161200 | + | 0.810407i | 0.973768 | + | 0.227541i | \(0.0730687\pi\) |
−0.812568 | + | 0.582866i | \(0.801931\pi\) | |||||||
\(108\) | −40.4263 | − | 60.5023i | −0.374318 | − | 0.560206i | ||||
\(109\) | −18.2754 | − | 3.63521i | −0.167665 | − | 0.0333506i | 0.110544 | − | 0.993871i | \(-0.464741\pi\) |
−0.278209 | + | 0.960521i | \(0.589741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.36011 | − | 17.7689i | −0.0663073 | − | 0.160080i | ||||
\(112\) | −76.9131 | − | 15.2990i | −0.686724 | − | 0.136598i | ||||
\(113\) | −50.4220 | + | 33.6909i | −0.446212 | + | 0.298150i | −0.758302 | − | 0.651903i | \(-0.773971\pi\) |
0.312090 | + | 0.950053i | \(0.398971\pi\) | |||||||
\(114\) | 1.34985 | + | 6.78616i | 0.0118408 | + | 0.0595277i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.81043 | + | 13.1857i | −0.0759520 | + | 0.113670i | ||||
\(117\) | −3.60553 | + | 8.70452i | −0.0308165 | + | 0.0743976i | ||||
\(118\) | −83.1426 | −0.704598 | ||||||||
\(119\) | −74.1828 | + | 111.022i | −0.623385 | + | 0.932962i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.3487 | − | 51.5403i | 0.176436 | − | 0.425953i | ||||
\(122\) | −61.3223 | + | 91.7753i | −0.502642 | + | 0.752257i | ||||
\(123\) | −12.5479 | + | 12.5479i | −0.102015 | + | 0.102015i | ||||
\(124\) | −65.0326 | + | 12.9358i | −0.524456 | + | 0.104321i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −194.495 | − | 38.6874i | −1.54361 | − | 0.307043i | ||||
\(127\) | 45.6333 | + | 110.168i | 0.359317 | + | 0.867468i | 0.995396 | + | 0.0958444i | \(0.0305551\pi\) |
−0.636079 | + | 0.771624i | \(0.719445\pi\) | |||||||
\(128\) | −99.8291 | + | 41.3506i | −0.779915 | + | 0.323051i | ||||
\(129\) | 3.68317 | − | 18.5166i | 0.0285517 | − | 0.143539i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 33.4238 | + | 168.033i | 0.255144 | + | 1.28269i | 0.869605 | + | 0.493748i | \(0.164373\pi\) |
−0.614461 | + | 0.788947i | \(0.710627\pi\) | |||||||
\(132\) | −23.9626 | − | 23.9626i | −0.181534 | − | 0.181534i | ||||
\(133\) | 18.3706 | + | 12.2748i | 0.138125 | + | 0.0922919i | ||||
\(134\) | −327.849 | − | 135.799i | −2.44663 | − | 1.01343i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 59.9454i | 0.440775i | ||||||||
\(137\) | − | 173.113i | − | 1.26360i | −0.775132 | − | 0.631799i | \(-0.782317\pi\) | ||
0.775132 | − | 0.631799i | \(-0.217683\pi\) | |||||||
\(138\) | 19.4988 | + | 8.07666i | 0.141295 | + | 0.0585265i | ||||
\(139\) | 149.307 | + | 99.7637i | 1.07415 | + | 0.717724i | 0.961193 | − | 0.275876i | \(-0.0889678\pi\) |
0.112957 | + | 0.993600i | \(0.463968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −62.7276 | + | 12.4773i | −0.444876 | + | 0.0884914i | ||||
\(142\) | −178.231 | − | 266.741i | −1.25515 | − | 1.87846i | ||||
\(143\) | −1.77982 | + | 8.94775i | −0.0124463 | + | 0.0625717i | ||||
\(144\) | 76.9278 | − | 31.8645i | 0.534221 | − | 0.221281i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 36.0474 | − | 181.223i | 0.246900 | − | 1.24125i | ||||
\(147\) | 8.57464 | − | 5.72939i | 0.0583309 | − | 0.0389755i | ||||
\(148\) | −119.906 | + | 23.8509i | −0.810178 | + | 0.161154i | ||||
\(149\) | −31.6842 | + | 31.6842i | −0.212646 | + | 0.212646i | −0.805391 | − | 0.592745i | \(-0.798044\pi\) |
0.592745 | + | 0.805391i | \(0.298044\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −121.384 | − | 50.2789i | −0.803868 | − | 0.332973i | −0.0573634 | − | 0.998353i | \(-0.518269\pi\) |
−0.746504 | + | 0.665380i | \(0.768269\pi\) | |||||||
\(152\) | 9.91898 | 0.0652565 | ||||||||
\(153\) | − | 141.777i | − | 0.926648i | ||||||
\(154\) | −192.019 | −1.24688 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.94184 | − | 2.63385i | −0.0252682 | − | 0.0168837i | ||||
\(157\) | −25.4694 | + | 25.4694i | −0.162225 | + | 0.162225i | −0.783552 | − | 0.621327i | \(-0.786594\pi\) |
0.621327 | + | 0.783552i | \(0.286594\pi\) | |||||||
\(158\) | 56.2765 | + | 282.921i | 0.356180 | + | 1.79064i | ||||
\(159\) | −40.5896 | + | 27.1211i | −0.255281 | + | 0.170573i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 62.2635 | − | 25.7904i | 0.386730 | − | 0.160189i | ||||
\(162\) | 177.914 | − | 73.6944i | 1.09823 | − | 0.454904i | ||||
\(163\) | −156.650 | − | 31.1596i | −0.961041 | − | 0.191163i | −0.310449 | − | 0.950590i | \(-0.600479\pi\) |
−0.650592 | + | 0.759427i | \(0.725479\pi\) | |||||||
\(164\) | 62.6684 | + | 93.7898i | 0.382124 | + | 0.571889i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 254.389 | − | 254.389i | 1.53246 | − | 1.53246i | ||||
\(167\) | −92.0734 | − | 61.5214i | −0.551337 | − | 0.368392i | 0.248478 | − | 0.968637i | \(-0.420070\pi\) |
−0.799816 | + | 0.600246i | \(0.795070\pi\) | |||||||
\(168\) | 8.61173 | − | 20.7905i | 0.0512603 | − | 0.123753i | ||||
\(169\) | − | 167.724i | − | 0.992448i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.4594 | −0.137190 | ||||||||
\(172\) | −110.873 | − | 45.9251i | −0.644611 | − | 0.267006i | ||||
\(173\) | −98.9216 | + | 148.047i | −0.571801 | + | 0.855761i | −0.998824 | − | 0.0484797i | \(-0.984562\pi\) |
0.427023 | + | 0.904241i | \(0.359562\pi\) | |||||||
\(174\) | 5.34048 | + | 5.34048i | 0.0306924 | + | 0.0306924i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 67.0386 | − | 44.7937i | 0.380901 | − | 0.254510i | ||||
\(177\) | −4.35338 | + | 21.8859i | −0.0245954 | + | 0.123649i | ||||
\(178\) | −100.684 | − | 243.074i | −0.565642 | − | 1.36558i | ||||
\(179\) | −96.5028 | − | 232.978i | −0.539122 | − | 1.30155i | −0.925337 | − | 0.379146i | \(-0.876218\pi\) |
0.386215 | − | 0.922409i | \(-0.373782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 167.421 | + | 250.563i | 0.924977 | + | 1.38433i | 0.923197 | + | 0.384328i | \(0.125567\pi\) |
0.00178027 | + | 0.999998i | \(0.499433\pi\) | |||||||
\(182\) | −26.3465 | + | 5.24064i | −0.144761 | + | 0.0287947i | ||||
\(183\) | 20.9475 | + | 20.9475i | 0.114467 | + | 0.114467i | ||||
\(184\) | 16.8092 | − | 25.1568i | 0.0913546 | − | 0.136722i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 31.5787i | 0.169778i | ||||||||
\(187\) | −26.7826 | − | 134.645i | −0.143222 | − | 0.720027i | ||||
\(188\) | 406.545i | 2.16247i | ||||||||
\(189\) | −42.3476 | + | 102.236i | −0.224061 | + | 0.540931i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 93.7287 | + | 93.7287i | 0.490726 | + | 0.490726i | 0.908535 | − | 0.417809i | \(-0.137202\pi\) |
−0.417809 | + | 0.908535i | \(0.637202\pi\) | |||||||
\(192\) | 14.9423 | + | 75.1202i | 0.0778247 | + | 0.391251i | ||||
\(193\) | −177.012 | − | 264.917i | −0.917161 | − | 1.37263i | −0.927957 | − | 0.372687i | \(-0.878436\pi\) |
0.0107958 | − | 0.999942i | \(-0.496564\pi\) | |||||||
\(194\) | 73.0150 | + | 14.5236i | 0.376366 | + | 0.0748639i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −25.0861 | − | 60.5632i | −0.127990 | − | 0.308996i | ||||
\(197\) | 113.442 | + | 22.5650i | 0.575847 | + | 0.114543i | 0.474418 | − | 0.880300i | \(-0.342659\pi\) |
0.101429 | + | 0.994843i | \(0.467659\pi\) | |||||||
\(198\) | 169.524 | − | 113.273i | 0.856184 | − | 0.572084i | ||||
\(199\) | 57.7166 | + | 290.161i | 0.290033 | + | 1.45809i | 0.801088 | + | 0.598547i | \(0.204255\pi\) |
−0.511055 | + | 0.859548i | \(0.670745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −52.9132 | + | 79.1902i | −0.263250 | + | 0.393981i | ||||
\(202\) | 8.92363 | − | 21.5436i | 0.0441764 | − | 0.106651i | ||||
\(203\) | 24.1169 | 0.118802 | ||||||||
\(204\) | 69.9686 | + | 13.9176i | 0.342983 | + | 0.0682236i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −48.1580 | + | 116.264i | −0.233777 | + | 0.564387i | ||||
\(207\) | −39.7556 | + | 59.4985i | −0.192056 | + | 0.287432i | ||||
\(208\) | 7.97568 | − | 7.97568i | 0.0383446 | − | 0.0383446i | ||||
\(209\) | −22.2793 | + | 4.43163i | −0.106600 | + | 0.0212040i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −225.325 | − | 44.8199i | −1.06789 | − | 0.212417i | −0.370300 | − | 0.928912i | \(-0.620745\pi\) |
−0.697592 | + | 0.716495i | \(0.745745\pi\) | |||||||
\(212\) | 118.750 | + | 286.687i | 0.560140 | + | 1.35230i | ||||
\(213\) | −79.5475 | + | 32.9496i | −0.373462 | + | 0.154693i | ||||
\(214\) | 52.2168 | − | 262.511i | 0.244004 | − | 1.22669i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.69205 | + | 48.7252i | 0.0448706 | + | 0.225580i | ||||
\(217\) | 71.3026 | + | 71.3026i | 0.328584 | + | 0.328584i | ||||
\(218\) | 46.9031 | + | 31.3396i | 0.215152 | + | 0.143760i | ||||
\(219\) | −45.8164 | − | 18.9778i | −0.209207 | − | 0.0866565i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.34955 | − | 17.7434i | −0.0332559 | − | 0.0802868i | ||||
\(222\) | 58.2245i | 0.262272i | ||||||||
\(223\) | 335.723 | + | 139.061i | 1.50549 | + | 0.623593i | 0.974621 | − | 0.223863i | \(-0.0718669\pi\) |
0.530865 | + | 0.847456i | \(0.321867\pi\) | |||||||
\(224\) | 289.509 | + | 193.443i | 1.29245 | + | 0.863587i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 180.056 | − | 35.8155i | 0.796710 | − | 0.158475i | ||||
\(227\) | −53.8478 | − | 80.5890i | −0.237215 | − | 0.355017i | 0.693693 | − | 0.720271i | \(-0.255982\pi\) |
−0.930908 | + | 0.365253i | \(0.880982\pi\) | |||||||
\(228\) | 2.30291 | − | 11.5775i | 0.0101005 | − | 0.0507785i | ||||
\(229\) | 334.120 | − | 138.397i | 1.45904 | − | 0.604353i | 0.494708 | − | 0.869059i | \(-0.335275\pi\) |
0.964329 | + | 0.264706i | \(0.0852749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0542 | + | 50.5458i | −0.0435246 | + | 0.218813i | ||||
\(232\) | 9.00241 | − | 6.01522i | 0.0388035 | − | 0.0259277i | ||||
\(233\) | 274.765 | − | 54.6542i | 1.17925 | − | 0.234567i | 0.433725 | − | 0.901045i | \(-0.357199\pi\) |
0.745525 | + | 0.666478i | \(0.232199\pi\) | |||||||
\(234\) | 20.1686 | − | 20.1686i | 0.0861905 | − | 0.0861905i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 131.048 | + | 54.2818i | 0.555288 | + | 0.230008i | ||||
\(237\) | 77.4209 | 0.326670 | ||||||||
\(238\) | 336.103 | − | 224.577i | 1.41220 | − | 0.943599i | ||||
\(239\) | −328.551 | −1.37469 | −0.687345 | − | 0.726331i | \(-0.741224\pi\) | ||||
−0.687345 | + | 0.726331i | \(0.741224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −201.560 | − | 134.678i | −0.836349 | − | 0.558831i | 0.0620186 | − | 0.998075i | \(-0.480246\pi\) |
−0.898368 | + | 0.439244i | \(0.855246\pi\) | |||||||
\(242\) | −119.420 | + | 119.420i | −0.493472 | + | 0.493472i | ||||
\(243\) | −34.8204 | − | 175.054i | −0.143294 | − | 0.720387i | ||||
\(244\) | 156.573 | − | 104.619i | 0.641693 | − | 0.428765i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 49.6320 | − | 20.5583i | 0.201756 | − | 0.0835701i | ||||
\(247\) | −2.93595 | + | 1.21611i | −0.0118864 | + | 0.00492352i | ||||
\(248\) | 44.4003 | + | 8.83176i | 0.179033 | + | 0.0356119i | ||||
\(249\) | −53.6438 | − | 80.2836i | −0.215437 | − | 0.322424i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −155.463 | + | 155.463i | −0.619375 | + | 0.619375i | −0.945371 | − | 0.325996i | \(-0.894300\pi\) |
0.325996 | + | 0.945371i | \(0.394300\pi\) | |||||||
\(252\) | 281.301 | + | 187.959i | 1.11627 | + | 0.745870i | ||||
\(253\) | −26.5161 | + | 64.0155i | −0.104807 | + | 0.253026i | ||||
\(254\) | − | 360.996i | − | 1.42125i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −49.9468 | −0.195105 | ||||||||
\(257\) | 300.480 | + | 124.463i | 1.16918 | + | 0.484292i | 0.880923 | − | 0.473260i | \(-0.156923\pi\) |
0.288261 | + | 0.957552i | \(0.406923\pi\) | |||||||
\(258\) | −31.7531 | + | 47.5219i | −0.123074 | + | 0.184194i | ||||
\(259\) | 131.467 | + | 131.467i | 0.507595 | + | 0.507595i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.2917 | + | 14.2266i | −0.0815772 | + | 0.0545082i | ||||
\(262\) | 101.185 | − | 508.693i | 0.386203 | − | 1.94158i | ||||
\(263\) | −53.0907 | − | 128.172i | −0.201866 | − | 0.487347i | 0.790233 | − | 0.612806i | \(-0.209959\pi\) |
−0.992099 | + | 0.125460i | \(0.959959\pi\) | |||||||
\(264\) | 8.85405 | + | 21.3756i | 0.0335381 | + | 0.0809681i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −37.1600 | − | 55.6139i | −0.139699 | − | 0.209075i | ||||
\(267\) | −69.2570 | + | 13.7761i | −0.259389 | + | 0.0515957i | ||||
\(268\) | 428.089 | + | 428.089i | 1.59735 | + | 1.59735i | ||||
\(269\) | 180.493 | − | 270.126i | 0.670976 | − | 1.00419i | −0.327267 | − | 0.944932i | \(-0.606128\pi\) |
0.998243 | − | 0.0592547i | \(-0.0188724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1867i | 0.0707996i | 0.999373 | + | 0.0353998i | \(0.0112705\pi\) | ||||
−0.999373 | + | 0.0353998i | \(0.988730\pi\) | |||||||
\(272\) | −64.9530 | + | 156.810i | −0.238798 | + | 0.576509i | ||||
\(273\) | 7.20968i | 0.0264091i | ||||||||
\(274\) | −200.554 | + | 484.179i | −0.731947 | + | 1.76708i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −25.4606 | − | 25.4606i | −0.0922484 | − | 0.0922484i | ||||
\(277\) | 60.0883 | + | 302.084i | 0.216925 | + | 1.09056i | 0.923700 | + | 0.383118i | \(0.125150\pi\) |
−0.706774 | + | 0.707439i | \(0.749850\pi\) | |||||||
\(278\) | −302.018 | − | 452.003i | −1.08640 | − | 1.62591i | ||||
\(279\) | −105.011 | − | 20.8880i | −0.376385 | − | 0.0748676i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −33.1106 | − | 79.9361i | −0.117831 | − | 0.284470i | 0.853949 | − | 0.520356i | \(-0.174201\pi\) |
−0.971781 | + | 0.235886i | \(0.924201\pi\) | |||||||
\(282\) | 189.898 | + | 37.7730i | 0.673396 | + | 0.133947i | ||||
\(283\) | 6.22073 | − | 4.15656i | 0.0219814 | − | 0.0146875i | −0.544531 | − | 0.838741i | \(-0.683292\pi\) |
0.566512 | + | 0.824053i | \(0.308292\pi\) | |||||||
\(284\) | 106.775 | + | 536.796i | 0.375969 | + | 1.89013i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.3440 | − | 22.9640i | 0.0536505 | − | 0.0802937i | ||||
\(287\) | 65.6466 | − | 158.485i | 0.228734 | − | 0.552213i | ||||
\(288\) | −369.706 | −1.28370 | ||||||||
\(289\) | 204.354 | + | 204.354i | 0.707107 | + | 0.707107i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.64619 | − | 18.4595i | 0.0262756 | − | 0.0634348i | ||||
\(292\) | −175.133 | + | 262.105i | −0.599771 | + | 0.897621i | ||||
\(293\) | 54.4583 | − | 54.4583i | 0.185864 | − | 0.185864i | −0.608041 | − | 0.793906i | \(-0.708044\pi\) |
0.793906 | + | 0.608041i | \(0.208044\pi\) | |||||||
\(294\) | −30.6200 | + | 6.09069i | −0.104150 | + | 0.0207166i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 81.8647 | + | 16.2839i | 0.276570 | + | 0.0550132i | ||||
\(297\) | −43.5392 | − | 105.113i | −0.146597 | − | 0.353915i | ||||
\(298\) | 125.324 | − | 51.9110i | 0.420551 | − | 0.174198i | ||||
\(299\) | −1.89108 | + | 9.50711i | −0.00632469 | + | 0.0317964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.6049 | + | 178.998i | 0.118289 | + | 0.594677i | ||||
\(302\) | 281.250 | + | 281.250i | 0.931291 | + | 0.931291i | ||||
\(303\) | −5.20374 | − | 3.47703i | −0.0171741 | − | 0.0114753i | ||||
\(304\) | 25.9470 | + | 10.7476i | 0.0853519 | + | 0.0353539i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −164.251 | + | 396.536i | −0.536767 | + | 1.29587i | ||||
\(307\) | − | 159.680i | − | 0.520132i | −0.965591 | − | 0.260066i | \(-0.916256\pi\) | ||
0.965591 | − | 0.260066i | \(-0.0837443\pi\) | |||||||
\(308\) | 302.657 | + | 125.365i | 0.982653 | + | 0.407028i | ||||
\(309\) | 28.0829 | + | 18.7644i | 0.0908832 | + | 0.0607262i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −326.615 | + | 64.9678i | −1.05021 | + | 0.208900i | −0.689879 | − | 0.723925i | \(-0.742336\pi\) |
−0.360331 | + | 0.932825i | \(0.617336\pi\) | |||||||
\(312\) | 1.79823 | + | 2.69125i | 0.00576357 | + | 0.00862579i | ||||
\(313\) | 76.9763 | − | 386.986i | 0.245931 | − | 1.23638i | −0.638470 | − | 0.769647i | \(-0.720432\pi\) |
0.884400 | − | 0.466729i | \(-0.154568\pi\) | |||||||
\(314\) | 100.742 | − | 41.7286i | 0.320834 | − | 0.132894i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 96.0103 | − | 482.676i | 0.303830 | − | 1.52746i | ||||
\(317\) | 115.654 | − | 77.2775i | 0.364839 | − | 0.243778i | −0.359615 | − | 0.933101i | \(-0.617092\pi\) |
0.724454 | + | 0.689323i | \(0.242092\pi\) | |||||||
\(318\) | 144.945 | − | 28.8314i | 0.455802 | − | 0.0906647i | ||||
\(319\) | −17.5331 | + | 17.5331i | −0.0549627 | + | 0.0549627i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −66.3677 | − | 27.4904i | −0.206753 | − | 0.0856399i | ||||
\(322\) | −204.023 | −0.633612 | ||||||||
\(323\) | 33.8138 | − | 33.8138i | 0.104687 | − | 0.104687i | ||||
\(324\) | −328.538 | −1.01401 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 402.034 | + | 268.631i | 1.23323 | + | 0.824021i | ||||
\(327\) | 10.7055 | − | 10.7055i | 0.0327385 | − | 0.0327385i | ||||
\(328\) | −15.0245 | − | 75.5332i | −0.0458064 | − | 0.230284i | ||||
\(329\) | 514.065 | − | 343.487i | 1.56251 | − | 1.04403i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 146.717 | − | 60.7720i | 0.443252 | − | 0.183601i | −0.149883 | − | 0.988704i | \(-0.547890\pi\) |
0.593136 | + | 0.805103i | \(0.297890\pi\) | |||||||
\(332\) | −567.048 | + | 234.879i | −1.70798 | + | 0.707467i | ||||
\(333\) | −193.619 | − | 38.5132i | −0.581438 | − | 0.115655i | ||||
\(334\) | 186.246 | + | 278.737i | 0.557624 | + | 0.834543i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 45.0546 | − | 45.0546i | 0.134091 | − | 0.134091i | ||||
\(337\) | −401.062 | − | 267.981i | −1.19009 | − | 0.795195i | −0.207008 | − | 0.978339i | \(-0.566372\pi\) |
−0.983086 | + | 0.183144i | \(0.941372\pi\) | |||||||
\(338\) | −194.310 | + | 469.106i | −0.574882 | + | 1.38789i | ||||
\(339\) | − | 49.2722i | − | 0.145346i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −103.675 | −0.304031 | ||||||||
\(342\) | 65.6136 | + | 27.1781i | 0.191853 | + | 0.0794680i | ||||
\(343\) | 158.436 | − | 237.116i | 0.461912 | − | 0.691299i | ||||
\(344\) | 57.9362 | + | 57.9362i | 0.168419 | + | 0.168419i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 448.188 | − | 299.469i | 1.29534 | − | 0.865518i | ||||
\(347\) | 3.86080 | − | 19.4096i | 0.0111262 | − | 0.0559353i | −0.974823 | − | 0.222979i | \(-0.928422\pi\) |
0.985950 | + | 0.167043i | \(0.0534220\pi\) | |||||||
\(348\) | −4.93090 | − | 11.9042i | −0.0141692 | − | 0.0342076i | ||||
\(349\) | 149.801 | + | 361.651i | 0.429229 | + | 1.03625i | 0.979533 | + | 0.201286i | \(0.0645120\pi\) |
−0.550304 | + | 0.834965i | \(0.685488\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.84268 | − | 13.2340i | −0.0251928 | − | 0.0377037i | ||||
\(352\) | −351.108 | + | 69.8398i | −0.997466 | + | 0.198408i | ||||
\(353\) | −138.024 | − | 138.024i | −0.391003 | − | 0.391003i | 0.484042 | − | 0.875045i | \(-0.339168\pi\) |
−0.875045 | + | 0.484042i | \(0.839168\pi\) | |||||||
\(354\) | 37.5311 | − | 56.1692i | 0.106020 | − | 0.158670i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 448.863i | 1.26085i | ||||||||
\(357\) | −41.5176 | − | 100.232i | −0.116296 | − | 0.280763i | ||||
\(358\) | 763.416i | 2.13245i | ||||||||
\(359\) | −136.163 | + | 328.726i | −0.379284 | + | 0.915672i | 0.612817 | + | 0.790225i | \(0.290036\pi\) |
−0.992100 | + | 0.125447i | \(0.959964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 249.670 | + | 249.670i | 0.691608 | + | 0.691608i | ||||
\(362\) | −177.978 | − | 894.758i | −0.491653 | − | 2.47171i | ||||
\(363\) | 25.1825 | + | 37.6883i | 0.0693733 | + | 0.103824i | ||||
\(364\) | 44.9484 | + | 8.94078i | 0.123485 | + | 0.0245626i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −34.3200 | − | 82.8558i | −0.0937705 | − | 0.226382i | ||||
\(367\) | −80.1568 | − | 15.9442i | −0.218411 | − | 0.0434446i | 0.0846717 | − | 0.996409i | \(-0.473016\pi\) |
−0.303083 | + | 0.952964i | \(0.598016\pi\) | |||||||
\(368\) | 71.2294 | − | 47.5940i | 0.193558 | − | 0.129331i | ||||
\(369\) | 35.5345 | + | 178.644i | 0.0962994 | + | 0.484130i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 262.177 | − | 392.376i | 0.706677 | − | 1.05762i | ||||
\(372\) | 20.6170 | − | 49.7738i | 0.0554220 | − | 0.133801i | ||||
\(373\) | 76.8209 | 0.205954 | 0.102977 | − | 0.994684i | \(-0.467163\pi\) | ||||
0.102977 | + | 0.994684i | \(0.467163\pi\) | |||||||
\(374\) | −81.0799 | + | 407.616i | −0.216791 | + | 1.08988i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 106.219 | − | 256.436i | 0.282498 | − | 0.682009i | ||||
\(377\) | −1.92716 | + | 2.88419i | −0.00511182 | + | 0.00765038i | ||||
\(378\) | 236.883 | − | 236.883i | 0.626676 | − | 0.626676i | ||||
\(379\) | −577.940 | + | 114.959i | −1.52491 | + | 0.303323i | −0.885169 | − | 0.465269i | \(-0.845957\pi\) |
−0.639739 | + | 0.768592i | \(0.720957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −95.0264 | − | 18.9019i | −0.249413 | − | 0.0496113i | ||||
\(382\) | −153.564 | − | 370.735i | −0.401999 | − | 0.970511i | ||||
\(383\) | −215.834 | + | 89.4016i | −0.563537 | + | 0.233424i | −0.646220 | − | 0.763151i | \(-0.723651\pi\) |
0.0826832 | + | 0.996576i | \(0.473651\pi\) | |||||||
\(384\) | 17.1280 | − | 86.1081i | 0.0446041 | − | 0.224240i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 188.175 | + | 946.017i | 0.487499 | + | 2.45082i | ||||
\(387\) | −137.025 | − | 137.025i | −0.354070 | − | 0.354070i | ||||
\(388\) | −105.603 | − | 70.5616i | −0.272172 | − | 0.181860i | ||||
\(389\) | −372.916 | − | 154.467i | −0.958653 | − | 0.397087i | −0.152177 | − | 0.988353i | \(-0.548628\pi\) |
−0.806477 | + | 0.591266i | \(0.798628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.4569 | − | 143.062i | −0.0727797 | − | 0.365888i | ||||
\(392\) | 44.7557i | 0.114173i | ||||||||
\(393\) | −128.607 | − | 53.2707i | −0.327244 | − | 0.135549i | ||||
\(394\) | −291.143 | − | 194.536i | −0.738943 | − | 0.493746i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −341.154 | + | 67.8598i | −0.861501 | + | 0.171363i | ||||
\(397\) | 146.553 | + | 219.332i | 0.369151 | + | 0.552474i | 0.968817 | − | 0.247776i | \(-0.0796998\pi\) |
−0.599666 | + | 0.800251i | \(0.704700\pi\) | |||||||
\(398\) | 174.728 | − | 878.415i | 0.439014 | − | 2.20707i | ||||
\(399\) | −16.5852 | + | 6.86980i | −0.0415668 | + | 0.0172175i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 46.6830 | − | 234.691i | 0.116416 | − | 0.585265i | −0.877904 | − | 0.478837i | \(-0.841059\pi\) |
0.994320 | − | 0.106428i | \(-0.0339414\pi\) | |||||||
\(402\) | 239.736 | − | 160.186i | 0.596358 | − | 0.398473i | ||||
\(403\) | −14.2250 | + | 2.82952i | −0.0352977 | + | 0.00702114i | ||||
\(404\) | −28.1305 | + | 28.1305i | −0.0696300 | + | 0.0696300i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −67.4525 | − | 27.9397i | −0.166139 | − | 0.0688171i | ||||
\(407\) | −191.154 | −0.469666 | ||||||||
\(408\) | −40.4977 | − | 27.0597i | −0.0992590 | − | 0.0663228i | ||||
\(409\) | −259.903 | −0.635461 | −0.317730 | − | 0.948181i | \(-0.602921\pi\) | ||||
−0.317730 | + | 0.948181i | \(0.602921\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 116.951 | + | 78.1442i | 0.284552 | + | 0.190132i | ||||
\(412\) | 151.812 | − | 151.812i | 0.368475 | − | 0.368475i | ||||
\(413\) | −42.0837 | − | 211.569i | −0.101898 | − | 0.512274i | ||||
\(414\) | 180.122 | − | 120.354i | 0.435078 | − | 0.290710i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −46.2687 | + | 19.1651i | −0.111223 | + | 0.0460700i | ||||
\(417\) | −134.796 | + | 55.8343i | −0.323252 | + | 0.133895i | ||||
\(418\) | 67.4471 | + | 13.4161i | 0.161357 | + | 0.0320958i | ||||
\(419\) | 95.3087 | + | 142.640i | 0.227467 | + | 0.340429i | 0.927594 | − | 0.373590i | \(-0.121873\pi\) |
−0.700127 | + | 0.714018i | \(0.746873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 443.214 | − | 443.214i | 1.05276 | − | 1.05276i | 0.0542356 | − | 0.998528i | \(-0.482728\pi\) |
0.998528 | − | 0.0542356i | \(-0.0172722\pi\) | |||||||
\(422\) | 578.287 | + | 386.399i | 1.37035 | + | 0.915637i | ||||
\(423\) | −251.219 | + | 606.497i | −0.593899 | + | 1.43380i | ||||
\(424\) | − | 211.859i | − | 0.499668i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 260.659 | 0.611875 | ||||||||
\(427\) | −264.575 | − | 109.591i | −0.619614 | − | 0.256653i | ||||
\(428\) | −253.691 | + | 379.675i | −0.592735 | + | 0.887090i | ||||
\(429\) | −5.24147 | − | 5.24147i | −0.0122179 | − | 0.0122179i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −633.734 | + | 423.447i | −1.47038 | + | 0.982477i | −0.475684 | + | 0.879616i | \(0.657799\pi\) |
−0.994696 | + | 0.102860i | \(0.967201\pi\) | |||||||
\(432\) | −27.4422 | + | 137.961i | −0.0635237 | + | 0.319355i | ||||
\(433\) | −36.2305 | − | 87.4681i | −0.0836732 | − | 0.202005i | 0.876505 | − | 0.481392i | \(-0.159869\pi\) |
−0.960179 | + | 0.279387i | \(0.909869\pi\) | |||||||
\(434\) | −116.821 | − | 282.031i | −0.269173 | − | 0.649841i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −53.4669 | − | 80.0189i | −0.122630 | − | 0.183530i | ||||
\(437\) | −23.6721 | + | 4.70868i | −0.0541696 | + | 0.0107750i | ||||
\(438\) | 106.158 | + | 106.158i | 0.242369 | + | 0.242369i | ||||
\(439\) | 20.5441 | − | 30.7465i | 0.0467976 | − | 0.0700375i | −0.807333 | − | 0.590096i | \(-0.799090\pi\) |
0.854131 | + | 0.520059i | \(0.174090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 105.852i | − | 0.240027i | ||||||
\(442\) | 58.1410i | 0.131541i | ||||||||
\(443\) | 634.146i | 1.43148i | 0.698367 | + | 0.715740i | \(0.253911\pi\) | ||||
−0.698367 | + | 0.715740i | \(0.746089\pi\) | |||||||
\(444\) | 38.0134 | − | 91.7724i | 0.0856157 | − | 0.206695i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −777.880 | − | 777.880i | −1.74412 | − | 1.74412i | ||||
\(447\) | −7.10268 | − | 35.7076i | −0.0158897 | − | 0.0798828i | ||||
\(448\) | −411.348 | − | 615.626i | −0.918187 | − | 1.37416i | ||||
\(449\) | −433.336 | − | 86.1959i | −0.965114 | − | 0.191973i | −0.312713 | − | 0.949848i | \(-0.601238\pi\) |
−0.652400 | + | 0.757874i | \(0.726238\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 67.4939 | + | 162.945i | 0.149654 | + | 0.361296i | ||||
\(452\) | −307.185 | − | 61.1029i | −0.679613 | − | 0.135183i | ||||
\(453\) | 88.7607 | − | 59.3080i | 0.195940 | − | 0.130923i | ||||
\(454\) | 57.2435 | + | 287.782i | 0.126087 | + | 0.633882i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.47749 | + | 6.70103i | −0.00981905 | + | 0.0146953i | ||||
\(457\) | −102.104 | + | 246.501i | −0.223423 | + | 0.539390i | −0.995350 | − | 0.0963202i | \(-0.969293\pi\) |
0.771928 | + | 0.635710i | \(0.219293\pi\) | |||||||
\(458\) | −1094.83 | −2.39046 | ||||||||
\(459\) | 199.145 | + | 133.064i | 0.433866 | + | 0.289900i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 172.768 | − | 417.100i | 0.374769 | − | 0.904772i | −0.618159 | − | 0.786053i | \(-0.712121\pi\) |
0.992928 | − | 0.118719i | \(-0.0378787\pi\) | |||||||
\(462\) | 86.6785 | − | 129.724i | 0.187616 | − | 0.280787i | ||||
\(463\) | −57.1171 | + | 57.1171i | −0.123363 | + | 0.123363i | −0.766093 | − | 0.642730i | \(-0.777802\pi\) |
0.642730 | + | 0.766093i | \(0.277802\pi\) | |||||||
\(464\) | 30.0670 | − | 5.98070i | 0.0647996 | − | 0.0128894i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −831.808 | − | 165.457i | −1.78499 | − | 0.355058i | ||||
\(467\) | 31.5580 | + | 76.1879i | 0.0675761 | + | 0.163143i | 0.954059 | − | 0.299617i | \(-0.0968590\pi\) |
−0.886483 | + | 0.462760i | \(0.846859\pi\) | |||||||
\(468\) | −44.9569 | + | 18.6218i | −0.0960619 | + | 0.0397901i | ||||
\(469\) | 179.617 | − | 902.998i | 0.382979 | − | 1.92537i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.70949 | − | 28.7035i | −0.0121221 | − | 0.0609417i | ||||
\(472\) | −68.4785 | − | 68.4785i | −0.145082 | − | 0.145082i | ||||
\(473\) | −156.017 | − | 104.247i | −0.329846 | − | 0.220396i | ||||
\(474\) | −216.538 | − | 89.6931i | −0.456832 | − | 0.189226i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −676.380 | + | 134.540i | −1.42097 | + | 0.282648i | ||||
\(477\) | 501.069i | 1.05046i | ||||||||
\(478\) | 918.923 | + | 380.630i | 1.92243 | + | 0.796298i | ||||
\(479\) | −382.794 | − | 255.775i | −0.799153 | − | 0.533977i | 0.0876357 | − | 0.996153i | \(-0.472069\pi\) |
−0.886788 | + | 0.462176i | \(0.847069\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.2278 | + | 5.21704i | −0.0545277 | + | 0.0108462i | ||||
\(482\) | 407.717 | + | 610.191i | 0.845885 | + | 1.26596i | ||||
\(483\) | −10.6827 | + | 53.7057i | −0.0221174 | + | 0.111192i | ||||
\(484\) | 266.195 | − | 110.261i | 0.549989 | − | 0.227813i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −105.413 | + | 529.948i | −0.216900 | + | 1.09043i | ||||
\(487\) | −434.982 | + | 290.646i | −0.893187 | + | 0.596809i | −0.915223 | − | 0.402948i | \(-0.867985\pi\) |
0.0220352 | + | 0.999757i | \(0.492985\pi\) | |||||||
\(488\) | −126.095 | + | 25.0819i | −0.258392 | + | 0.0513974i | ||||
\(489\) | 91.7633 | − | 91.7633i | 0.187655 | − | 0.187655i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −451.862 | − | 187.167i | −0.920289 | − | 0.381196i | −0.128303 | − | 0.991735i | \(-0.540953\pi\) |
−0.791986 | + | 0.610539i | \(0.790953\pi\) | |||||||
\(492\) | −91.6511 | −0.186283 | ||||||||
\(493\) | 10.1833 | − | 51.1951i | 0.0206559 | − | 0.103844i | ||||
\(494\) | 9.62041 | 0.0194745 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 106.577 | + | 71.2122i | 0.214872 | + | 0.143573i | ||||
\(497\) | 588.550 | − | 588.550i | 1.18421 | − | 1.18421i | ||||
\(498\) | 57.0266 | + | 286.692i | 0.114511 | + | 0.575687i | ||||
\(499\) | 421.610 | − | 281.711i | 0.844910 | − | 0.564551i | −0.0560623 | − | 0.998427i | \(-0.517855\pi\) |
0.900972 | + | 0.433876i | \(0.142855\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 83.1249 | − | 34.4315i | 0.165918 | − | 0.0687255i | ||||
\(502\) | 614.921 | − | 254.709i | 1.22494 | − | 0.507388i | ||||
\(503\) | 661.484 | + | 131.577i | 1.31508 | + | 0.261585i | 0.802292 | − | 0.596932i | \(-0.203614\pi\) |
0.512785 | + | 0.858517i | \(0.328614\pi\) | |||||||
\(504\) | −128.327 | − | 192.055i | −0.254617 | − | 0.381062i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 148.326 | − | 148.326i | 0.293134 | − | 0.293134i | ||||
\(507\) | 113.310 | + | 75.7115i | 0.223492 | + | 0.149332i | ||||
\(508\) | −235.686 | + | 568.996i | −0.463949 | + | 1.12007i | ||||
\(509\) | 349.504i | 0.686648i | 0.939217 | + | 0.343324i | \(0.111553\pi\) | ||||
−0.939217 | + | 0.343324i | \(0.888447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 479.395 | 0.938150 | ||||||||
\(512\) | 539.012 | + | 223.266i | 1.05276 | + | 0.436067i | ||||
\(513\) | 22.0177 | − | 32.9519i | 0.0429196 | − | 0.0642337i | ||||
\(514\) | −696.221 | − | 696.221i | −1.35451 | − | 1.35451i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 81.0747 | − | 54.1724i | 0.157121 | − | 0.104985i | ||||
\(517\) | −124.011 | + | 623.444i | −0.239866 | + | 1.20589i | ||||
\(518\) | −215.393 | − | 520.006i | −0.415818 | − | 1.00387i | ||||
\(519\) | −55.3631 | − | 133.658i | −0.106673 | − | 0.257530i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −175.223 | − | 262.240i | −0.336320 | − | 0.503339i | 0.624307 | − | 0.781179i | \(-0.285381\pi\) |
−0.960627 | + | 0.277840i | \(0.910381\pi\) | |||||||
\(522\) | 76.0323 | − | 15.1238i | 0.145656 | − | 0.0289727i | ||||
\(523\) | 145.221 | + | 145.221i | 0.277669 | + | 0.277669i | 0.832178 | − | 0.554509i | \(-0.187094\pi\) |
−0.554509 | + | 0.832178i | \(0.687094\pi\) | |||||||
\(524\) | −491.600 | + | 735.731i | −0.938168 | + | 1.40407i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 419.991i | 0.798461i | ||||||||
\(527\) | 181.468 | − | 121.253i | 0.344342 | − | 0.230082i | ||||
\(528\) | 65.5098i | 0.124072i | ||||||||
\(529\) | 174.266 | − | 420.715i | 0.329425 | − | 0.795302i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 161.959 | + | 161.959i | 0.305007 | + | 0.305007i | ||||
\(532\) | 22.2620 | + | 111.919i | 0.0418459 | + | 0.210373i | ||||
\(533\) | 13.7078 | + | 20.5152i | 0.0257182 | + | 0.0384901i | ||||
\(534\) | 209.664 | + | 41.7048i | 0.392630 | + | 0.0780989i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −158.177 | − | 381.873i | −0.295106 | − | 0.712450i | ||||
\(537\) | 200.957 | + | 39.9728i | 0.374221 | + | 0.0744372i | ||||
\(538\) | −817.764 | + | 546.412i | −1.52001 | + | 1.01564i | ||||
\(539\) | −19.9961 | − | 100.527i | −0.0370985 | − | 0.186507i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 439.282 | − | 657.431i | 0.811981 | − | 1.21522i | −0.161596 | − | 0.986857i | \(-0.551664\pi\) |
0.973577 | − | 0.228358i | \(-0.0733358\pi\) | |||||||
\(542\) | 22.2280 | − | 53.6632i | 0.0410111 | − | 0.0990096i | ||||
\(543\) | −244.849 | −0.450919 | ||||||||
\(544\) | 532.885 | − | 532.885i | 0.979568 | − | 0.979568i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.35251 | − | 20.1647i | 0.0152976 | − | 0.0369317i | ||||
\(547\) | 523.758 | − | 783.860i | 0.957511 | − | 1.43302i | 0.0569051 | − | 0.998380i | \(-0.481877\pi\) |
0.900606 | − | 0.434637i | \(-0.143123\pi\) | |||||||
\(548\) | 632.218 | − | 632.218i | 1.15368 | − | 1.15368i | ||||
\(549\) | 298.229 | − | 59.3214i | 0.543222 | − | 0.108054i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.47111 | − | 1.68501i | −0.0153741 | − | 0.00305809i | ||||
\(552\) | 9.40756 | + | 22.7119i | 0.0170427 | + | 0.0411447i | ||||
\(553\) | −691.450 | + | 286.408i | −1.25036 | + | 0.517917i | ||||
\(554\) | 181.908 | − | 914.512i | 0.328353 | − | 1.65074i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 180.934 | + | 909.619i | 0.325422 | + | 1.63601i | ||||
\(557\) | −303.284 | − | 303.284i | −0.544495 | − | 0.544495i | 0.380348 | − | 0.924843i | \(-0.375804\pi\) |
−0.924843 | + | 0.380348i | \(0.875804\pi\) | |||||||
\(558\) | 269.507 | + | 180.079i | 0.482987 | + | 0.322722i | ||||
\(559\) | −24.2519 | − | 10.0455i | −0.0433844 | − | 0.0179704i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 103.053 | + | 42.6859i | 0.183695 | + | 0.0760889i | ||||
\(562\) | 261.932i | 0.466071i | ||||||||
\(563\) | 639.473 | + | 264.879i | 1.13583 | + | 0.470477i | 0.869759 | − | 0.493476i | \(-0.164274\pi\) |
0.266072 | + | 0.963953i | \(0.414274\pi\) | |||||||
\(564\) | −274.652 | − | 183.517i | −0.486972 | − | 0.325384i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.2142 | + | 4.41867i | −0.0392476 | + | 0.00780684i | ||||
\(567\) | 277.580 | + | 415.428i | 0.489559 | + | 0.732677i | ||||
\(568\) | 72.8996 | − | 366.491i | 0.128344 | − | 0.645231i | ||||
\(569\) | 370.173 | − | 153.331i | 0.650567 | − | 0.269474i | −0.0328958 | − | 0.999459i | \(-0.510473\pi\) |
0.683463 | + | 0.729985i | \(0.260473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 127.142 | − | 639.187i | 0.222666 | − | 1.11942i | −0.694065 | − | 0.719912i | \(-0.744182\pi\) |
0.916731 | − | 0.399505i | \(-0.130818\pi\) | |||||||
\(572\) | −39.1776 | + | 26.1777i | −0.0684924 | + | 0.0457651i | ||||
\(573\) | −105.631 | + | 21.0112i | −0.184347 | + | 0.0366688i | ||||
\(574\) | −367.214 | + | 367.214i | −0.639745 | + | 0.639745i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 726.319 | + | 300.851i | 1.26097 | + | 0.522311i | ||||
\(577\) | −684.109 | −1.18563 | −0.592815 | − | 0.805339i | \(-0.701983\pi\) | ||||
−0.592815 | + | 0.805339i | \(0.701983\pi\) | |||||||
\(578\) | −334.810 | − | 808.303i | −0.579256 | − | 1.39845i | ||||
\(579\) | 258.876 | 0.447109 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 776.094 | + | 518.569i | 1.33579 | + | 0.892546i | ||||
\(582\) | −42.7712 | + | 42.7712i | −0.0734900 | + | 0.0734900i | ||||
\(583\) | 94.6550 | + | 475.863i | 0.162359 | + | 0.816232i | ||||
\(584\) | 178.950 | − | 119.570i | 0.306420 | − | 0.204744i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −215.405 | + | 89.2236i | −0.367585 | + | 0.152259i | ||||
\(587\) | 342.216 | − | 141.750i | 0.582991 | − | 0.241483i | −0.0716408 | − | 0.997430i | \(-0.522824\pi\) |
0.654632 | + | 0.755948i | \(0.272824\pi\) | |||||||
\(588\) | 52.2391 | + | 10.3910i | 0.0888420 | + | 0.0176718i | ||||
\(589\) | −20.0634 | − | 30.0270i | −0.0340635 | − | 0.0509796i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −66.4527 | + | 66.4527i | −0.112441 | + | 0.112441i | ||||
\(592\) | 196.505 | + | 131.300i | 0.331934 | + | 0.221791i | ||||
\(593\) | 242.416 | − | 585.245i | 0.408797 | − | 0.986922i | −0.576658 | − | 0.816985i | \(-0.695644\pi\) |
0.985455 | − | 0.169937i | \(-0.0543564\pi\) | |||||||
\(594\) | 344.431i | 0.579850i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −231.425 | −0.388297 | ||||||||
\(597\) | −222.080 | − | 91.9883i | −0.371992 | − | 0.154084i | ||||
\(598\) | 16.3033 | − | 24.3996i | 0.0272630 | − | 0.0408020i | ||||
\(599\) | −315.855 | − | 315.855i | −0.527304 | − | 0.527304i | 0.392463 | − | 0.919768i | \(-0.371623\pi\) |
−0.919768 | + | 0.392463i | \(0.871623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 362.279 | − | 242.067i | 0.602794 | − | 0.402774i | −0.216388 | − | 0.976307i | \(-0.569428\pi\) |
0.819182 | + | 0.573533i | \(0.194428\pi\) | |||||||
\(602\) | 107.788 | − | 541.887i | 0.179050 | − | 0.900145i | ||||
\(603\) | 374.105 | + | 903.170i | 0.620407 | + | 1.49779i | ||||
\(604\) | −259.680 | − | 626.922i | −0.429933 | − | 1.03795i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.5261 | + | 15.7535i | 0.0173699 | + | 0.0259958i | ||||
\(607\) | −622.400 | + | 123.803i | −1.02537 | + | 0.203959i | −0.679000 | − | 0.734139i | \(-0.737586\pi\) |
−0.346371 | + | 0.938098i | \(0.612586\pi\) | |||||||
\(608\) | −88.1749 | − | 88.1749i | −0.145025 | − | 0.145025i | ||||
\(609\) | −10.8865 | + | 16.2928i | −0.0178760 | + | 0.0267534i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 88.9259i | 0.145542i | ||||||||
\(612\) | 517.778 | − | 517.778i | 0.846042 | − | 0.846042i | ||||
\(613\) | 692.422i | 1.12956i | 0.825240 | + | 0.564782i | \(0.191040\pi\) | ||||
−0.825240 | + | 0.564782i | \(0.808960\pi\) | |||||||
\(614\) | −184.992 | + | 446.610i | −0.301290 | + | 0.727377i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −158.152 | − | 158.152i | −0.256740 | − | 0.256740i | ||||
\(617\) | −52.3292 | − | 263.077i | −0.0848124 | − | 0.426381i | −0.999741 | − | 0.0227645i | \(-0.992753\pi\) |
0.914928 | − | 0.403616i | \(-0.132247\pi\) | |||||||
\(618\) | −56.8062 | − | 85.0165i | −0.0919195 | − | 0.137567i | ||||
\(619\) | 153.549 | + | 30.5428i | 0.248060 | + | 0.0493422i | 0.317554 | − | 0.948240i | \(-0.397138\pi\) |
−0.0694940 | + | 0.997582i | \(0.522138\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −46.2610 | − | 111.684i | −0.0744944 | − | 0.179845i | ||||
\(622\) | 988.775 | + | 196.680i | 1.58967 | + | 0.316205i | ||||
\(623\) | 567.575 | − | 379.241i | 0.911035 | − | 0.608734i | ||||
\(624\) | 1.78791 | + | 8.98845i | 0.00286525 | + | 0.0144046i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −663.623 | + | 993.182i | −1.06010 | + | 1.58655i | ||||
\(627\) | 7.06311 | − | 17.0519i | 0.0112649 | − | 0.0271959i | ||||
\(628\) | −186.031 | −0.296228 | ||||||||
\(629\) | 334.589 | − | 223.565i | 0.531938 | − | 0.355429i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −119.803 | + | 289.230i | −0.189862 | + | 0.458368i | −0.989933 | − | 0.141538i | \(-0.954795\pi\) |
0.800071 | + | 0.599906i | \(0.204795\pi\) | |||||||
\(632\) | −186.670 | + | 279.372i | −0.295365 | + | 0.442044i | ||||
\(633\) | 131.992 | − | 131.992i | 0.208519 | − | 0.208519i | ||||
\(634\) | −412.999 | + | 82.1506i | −0.651418 | + | 0.129575i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −247.283 | − | 49.1877i | −0.388810 | − | 0.0773392i | ||||
\(637\) | −5.48723 | − | 13.2473i | −0.00861418 | − | 0.0207965i | ||||
\(638\) | 69.3506 | − | 28.7259i | 0.108700 | − | 0.0450250i | ||||
\(639\) | −172.415 | + | 866.790i | −0.269820 | + | 1.35648i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −72.2074 | − | 363.011i | −0.112648 | − | 0.566320i | −0.995345 | − | 0.0963771i | \(-0.969275\pi\) |
0.882697 | − | 0.469943i | \(-0.155725\pi\) | |||||||
\(642\) | 153.776 | + | 153.776i | 0.239526 | + | 0.239526i | ||||
\(643\) | 182.915 | + | 122.220i | 0.284471 | + | 0.190077i | 0.689616 | − | 0.724175i | \(-0.257779\pi\) |
−0.405146 | + | 0.914252i | \(0.632779\pi\) | |||||||
\(644\) | 321.577 | + | 133.202i | 0.499344 | + | 0.206835i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −133.748 | + | 55.4001i | −0.207040 | + | 0.0857586i | ||||
\(647\) | 769.098i | 1.18871i | 0.804201 | + | 0.594357i | \(0.202593\pi\) | ||||
−0.804201 | + | 0.594357i | \(0.797407\pi\) | |||||||
\(648\) | 207.231 | + | 85.8381i | 0.319802 | + | 0.132466i | ||||
\(649\) | 184.407 | + | 123.217i | 0.284140 | + | 0.189856i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −80.3568 | + | 15.9840i | −0.123436 | + | 0.0245529i | ||||
\(652\) | −458.297 | − | 685.889i | −0.702909 | − | 1.05198i | ||||
\(653\) | −8.27876 | + | 41.6201i | −0.0126780 | + | 0.0637368i | −0.986606 | − | 0.163119i | \(-0.947845\pi\) |
0.973928 | + | 0.226856i | \(0.0728446\pi\) | |||||||
\(654\) | −42.3446 | + | 17.5397i | −0.0647472 | + | 0.0268192i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 42.5406 | − | 213.866i | 0.0648485 | − | 0.326015i | ||||
\(657\) | −423.234 | + | 282.796i | −0.644192 | + | 0.430436i | ||||
\(658\) | −1835.72 | + | 365.148i | −2.78985 | + | 0.554936i | ||||
\(659\) | −472.719 | + | 472.719i | −0.717328 | + | 0.717328i | −0.968057 | − | 0.250729i | \(-0.919330\pi\) |
0.250729 | + | 0.968057i | \(0.419330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −380.158 | − | 157.467i | −0.575126 | − | 0.238225i | 0.0761113 | − | 0.997099i | \(-0.475750\pi\) |
−0.651237 | + | 0.758874i | \(0.725750\pi\) | |||||||
\(662\) | −480.756 | −0.726218 | ||||||||
\(663\) | 15.3046 | + | 3.04428i | 0.0230839 | + | 0.00459168i | ||||
\(664\) | 419.043 | 0.631089 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 496.914 | + | 332.027i | 0.746116 | + | 0.498539i | ||||
\(667\) | −18.6292 | + | 18.6292i | −0.0279298 | + | 0.0279298i | ||||
\(668\) | −111.577 | − | 560.937i | −0.167032 | − | 0.839725i | ||||
\(669\) | −245.494 | + | 164.034i | −0.366957 | + | 0.245193i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 272.020 | − | 112.675i | 0.405395 | − | 0.167920i | ||||
\(672\) | −261.372 | + | 108.264i | −0.388946 | + | 0.161107i | ||||
\(673\) | −15.9051 | − | 3.16371i | −0.0236331 | − | 0.00470091i | 0.183260 | − | 0.983065i | \(-0.441335\pi\) |
−0.206893 | + | 0.978364i | \(0.566335\pi\) | |||||||
\(674\) | 811.269 | + | 1214.15i | 1.20366 | + | 1.80141i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 612.536 | − | 612.536i | 0.906119 | − | 0.906119i | ||||
\(677\) | −854.921 | − | 571.240i | −1.26281 | − | 0.843782i | −0.269926 | − | 0.962881i | \(-0.586999\pi\) |
−0.992882 | + | 0.119099i | \(0.961999\pi\) | |||||||
\(678\) | −57.0825 | + | 137.809i | −0.0841924 | + | 0.203258i | ||||
\(679\) | 193.149i | 0.284461i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 78.7512 | 0.115641 | ||||||||
\(682\) | 289.967 | + | 120.108i | 0.425172 | + | 0.176112i | ||||
\(683\) | 125.752 | − | 188.201i | 0.184117 | − | 0.275551i | −0.727917 | − | 0.685666i | \(-0.759511\pi\) |
0.912034 | + | 0.410114i | \(0.134511\pi\) | |||||||
\(684\) | −85.6752 | − | 85.6752i | −0.125256 | − | 0.125256i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −717.830 | + | 479.639i | −1.04640 | + | 0.699181i | ||||
\(687\) | −57.3259 | + | 288.197i | −0.0834438 | + | 0.419500i | ||||
\(688\) | 88.7787 | + | 214.331i | 0.129039 | + | 0.311527i | ||||
\(689\) | 25.9748 | + | 62.7087i | 0.0376993 | + | 0.0910141i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.7058 | − | 32.4851i | −0.0314122 | − | 0.0470117i | 0.815431 | − | 0.578854i | \(-0.196500\pi\) |
−0.846843 | + | 0.531842i | \(0.821500\pi\) | |||||||
\(692\) | −901.942 | + | 179.407i | −1.30338 | + | 0.259259i | ||||
\(693\) | 374.046 | + | 374.046i | 0.539749 | + | 0.539749i | ||||
\(694\) | −33.2845 | + | 49.8138i | −0.0479604 | + | 0.0717778i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.79713i | 0.0126395i | ||||||||
\(697\) | −308.711 | − | 206.274i | −0.442914 | − | 0.295946i | ||||
\(698\) | − | 1185.05i | − | 1.69778i | ||||||
\(699\) | −87.1075 | + | 210.296i | −0.124617 | + | 0.300853i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −401.261 | − | 401.261i | −0.572412 | − | 0.572412i | 0.360390 | − | 0.932802i | \(-0.382644\pi\) |
−0.932802 | + | 0.360390i | \(0.882644\pi\) | |||||||
\(702\) | 9.40031 | + | 47.2585i | 0.0133908 | + | 0.0673198i | ||||
\(703\) | −36.9927 | − | 55.3634i | −0.0526212 | − | 0.0787531i | ||||
\(704\) | 746.614 | + | 148.511i | 1.06053 | + | 0.210953i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 226.136 | + | 545.941i | 0.320306 | + | 0.773288i | ||||
\(707\) | 59.3377 | + | 11.8030i | 0.0839288 | + | 0.0166945i | ||||
\(708\) | −95.8273 | + | 64.0298i | −0.135349 | + | 0.0904375i | ||||
\(709\) | −55.6759 | − | 279.901i | −0.0785273 | − | 0.394783i | −0.999980 | − | 0.00629329i | \(-0.997997\pi\) |
0.921453 | − | 0.388490i | \(-0.127003\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 441.495 | − | 660.744i | 0.620950 | − | 0.929317i | ||||
\(712\) | 117.276 | − | 283.128i | 0.164713 | − | 0.397652i | ||||
\(713\) | −110.156 | −0.154496 | ||||||||
\(714\) | 328.438i | 0.459998i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 498.416 | − | 1203.28i | 0.696112 | − | 1.68056i | ||||
\(717\) | 148.310 | − | 221.961i | 0.206848 | − | 0.309569i | ||||
\(718\) | 761.667 | − | 761.667i | 1.06082 | − | 1.06082i | ||||
\(719\) | −601.644 | + | 119.674i | −0.836779 | + | 0.166446i | −0.594838 | − | 0.803845i | \(-0.702784\pi\) |
−0.241941 | + | 0.970291i | \(0.577784\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −320.226 | − | 63.6970i | −0.444142 | − | 0.0883453i | ||||
\(722\) | −409.056 | − | 987.549i | −0.566560 | − | 1.36780i | ||||
\(723\) | 181.971 | − | 75.3748i | 0.251689 | − | 0.104253i | ||||
\(724\) | −303.640 | + | 1526.50i | −0.419392 | + | 2.10842i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26.7705 | − | 134.585i | −0.0368740 | − | 0.185378i | ||||
\(727\) | 244.413 | + | 244.413i | 0.336194 | + | 0.336194i | 0.854933 | − | 0.518739i | \(-0.173598\pi\) |
−0.518739 | + | 0.854933i | \(0.673598\pi\) | |||||||
\(728\) | −26.0160 | − | 17.3833i | −0.0357363 | − | 0.0238782i | ||||
\(729\) | −394.941 | − | 163.590i | −0.541758 | − | 0.224403i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 395.009 | 0.540368 | ||||||||
\(732\) | 153.003i | 0.209020i | ||||||||
\(733\) | −1246.38 | − | 516.266i | −1.70038 | − | 0.704319i | −0.700421 | − | 0.713730i | \(-0.747004\pi\) |
−0.999956 | + | 0.00941053i | \(0.997004\pi\) | |||||||
\(734\) | 205.719 | + | 137.457i | 0.280271 | + | 0.187271i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −373.058 | + | 74.2058i | −0.506872 | + | 0.100823i | ||||
\(737\) | 525.901 | + | 787.066i | 0.713569 | + | 1.06793i | ||||
\(738\) | 107.575 | − | 540.816i | 0.145766 | − | 0.732813i | ||||
\(739\) | −602.925 | + | 249.740i | −0.815866 | + | 0.337943i | −0.751292 | − | 0.659970i | \(-0.770569\pi\) |
−0.0645741 | + | 0.997913i | \(0.520569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.503729 | − | 2.53241i | 0.000679796 | − | 0.00341756i | ||||
\(742\) | −1187.86 | + | 793.700i | −1.60088 | + | 1.06968i | ||||
\(743\) | −218.711 | + | 43.5044i | −0.294362 | + | 0.0585523i | −0.340062 | − | 0.940403i | \(-0.610448\pi\) |
0.0456999 | + | 0.998955i | \(0.485448\pi\) | |||||||
\(744\) | −26.0091 | + | 26.0091i | −0.0349584 | + | 0.0349584i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −214.860 | − | 88.9980i | −0.288016 | − | 0.119300i | ||||
\(747\) | −991.082 | −1.32675 | ||||||||
\(748\) | 393.920 | − | 589.542i | 0.526631 | − | 0.788158i | ||||
\(749\) | 694.430 | 0.927143 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −373.353 | − | 249.467i | −0.497142 | − | 0.332180i | 0.281592 | − | 0.959534i | \(-0.409138\pi\) |
−0.778734 | + | 0.627355i | \(0.784138\pi\) | |||||||
\(752\) | 555.715 | − | 555.715i | 0.738982 | − | 0.738982i | ||||
\(753\) | −34.8503 | − | 175.204i | −0.0462820 | − | 0.232675i | ||||
\(754\) | 8.73143 | − | 5.83416i | 0.0115802 | − | 0.00773761i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −528.027 | + | 218.716i | −0.698449 | + | 0.289307i | ||||
\(757\) | 42.5792 | − | 17.6369i | 0.0562473 | − | 0.0232984i | −0.354382 | − | 0.935101i | \(-0.615309\pi\) |
0.410630 | + | 0.911802i | \(0.365309\pi\) | |||||||
\(758\) | 1749.62 | + | 348.021i | 2.30821 | + | 0.459131i | ||||
\(759\) | −31.2779 | − | 46.8107i | −0.0412093 | − | 0.0616741i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −552.081 | + | 552.081i | −0.725467 | + | 0.725467i | −0.969713 | − | 0.244246i | \(-0.921460\pi\) |
0.244246 | + | 0.969713i | \(0.421460\pi\) | |||||||
\(762\) | 243.881 | + | 162.956i | 0.320054 | + | 0.213853i | ||||
\(763\) | −56.0079 | + | 135.215i | −0.0734048 | + | 0.177215i | ||||
\(764\) | 684.604i | 0.896079i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 707.240 | 0.923289 | ||||||||
\(767\) | 28.6649 | + | 11.8734i | 0.0373727 | + | 0.0154803i | ||||
\(768\) | 22.5463 | − | 33.7429i | 0.0293571 | − | 0.0439360i | ||||
\(769\) | 625.504 | + | 625.504i | 0.813400 | + | 0.813400i | 0.985142 | − | 0.171742i | \(-0.0549396\pi\) |
−0.171742 | + | 0.985142i | \(0.554940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −219.723 | + | 146.814i | −0.284984 | + | 0.190420i | ||||
\(772\) | 321.035 | − | 1613.95i | 0.415848 | − | 2.09061i | ||||
\(773\) | −465.474 | − | 1123.75i | −0.602166 | − | 1.45376i | −0.871347 | − | 0.490667i | \(-0.836753\pi\) |
0.269181 | − | 0.963090i | \(-0.413247\pi\) | |||||||
\(774\) | 224.500 | + | 541.991i | 0.290052 | + | 0.700247i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 48.1751 | + | 72.0992i | 0.0620813 | + | 0.0929113i | ||||
\(777\) | −148.161 | + | 29.4711i | −0.190683 | + | 0.0379293i | ||||
\(778\) | 864.056 | + | 864.056i | 1.11061 | + | 1.11061i | ||||
\(779\) | −34.1316 | + | 51.0816i | −0.0438146 | + | 0.0655733i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 855.757i | 1.09572i | ||||||||
\(782\) | −86.1486 | + | 433.098i | −0.110164 | + | 0.553834i | ||||
\(783\) | − | 43.2592i | − | 0.0552481i | ||||||
\(784\) | −48.4944 | + | 117.076i | −0.0618551 | + | 0.149331i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 297.985 | + | 297.985i | 0.379116 | + | 0.379116i | ||||
\(787\) | −37.8601 | − | 190.336i | −0.0481069 | − | 0.241850i | 0.949249 | − | 0.314527i | \(-0.101846\pi\) |
−0.997356 | + | 0.0726771i | \(0.976846\pi\) | |||||||
\(788\) | 331.887 | + | 496.704i | 0.421177 | + | 0.630336i | ||||
\(789\) | 110.556 | + | 21.9909i | 0.140121 | + | 0.0278718i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 182.276 | + | 440.053i | 0.230437 | + | 0.556324i | ||||
\(792\) | 232.919 | + | 46.3305i | 0.294090 | + | 0.0584981i | ||||
\(793\) | 34.2481 | − | 22.8839i | 0.0431881 | − | 0.0288573i | ||||
\(794\) | −155.795 | − | 783.233i | −0.196215 | − | 0.986440i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −848.899 | + | 1270.47i | −1.06646 | + | 1.59606i | ||||
\(797\) | −49.1164 | + | 118.577i | −0.0616266 | + | 0.148780i | −0.951693 | − | 0.307051i | \(-0.900658\pi\) |
0.890066 | + | 0.455831i | \(0.150658\pi\) | |||||||
\(798\) | 54.3457 | 0.0681024 | ||||||||
\(799\) | −512.088 | − | 1236.29i | −0.640911 | − | 1.54730i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −277.369 | + | 669.628i | −0.346278 | + | 0.835990i | ||||
\(802\) | −402.460 | + | 602.324i | −0.501821 | + | 0.751028i | ||||
\(803\) | −348.522 | + | 348.522i | −0.434025 | + | 0.434025i | ||||
\(804\) | −482.449 | + | 95.9651i | −0.600061 | + | 0.119360i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 43.0638 | + | 8.56592i | 0.0534290 | + | 0.0106277i | ||||
\(807\) | 101.016 | + | 243.873i | 0.125174 | + | 0.302197i | ||||
\(808\) | 25.0936 | − | 10.3941i | 0.0310564 | − | 0.0128640i | ||||
\(809\) | −68.1098 | + | 342.411i | −0.0841902 | + | 0.423253i | 0.915587 | + | 0.402121i | \(0.131727\pi\) |
−0.999777 | + | 0.0211316i | \(0.993273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.2150 | + | 182.065i | 0.0446547 | + | 0.224494i | 0.996668 | − | 0.0815613i | \(-0.0259906\pi\) |
−0.952014 | + | 0.306056i | \(0.900991\pi\) | |||||||
\(812\) | 88.0762 | + | 88.0762i | 0.108468 | + | 0.108468i | ||||
\(813\) | −12.9621 | − | 8.66099i | −0.0159435 | − | 0.0106531i | ||||
\(814\) | 534.639 | + | 221.455i | 0.656804 | + | 0.272057i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −76.6173 | − | 114.666i | −0.0938937 | − | 0.140522i | ||||
\(817\) | − | 65.3610i | − | 0.0800013i | ||||||
\(818\) | 726.923 | + | 301.101i | 0.888659 | + | 0.368095i | ||||
\(819\) | 61.5306 | + | 41.1134i | 0.0751290 | + | 0.0501996i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1545.78 | − | 307.474i | 1.88280 | − | 0.374512i | 0.886669 | − | 0.462404i | \(-0.153013\pi\) |
0.996130 | + | 0.0878920i | \(0.0280130\pi\) | |||||||
\(822\) | −236.569 | − | 354.051i | −0.287797 | − | 0.430718i | ||||
\(823\) | 196.185 | − | 986.291i | 0.238378 | − | 1.19841i | −0.657273 | − | 0.753653i | \(-0.728290\pi\) |
0.895651 | − | 0.444757i | \(-0.146710\pi\) | |||||||
\(824\) | −135.422 | + | 56.0937i | −0.164347 | + | 0.0680749i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −127.402 | + | 640.491i | −0.154239 | + | 0.775413i | ||||
\(827\) | 1321.52 | − | 883.014i | 1.59797 | − | 1.06773i | 0.645216 | − | 0.764001i | \(-0.276768\pi\) |
0.952758 | − | 0.303731i | \(-0.0982324\pi\) | |||||||
\(828\) | −362.481 | + | 72.1020i | −0.437780 | + | 0.0870798i | ||||
\(829\) | 269.747 | − | 269.747i | 0.325388 | − | 0.325388i | −0.525442 | − | 0.850830i | \(-0.676100\pi\) |
0.850830 | + | 0.525442i | \(0.176100\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −231.205 | − | 95.7684i | −0.278225 | − | 0.115245i | ||||
\(832\) | 106.494 | 0.127998 | ||||||||
\(833\) | 152.572 | + | 152.572i | 0.183160 | + | 0.183160i | ||||
\(834\) | 441.695 | 0.529611 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −97.5499 | − | 65.1807i | −0.116686 | − | 0.0779674i | ||||
\(837\) | 127.898 | − | 127.898i | 0.152805 | − | 0.152805i | ||||
\(838\) | −101.319 | − | 509.365i | −0.120906 | − | 0.607834i | ||||
\(839\) | 30.7798 | − | 20.5664i | 0.0366862 | − | 0.0245130i | −0.537092 | − | 0.843524i | \(-0.680477\pi\) |
0.573778 | + | 0.819011i | \(0.305477\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 768.273 | − | 318.229i | 0.913523 | − | 0.378393i | ||||
\(842\) | −1753.09 | + | 726.154i | −2.08206 | + | 0.862416i | ||||
\(843\) | 68.9493 | + | 13.7149i | 0.0817904 | + | 0.0162691i | ||||
\(844\) | −659.215 | − | 986.584i | −0.781060 | − | 1.16894i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1405.27 | − | 1405.27i | 1.66107 | − | 1.66107i | ||||
\(847\) | −364.329 | − | 243.437i | −0.430141 | − | 0.287411i | ||||
\(848\) | 229.557 | − | 554.200i | 0.270704 | − | 0.653538i | ||||
\(849\) | 6.07887i | 0.00716004i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −203.104 | −0.238665 | ||||||||
\(852\) | −410.846 | − | 170.178i | −0.482213 | − | 0.199739i | ||||
\(853\) | −43.8137 | + | 65.5718i | −0.0513642 | + | 0.0768720i | −0.856263 | − | 0.516540i | \(-0.827220\pi\) |
0.804899 | + | 0.593412i | \(0.202220\pi\) | |||||||
\(854\) | 613.028 | + | 613.028i | 0.717831 | + | 0.717831i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 259.219 | − | 173.204i | 0.302825 | − | 0.202342i | ||||
\(857\) | 129.947 | − | 653.288i | 0.151630 | − | 0.762297i | −0.827880 | − | 0.560905i | \(-0.810453\pi\) |
0.979511 | − | 0.201392i | \(-0.0645465\pi\) | |||||||
\(858\) | 8.58754 | + | 20.7322i | 0.0100088 | + | 0.0241634i | ||||
\(859\) | 530.649 | + | 1281.10i | 0.617752 | + | 1.49138i | 0.854308 | + | 0.519767i | \(0.173981\pi\) |
−0.236556 | + | 0.971618i | \(0.576019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 77.4355 | + | 115.890i | 0.0899367 | + | 0.134600i | ||||
\(862\) | 2263.06 | − | 450.150i | 2.62536 | − | 0.522216i | ||||
\(863\) | 375.548 | + | 375.548i | 0.435166 | + | 0.435166i | 0.890381 | − | 0.455215i | \(-0.150438\pi\) |
−0.455215 | + | 0.890381i | \(0.650438\pi\) | |||||||
\(864\) | 346.986 | − | 519.301i | 0.401604 | − | 0.601042i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 286.613i | 0.330962i | ||||||||
\(867\) | −230.303 | + | 45.8102i | −0.265632 | + | 0.0528376i | ||||
\(868\) | 520.802i | 0.600002i | ||||||||
\(869\) | 294.467 | − | 710.907i | 0.338858 | − | 0.818075i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 93.6384 | + | 93.6384i | 0.107507 | + | 0.107507i | ||||
\(872\) | 12.8185 | + | 64.4428i | 0.0147001 | + | 0.0739023i | ||||
\(873\) | −113.939 | − | 170.522i | −0.130515 | − | 0.195329i | ||||
\(874\) | 71.6635 | + | 14.2548i | 0.0819949 | + | 0.0163098i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −98.0161 | − | 236.632i | −0.111891 | − | 0.270128i | ||||
\(877\) | −243.780 | − | 48.4908i | −0.277970 | − | 0.0552917i | 0.0541366 | − | 0.998534i | \(-0.482759\pi\) |
−0.332107 | + | 0.943242i | \(0.607759\pi\) | |||||||
\(878\) | −93.0800 | + | 62.1940i | −0.106014 | + | 0.0708360i | ||||
\(879\) | 12.2080 | + | 61.3735i | 0.0138885 | + | 0.0698220i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −81.3688 | + | 121.777i | −0.0923595 | + | 0.138226i | −0.874772 | − | 0.484535i | \(-0.838989\pi\) |
0.782412 | + | 0.622761i | \(0.213989\pi\) | |||||||
\(882\) | −122.631 | + | 296.057i | −0.139037 | + | 0.335665i | ||||
\(883\) | 322.505 | 0.365237 | 0.182619 | − | 0.983184i | \(-0.441543\pi\) | ||||
0.182619 | + | 0.983184i | \(0.441543\pi\) | |||||||
\(884\) | 37.9588 | − | 91.6407i | 0.0429399 | − | 0.103666i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 734.666 | − | 1773.64i | 0.829194 | − | 2.00185i | ||||
\(887\) | 34.9202 | − | 52.2618i | 0.0393689 | − | 0.0589197i | −0.811263 | − | 0.584681i | \(-0.801220\pi\) |
0.850632 | + | 0.525762i | \(0.176220\pi\) | |||||||
\(888\) | −47.9552 | + | 47.9552i | −0.0540037 | + | 0.0540037i | ||||
\(889\) | 918.610 | − | 182.723i | 1.03331 | − | 0.205538i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −503.820 | − | 100.216i | −0.565454 | − | 0.112476i | ||||
\(892\) | 718.221 | + | 1733.94i | 0.805180 | + | 1.94388i | ||||
\(893\) | −204.565 | + | 84.7337i | −0.229077 | + | 0.0948866i | ||||
\(894\) | −21.5022 | + | 108.099i | −0.0240517 | + | 0.120916i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 165.574 | + | 832.399i | 0.184793 | + | 0.929016i | ||||
\(897\) | −5.56914 | − | 5.56914i | −0.00620863 | − | 0.00620863i | ||||
\(898\) | 1112.14 | + | 743.106i | 1.23846 | + | 0.827513i | ||||
\(899\) | −36.4189 | − | 15.0852i | −0.0405104 | − | 0.0167800i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −722.228 | − | 722.228i | −0.801585 | − | 0.801585i | ||||
\(902\) | − | 533.932i | − | 0.591942i | ||||||
\(903\) | −136.999 | − | 56.7469i | −0.151715 | − | 0.0628426i | ||||
\(904\) | 177.798 | + | 118.801i | 0.196679 | + | 0.131417i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −316.964 | + | 63.0480i | −0.349850 | + | 0.0695894i | ||||
\(907\) | −122.120 | − | 182.765i | −0.134641 | − | 0.201505i | 0.758022 | − | 0.652229i | \(-0.226166\pi\) |
−0.892663 | + | 0.450724i | \(0.851166\pi\) | |||||||
\(908\) | 97.6601 | − | 490.970i | 0.107555 | − | 0.540716i | ||||
\(909\) | −59.3490 | + | 24.5832i | −0.0652904 | + | 0.0270442i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 98.5913 | − | 495.652i | 0.108223 | − | 0.544074i | −0.888192 | − | 0.459473i | \(-0.848038\pi\) |
0.996415 | − | 0.0846014i | \(-0.0269617\pi\) | |||||||
\(912\) | −18.9734 | + | 12.6776i | −0.0208042 | + | 0.0139009i | ||||
\(913\) | −941.226 | + | 187.221i | −1.03092 | + | 0.205062i | ||||
\(914\) | 571.150 | − | 571.150i | 0.624890 | − | 0.624890i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1725.66 | + | 714.790i | 1.88390 | + | 0.780338i | ||||
\(917\) | 1345.66 | 1.46746 | ||||||||
\(918\) | −402.830 | − | 602.878i | −0.438813 | − | 0.656730i | ||||
\(919\) | 930.196 | 1.01218 | 0.506091 | − | 0.862480i | \(-0.331090\pi\) | ||||
0.506091 | + | 0.862480i | \(0.331090\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 107.876 | + | 72.0807i | 0.117130 | + | 0.0782635i | ||||
\(922\) | −966.431 | + | 966.431i | −1.04819 | + | 1.04819i | ||||
\(923\) | 23.3556 | + | 117.416i | 0.0253040 | + | 0.127212i | ||||
\(924\) | −221.315 | + | 147.878i | −0.239518 | + | 0.160041i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 225.922 | − | 93.5798i | 0.243976 | − | 0.101058i | ||||
\(927\) | 320.288 | − | 132.667i | 0.345510 | − | 0.143115i | ||||
\(928\) | −133.499 | − | 26.5547i | −0.143857 | − | 0.0286150i | ||||
\(929\) | −637.592 | − | 954.224i | −0.686321 | − | 1.02715i | −0.997058 | − | 0.0766557i | \(-0.975576\pi\) |
0.310737 | − | 0.950496i | \(-0.399424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.2457 | − | 25.2457i | 0.0271167 | − | 0.0271167i | ||||
\(932\) | 1203.06 | + | 803.857i | 1.29083 | + | 0.862508i | ||||
\(933\) | 103.545 | − | 249.980i | 0.110981 | − | 0.267932i | ||||
\(934\) | − | 249.650i | − | 0.267291i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 33.2228 | 0.0354944 | ||||||||
\(937\) | 1249.07 | + | 517.380i | 1.33305 | + | 0.552166i | 0.931523 | − | 0.363682i | \(-0.118481\pi\) |
0.401524 | + | 0.915848i | \(0.368481\pi\) | |||||||
\(938\) | −1548.51 | + | 2317.50i | −1.65086 | + | 2.47068i | ||||
\(939\) | 226.691 | + | 226.691i | 0.241418 | + | 0.241418i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1529.70 | + | 1022.11i | −1.62561 | + | 1.08620i | −0.695743 | + | 0.718291i | \(0.744925\pi\) |
−0.929864 | + | 0.367905i | \(0.880075\pi\) | |||||||
\(942\) | −17.2846 | + | 86.8953i | −0.0183488 | + | 0.0922455i | ||||
\(943\) | 71.7133 | + | 173.131i | 0.0760480 | + | 0.183596i | ||||
\(944\) | −104.933 | − | 253.331i | −0.111158 | − | 0.268359i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 315.592 | + | 472.317i | 0.333607 | + | 0.499278i | ||||
\(947\) | 38.5945 | − | 7.67691i | 0.0407544 | − | 0.00810656i | −0.174671 | − | 0.984627i | \(-0.555886\pi\) |
0.215425 | + | 0.976520i | \(0.430886\pi\) | |||||||
\(948\) | 282.745 | + | 282.745i | 0.298255 | + | 0.298255i | ||||
\(949\) | −38.3079 | + | 57.3319i | −0.0403666 | + | 0.0604129i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 113.017i | 0.118840i | ||||||||
\(952\) | 461.791 | + | 91.8559i | 0.485074 | + | 0.0964873i | ||||
\(953\) | − | 183.445i | − | 0.192492i | −0.995358 | − | 0.0962458i | \(-0.969317\pi\) | ||
0.995358 | − | 0.0962458i | \(-0.0306835\pi\) | |||||||
\(954\) | 580.495 | − | 1401.44i | 0.608485 | − | 1.46901i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1199.89 | − | 1199.89i | −1.25511 | − | 1.25511i | ||||
\(957\) | −3.93041 | − | 19.7595i | −0.00410701 | − | 0.0206473i | ||||
\(958\) | 774.317 | + | 1158.85i | 0.808264 | + | 1.20965i | ||||
\(959\) | −1333.58 | − | 265.266i | −1.39059 | − | 0.276606i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 304.685 | + | 735.574i | 0.317050 | + | 0.765426i | ||||
\(962\) | 79.4005 | + | 15.7937i | 0.0825369 | + | 0.0164176i | ||||
\(963\) | −613.079 | + | 409.646i | −0.636635 | + | 0.425386i | ||||
\(964\) | −244.257 | − | 1227.96i | −0.253378 | − | 1.27382i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 92.0972 | − | 137.833i | 0.0953387 | − | 0.142684i | ||||
\(967\) | −489.471 | + | 1181.69i | −0.506175 | + | 1.22201i | 0.439894 | + | 0.898050i | \(0.355016\pi\) |
−0.946069 | + | 0.323965i | \(0.894984\pi\) | |||||||
\(968\) | −196.715 | −0.203218 | ||||||||
\(969\) | 7.58007 | + | 38.1076i | 0.00782257 | + | 0.0393267i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −349.777 | + | 844.437i | −0.360224 | + | 0.869657i | 0.635043 | + | 0.772477i | \(0.280982\pi\) |
−0.995267 | + | 0.0971803i | \(0.969018\pi\) | |||||||
\(972\) | 512.141 | − | 766.473i | 0.526894 | − | 0.788553i | ||||
\(973\) | 997.319 | − | 997.319i | 1.02499 | − | 1.02499i | ||||
\(974\) | 1553.32 | − | 308.974i | 1.59478 | − | 0.317222i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −357.029 | − | 71.0174i | −0.365808 | − | 0.0727637i | ||||
\(977\) | −169.210 | − | 408.510i | −0.173194 | − | 0.418126i | 0.813318 | − | 0.581820i | \(-0.197659\pi\) |
−0.986511 | + | 0.163694i | \(0.947659\pi\) | |||||||
\(978\) | −362.961 | + | 150.343i | −0.371126 | + | 0.153725i | ||||
\(979\) | −136.919 | + | 688.340i | −0.139856 | + | 0.703105i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.3170 | − | 152.414i | −0.0309042 | − | 0.155366i | ||||
\(982\) | 1046.98 | + | 1046.98i | 1.06617 | + | 1.06617i | ||||
\(983\) | −553.287 | − | 369.695i | −0.562856 | − | 0.376088i | 0.241351 | − | 0.970438i | \(-0.422410\pi\) |
−0.804207 | + | 0.594350i | \(0.797410\pi\) | |||||||
\(984\) | 57.8106 | + | 23.9459i | 0.0587506 | + | 0.0243353i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −87.7920 | + | 131.390i | −0.0890385 | + | 0.133256i | ||||
\(987\) | 502.343i | 0.508959i | ||||||||
\(988\) | −15.1635 | − | 6.28094i | −0.0153477 | − | 0.00635723i | ||||
\(989\) | −165.770 | − | 110.764i | −0.167614 | − | 0.111996i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1534.80 | + | 305.291i | −1.54874 | + | 0.308063i | −0.894096 | − | 0.447876i | \(-0.852181\pi\) |
−0.654642 | + | 0.755939i | \(0.727181\pi\) | |||||||
\(992\) | −316.187 | − | 473.207i | −0.318736 | − | 0.477023i | ||||
\(993\) | −25.1726 | + | 126.551i | −0.0253500 | + | 0.127443i | ||||
\(994\) | −2327.96 | + | 964.271i | −2.34201 | + | 0.970092i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 97.2901 | − | 489.110i | 0.0976808 | − | 0.491075i | ||||
\(997\) | 1280.55 | − | 855.639i | 1.28441 | − | 0.858213i | 0.289321 | − | 0.957232i | \(-0.406570\pi\) |
0.995086 | + | 0.0990189i | \(0.0315704\pi\) | |||||||
\(998\) | −1505.57 | + | 299.476i | −1.50858 | + | 0.300076i | ||||
\(999\) | 235.817 | − | 235.817i | 0.236053 | − | 0.236053i |
(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 | 425.3.t.a.299.1 | 8 | ||
5.2 | odd | 4 | 425.3.u.b.401.1 | 8 | |||
5.3 | odd | 4 | 17.3.e.a.10.1 | ✓ | 8 | ||
5.4 | even | 2 | 425.3.t.c.299.1 | 8 | |||
15.8 | even | 4 | 153.3.p.b.10.1 | 8 | |||
17.12 | odd | 16 | 425.3.t.c.199.1 | 8 | |||
20.3 | even | 4 | 272.3.bh.c.129.1 | 8 | |||
85.3 | even | 16 | 289.3.e.i.158.1 | 8 | |||
85.8 | odd | 8 | 289.3.e.l.249.1 | 8 | |||
85.12 | even | 16 | 425.3.u.b.301.1 | 8 | |||
85.13 | odd | 4 | 289.3.e.m.75.1 | 8 | |||
85.23 | even | 16 | 289.3.e.d.224.1 | 8 | |||
85.28 | even | 16 | 289.3.e.b.224.1 | 8 | |||
85.29 | odd | 16 | inner | 425.3.t.a.199.1 | 8 | ||
85.33 | odd | 4 | 289.3.e.c.214.1 | 8 | |||
85.38 | odd | 4 | 289.3.e.i.75.1 | 8 | |||
85.43 | odd | 8 | 289.3.e.k.249.1 | 8 | |||
85.48 | even | 16 | 289.3.e.m.158.1 | 8 | |||
85.53 | odd | 8 | 289.3.e.d.40.1 | 8 | |||
85.58 | even | 16 | 289.3.e.k.65.1 | 8 | |||
85.63 | even | 16 | 17.3.e.a.12.1 | yes | 8 | ||
85.73 | even | 16 | 289.3.e.c.131.1 | 8 | |||
85.78 | even | 16 | 289.3.e.l.65.1 | 8 | |||
85.83 | odd | 8 | 289.3.e.b.40.1 | 8 | |||
255.233 | odd | 16 | 153.3.p.b.46.1 | 8 | |||
340.63 | odd | 16 | 272.3.bh.c.97.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.3.e.a.10.1 | ✓ | 8 | 5.3 | odd | 4 | ||
17.3.e.a.12.1 | yes | 8 | 85.63 | even | 16 | ||
153.3.p.b.10.1 | 8 | 15.8 | even | 4 | |||
153.3.p.b.46.1 | 8 | 255.233 | odd | 16 | |||
272.3.bh.c.97.1 | 8 | 340.63 | odd | 16 | |||
272.3.bh.c.129.1 | 8 | 20.3 | even | 4 | |||
289.3.e.b.40.1 | 8 | 85.83 | odd | 8 | |||
289.3.e.b.224.1 | 8 | 85.28 | even | 16 | |||
289.3.e.c.131.1 | 8 | 85.73 | even | 16 | |||
289.3.e.c.214.1 | 8 | 85.33 | odd | 4 | |||
289.3.e.d.40.1 | 8 | 85.53 | odd | 8 | |||
289.3.e.d.224.1 | 8 | 85.23 | even | 16 | |||
289.3.e.i.75.1 | 8 | 85.38 | odd | 4 | |||
289.3.e.i.158.1 | 8 | 85.3 | even | 16 | |||
289.3.e.k.65.1 | 8 | 85.58 | even | 16 | |||
289.3.e.k.249.1 | 8 | 85.43 | odd | 8 | |||
289.3.e.l.65.1 | 8 | 85.78 | even | 16 | |||
289.3.e.l.249.1 | 8 | 85.8 | odd | 8 | |||
289.3.e.m.75.1 | 8 | 85.13 | odd | 4 | |||
289.3.e.m.158.1 | 8 | 85.48 | even | 16 | |||
425.3.t.a.199.1 | 8 | 85.29 | odd | 16 | inner | ||
425.3.t.a.299.1 | 8 | 1.1 | even | 1 | trivial | ||
425.3.t.c.199.1 | 8 | 17.12 | odd | 16 | |||
425.3.t.c.299.1 | 8 | 5.4 | even | 2 | |||
425.3.u.b.301.1 | 8 | 85.12 | even | 16 | |||
425.3.u.b.401.1 | 8 | 5.2 | odd | 4 |