Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [102,3,Mod(47,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.e (of order \(4\), 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: | \(2.77929869648\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{18} + 149 x^{16} - 800 x^{14} - 1986 x^{12} + 2844 x^{10} - 160866 x^{8} + \cdots + 3486784401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Root | \(2.40171 - 1.79772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 102.47 |
Dual form | 102.3.e.b.89.1 |
$q$-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 \(\left(\mathbb{Z}/102\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −2.96944 | − | 0.427083i | −0.989815 | − | 0.142361i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −1.26169 | + | 1.26169i | −0.252338 | + | 0.252338i | −0.821929 | − | 0.569591i | \(-0.807102\pi\) |
0.569591 | + | 0.821929i | \(0.307102\pi\) | |||||||
\(6\) | 4.19943 | + | 0.603986i | 0.699905 | + | 0.100664i | ||||
\(7\) | 2.01679 | − | 2.01679i | 0.288112 | − | 0.288112i | −0.548221 | − | 0.836333i | \(-0.684695\pi\) |
0.836333 | + | 0.548221i | \(0.184695\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 8.63520 | + | 2.53640i | 0.959467 | + | 0.281822i | ||||
\(10\) | 1.78430 | − | 1.78430i | 0.178430 | − | 0.178430i | ||||
\(11\) | 8.23314 | + | 8.23314i | 0.748467 | + | 0.748467i | 0.974191 | − | 0.225724i | \(-0.0724747\pi\) |
−0.225724 | + | 0.974191i | \(0.572475\pi\) | |||||||
\(12\) | −5.93889 | − | 0.854166i | −0.494907 | − | 0.0711805i | ||||
\(13\) | 22.6733 | 1.74410 | 0.872050 | − | 0.489416i | \(-0.162790\pi\) | ||||
0.872050 | + | 0.489416i | \(0.162790\pi\) | |||||||
\(14\) | −2.85217 | + | 2.85217i | −0.203726 | + | 0.203726i | ||||
\(15\) | 4.28536 | − | 3.20767i | 0.285691 | − | 0.213845i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 8.81003 | − | 14.5390i | 0.518237 | − | 0.855237i | ||||
\(18\) | −12.2120 | − | 3.58701i | −0.678445 | − | 0.199278i | ||||
\(19\) | 19.5669i | 1.02984i | 0.857239 | + | 0.514920i | \(0.172178\pi\) | ||||
−0.857239 | + | 0.514920i | \(0.827822\pi\) | |||||||
\(20\) | −2.52338 | + | 2.52338i | −0.126169 | + | 0.126169i | ||||
\(21\) | −6.85007 | + | 5.12740i | −0.326194 | + | 0.244162i | ||||
\(22\) | −11.6434 | − | 11.6434i | −0.529246 | − | 0.529246i | ||||
\(23\) | −6.84267 | − | 6.84267i | −0.297507 | − | 0.297507i | 0.542529 | − | 0.840037i | \(-0.317467\pi\) |
−0.840037 | + | 0.542529i | \(0.817467\pi\) | |||||||
\(24\) | 8.39886 | + | 1.20797i | 0.349952 | + | 0.0503322i | ||||
\(25\) | 21.8163i | 0.872651i | ||||||||
\(26\) | −32.0649 | −1.23327 | ||||||||
\(27\) | −24.5585 | − | 11.2196i | −0.909574 | − | 0.415542i | ||||
\(28\) | 4.03357 | − | 4.03357i | 0.144056 | − | 0.144056i | ||||
\(29\) | 8.85961 | − | 8.85961i | 0.305504 | − | 0.305504i | −0.537659 | − | 0.843162i | \(-0.680691\pi\) |
0.843162 | + | 0.537659i | \(0.180691\pi\) | |||||||
\(30\) | −6.06042 | + | 4.53633i | −0.202014 | + | 0.151211i | ||||
\(31\) | −16.6659 | − | 16.6659i | −0.537608 | − | 0.537608i | 0.385218 | − | 0.922826i | \(-0.374126\pi\) |
−0.922826 | + | 0.385218i | \(0.874126\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | −20.9316 | − | 27.9641i | −0.634292 | − | 0.847397i | ||||
\(34\) | −12.4593 | + | 20.5613i | −0.366449 | + | 0.604744i | ||||
\(35\) | 5.08912i | 0.145403i | ||||||||
\(36\) | 17.2704 | + | 5.07280i | 0.479733 | + | 0.140911i | ||||
\(37\) | 23.1242 | + | 23.1242i | 0.624978 | + | 0.624978i | 0.946800 | − | 0.321822i | \(-0.104295\pi\) |
−0.321822 | + | 0.946800i | \(0.604295\pi\) | |||||||
\(38\) | − | 27.6718i | − | 0.728206i | ||||||
\(39\) | −67.3271 | − | 9.68338i | −1.72634 | − | 0.248292i | ||||
\(40\) | 3.56860 | − | 3.56860i | 0.0892149 | − | 0.0892149i | ||||
\(41\) | 17.3200 | + | 17.3200i | 0.422438 | + | 0.422438i | 0.886042 | − | 0.463604i | \(-0.153444\pi\) |
−0.463604 | + | 0.886042i | \(0.653444\pi\) | |||||||
\(42\) | 9.68746 | − | 7.25124i | 0.230654 | − | 0.172649i | ||||
\(43\) | − | 53.6267i | − | 1.24713i | −0.781770 | − | 0.623567i | \(-0.785683\pi\) | ||
0.781770 | − | 0.623567i | \(-0.214317\pi\) | |||||||
\(44\) | 16.4663 | + | 16.4663i | 0.374234 | + | 0.374234i | ||||
\(45\) | −14.0951 | + | 7.69480i | −0.313224 | + | 0.170995i | ||||
\(46\) | 9.67699 | + | 9.67699i | 0.210369 | + | 0.210369i | ||||
\(47\) | 12.1592i | 0.258706i | 0.991599 | + | 0.129353i | \(0.0412900\pi\) | ||||
−0.991599 | + | 0.129353i | \(0.958710\pi\) | |||||||
\(48\) | −11.8778 | − | 1.70833i | −0.247454 | − | 0.0355902i | ||||
\(49\) | 40.8651i | 0.833983i | ||||||||
\(50\) | − | 30.8529i | − | 0.617058i | ||||||
\(51\) | −32.3703 | + | 39.4102i | −0.634711 | + | 0.772750i | ||||
\(52\) | 45.3466 | 0.872050 | ||||||||
\(53\) | 58.5783 | 1.10525 | 0.552626 | − | 0.833430i | \(-0.313626\pi\) | ||||
0.552626 | + | 0.833430i | \(0.313626\pi\) | |||||||
\(54\) | 34.7310 | + | 15.8670i | 0.643166 | + | 0.293833i | ||||
\(55\) | −20.7753 | −0.377733 | ||||||||
\(56\) | −5.70433 | + | 5.70433i | −0.101863 | + | 0.101863i | ||||
\(57\) | 8.35671 | − | 58.1029i | 0.146609 | − | 1.01935i | ||||
\(58\) | −12.5294 | + | 12.5294i | −0.216024 | + | 0.216024i | ||||
\(59\) | −3.52326 | −0.0597162 | −0.0298581 | − | 0.999554i | \(-0.509506\pi\) | ||||
−0.0298581 | + | 0.999554i | \(0.509506\pi\) | |||||||
\(60\) | 8.57073 | − | 6.41534i | 0.142845 | − | 0.106922i | ||||
\(61\) | 21.2812 | − | 21.2812i | 0.348872 | − | 0.348872i | −0.510817 | − | 0.859689i | \(-0.670657\pi\) |
0.859689 | + | 0.510817i | \(0.170657\pi\) | |||||||
\(62\) | 23.5691 | + | 23.5691i | 0.380146 | + | 0.380146i | ||||
\(63\) | 22.5307 | − | 12.3000i | 0.357631 | − | 0.195238i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −28.6067 | + | 28.6067i | −0.440103 | + | 0.440103i | ||||
\(66\) | 29.6018 | + | 39.5472i | 0.448512 | + | 0.599200i | ||||
\(67\) | 29.5242 | 0.440659 | 0.220330 | − | 0.975425i | \(-0.429287\pi\) | ||||
0.220330 | + | 0.975425i | \(0.429287\pi\) | |||||||
\(68\) | 17.6201 | − | 29.0781i | 0.259119 | − | 0.427619i | ||||
\(69\) | 17.3965 | + | 23.2413i | 0.252124 | + | 0.336831i | ||||
\(70\) | − | 7.19710i | − | 0.102816i | ||||||
\(71\) | −63.8514 | + | 63.8514i | −0.899315 | + | 0.899315i | −0.995376 | − | 0.0960602i | \(-0.969376\pi\) |
0.0960602 | + | 0.995376i | \(0.469376\pi\) | |||||||
\(72\) | −24.4240 | − | 7.17402i | −0.339223 | − | 0.0996391i | ||||
\(73\) | −54.3732 | − | 54.3732i | −0.744838 | − | 0.744838i | 0.228667 | − | 0.973505i | \(-0.426563\pi\) |
−0.973505 | + | 0.228667i | \(0.926563\pi\) | |||||||
\(74\) | −32.7025 | − | 32.7025i | −0.441926 | − | 0.441926i | ||||
\(75\) | 9.31736 | − | 64.7822i | 0.124231 | − | 0.863763i | ||||
\(76\) | 39.1339i | 0.514920i | ||||||||
\(77\) | 33.2090 | 0.431285 | ||||||||
\(78\) | 95.2149 | + | 13.6944i | 1.22070 | + | 0.175569i | ||||
\(79\) | 31.8519 | − | 31.8519i | 0.403188 | − | 0.403188i | −0.476167 | − | 0.879355i | \(-0.657974\pi\) |
0.879355 | + | 0.476167i | \(0.157974\pi\) | |||||||
\(80\) | −5.04676 | + | 5.04676i | −0.0630845 | + | 0.0630845i | ||||
\(81\) | 68.1334 | + | 43.8046i | 0.841153 | + | 0.540798i | ||||
\(82\) | −24.4941 | − | 24.4941i | −0.298709 | − | 0.298709i | ||||
\(83\) | 104.486 | 1.25887 | 0.629435 | − | 0.777053i | \(-0.283286\pi\) | ||||
0.629435 | + | 0.777053i | \(0.283286\pi\) | |||||||
\(84\) | −13.7001 | + | 10.2548i | −0.163097 | + | 0.122081i | ||||
\(85\) | 7.22822 | + | 29.4593i | 0.0850379 | + | 0.346580i | ||||
\(86\) | 75.8396i | 0.881856i | ||||||||
\(87\) | −30.0919 | + | 22.5243i | −0.345884 | + | 0.258900i | ||||
\(88\) | −23.2868 | − | 23.2868i | −0.264623 | − | 0.264623i | ||||
\(89\) | 74.8065i | 0.840522i | 0.907403 | + | 0.420261i | \(0.138062\pi\) | ||||
−0.907403 | + | 0.420261i | \(0.861938\pi\) | |||||||
\(90\) | 19.9335 | − | 10.8821i | 0.221483 | − | 0.120912i | ||||
\(91\) | 45.7272 | − | 45.7272i | 0.502497 | − | 0.502497i | ||||
\(92\) | −13.6853 | − | 13.6853i | −0.148754 | − | 0.148754i | ||||
\(93\) | 42.3706 | + | 56.6060i | 0.455598 | + | 0.608667i | ||||
\(94\) | − | 17.1957i | − | 0.182933i | ||||||
\(95\) | −24.6874 | − | 24.6874i | −0.259867 | − | 0.259867i | ||||
\(96\) | 16.7977 | + | 2.41595i | 0.174976 | + | 0.0251661i | ||||
\(97\) | −97.0758 | − | 97.0758i | −1.00078 | − | 1.00078i | −1.00000 | 0.000781527i | \(-0.999751\pi\) | |
−0.000781527 | − | 1.00000i | \(-0.500249\pi\) | |||||||
\(98\) | − | 57.7920i | − | 0.589715i | ||||||
\(99\) | 50.2123 | + | 91.9774i | 0.507195 | + | 0.929064i | ||||
\(100\) | 43.6326i | 0.436326i | ||||||||
\(101\) | − | 184.812i | − | 1.82983i | −0.403652 | − | 0.914913i | \(-0.632259\pi\) | ||
0.403652 | − | 0.914913i | \(-0.367741\pi\) | |||||||
\(102\) | 45.7785 | − | 55.7345i | 0.448809 | − | 0.546416i | ||||
\(103\) | −169.361 | −1.64428 | −0.822140 | − | 0.569286i | \(-0.807220\pi\) | ||||
−0.822140 | + | 0.569286i | \(0.807220\pi\) | |||||||
\(104\) | −64.1298 | −0.616633 | ||||||||
\(105\) | 2.17347 | − | 15.1119i | 0.0206998 | − | 0.143922i | ||||
\(106\) | −82.8423 | −0.781531 | ||||||||
\(107\) | −126.181 | + | 126.181i | −1.17926 | + | 1.17926i | −0.199331 | + | 0.979932i | \(0.563877\pi\) |
−0.979932 | + | 0.199331i | \(0.936123\pi\) | |||||||
\(108\) | −49.1170 | − | 22.4393i | −0.454787 | − | 0.207771i | ||||
\(109\) | −110.815 | + | 110.815i | −1.01665 | + | 1.01665i | −0.0167883 | + | 0.999859i | \(0.505344\pi\) |
−0.999859 | + | 0.0167883i | \(0.994656\pi\) | |||||||
\(110\) | 29.3808 | 0.267098 | ||||||||
\(111\) | −58.7900 | − | 78.5419i | −0.529640 | − | 0.707585i | ||||
\(112\) | 8.06715 | − | 8.06715i | 0.0720281 | − | 0.0720281i | ||||
\(113\) | −102.172 | − | 102.172i | −0.904174 | − | 0.904174i | 0.0916197 | − | 0.995794i | \(-0.470796\pi\) |
−0.995794 | + | 0.0916197i | \(0.970796\pi\) | |||||||
\(114\) | −11.8182 | + | 82.1700i | −0.103668 | + | 0.720789i | ||||
\(115\) | 17.2666 | 0.150145 | ||||||||
\(116\) | 17.7192 | − | 17.7192i | 0.152752 | − | 0.152752i | ||||
\(117\) | 195.789 | + | 57.5085i | 1.67341 | + | 0.491526i | ||||
\(118\) | 4.98264 | 0.0422257 | ||||||||
\(119\) | −11.5542 | − | 47.0901i | −0.0970939 | − | 0.395715i | ||||
\(120\) | −12.1208 | + | 9.07266i | −0.101007 | + | 0.0756055i | ||||
\(121\) | 14.5692i | 0.120407i | ||||||||
\(122\) | −30.0962 | + | 30.0962i | −0.246690 | + | 0.246690i | ||||
\(123\) | −44.0336 | − | 58.8278i | −0.357997 | − | 0.478275i | ||||
\(124\) | −33.3317 | − | 33.3317i | −0.268804 | − | 0.268804i | ||||
\(125\) | −59.0676 | − | 59.0676i | −0.472541 | − | 0.472541i | ||||
\(126\) | −31.8633 | + | 17.3948i | −0.252883 | + | 0.138054i | ||||
\(127\) | 121.748i | 0.958648i | 0.877638 | + | 0.479324i | \(0.159118\pi\) | ||||
−0.877638 | + | 0.479324i | \(0.840882\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | −22.9031 | + | 159.242i | −0.177543 | + | 1.23443i | ||||
\(130\) | 40.4560 | − | 40.4560i | 0.311200 | − | 0.311200i | ||||
\(131\) | 149.498 | − | 149.498i | 1.14121 | − | 1.14121i | 0.152979 | − | 0.988229i | \(-0.451113\pi\) |
0.988229 | − | 0.152979i | \(-0.0488866\pi\) | |||||||
\(132\) | −41.8632 | − | 55.9282i | −0.317146 | − | 0.423698i | ||||
\(133\) | 39.4623 | + | 39.4623i | 0.296709 | + | 0.296709i | ||||
\(134\) | −41.7535 | −0.311593 | ||||||||
\(135\) | 45.1409 | − | 16.8295i | 0.334377 | − | 0.124663i | ||||
\(136\) | −24.9185 | + | 41.1226i | −0.183224 | + | 0.302372i | ||||
\(137\) | − | 80.9478i | − | 0.590860i | −0.955364 | − | 0.295430i | \(-0.904537\pi\) | ||
0.955364 | − | 0.295430i | \(-0.0954629\pi\) | |||||||
\(138\) | −24.6024 | − | 32.8682i | −0.178278 | − | 0.238175i | ||||
\(139\) | 14.2739 | + | 14.2739i | 0.102690 | + | 0.102690i | 0.756585 | − | 0.653895i | \(-0.226866\pi\) |
−0.653895 | + | 0.756585i | \(0.726866\pi\) | |||||||
\(140\) | 10.1782i | 0.0727017i | ||||||||
\(141\) | 5.19297 | − | 36.1060i | 0.0368296 | − | 0.256071i | ||||
\(142\) | 90.2995 | − | 90.2995i | 0.635912 | − | 0.635912i | ||||
\(143\) | 186.673 | + | 186.673i | 1.30540 | + | 1.30540i | ||||
\(144\) | 34.5408 | + | 10.1456i | 0.239867 | + | 0.0704555i | ||||
\(145\) | 22.3561i | 0.154180i | ||||||||
\(146\) | 76.8953 | + | 76.8953i | 0.526680 | + | 0.526680i | ||||
\(147\) | 17.4528 | − | 121.347i | 0.118727 | − | 0.825488i | ||||
\(148\) | 46.2484 | + | 46.2484i | 0.312489 | + | 0.312489i | ||||
\(149\) | 219.571i | 1.47363i | 0.676095 | + | 0.736814i | \(0.263671\pi\) | ||||
−0.676095 | + | 0.736814i | \(0.736329\pi\) | |||||||
\(150\) | −13.1767 | + | 91.6159i | −0.0878449 | + | 0.610773i | ||||
\(151\) | − | 140.565i | − | 0.930892i | −0.885076 | − | 0.465446i | \(-0.845894\pi\) | ||
0.885076 | − | 0.465446i | \(-0.154106\pi\) | |||||||
\(152\) | − | 55.3437i | − | 0.364103i | ||||||
\(153\) | 112.953 | − | 103.202i | 0.738256 | − | 0.674521i | ||||
\(154\) | −46.9646 | −0.304965 | ||||||||
\(155\) | 42.0543 | 0.271318 | ||||||||
\(156\) | −134.654 | − | 19.3668i | −0.863168 | − | 0.124146i | ||||
\(157\) | 29.0933 | 0.185308 | 0.0926538 | − | 0.995698i | \(-0.470465\pi\) | ||||
0.0926538 | + | 0.995698i | \(0.470465\pi\) | |||||||
\(158\) | −45.0454 | + | 45.0454i | −0.285097 | + | 0.285097i | ||||
\(159\) | −173.945 | − | 25.0178i | −1.09399 | − | 0.157345i | ||||
\(160\) | 7.13719 | − | 7.13719i | 0.0446075 | − | 0.0446075i | ||||
\(161\) | −27.6004 | −0.171431 | ||||||||
\(162\) | −96.3551 | − | 61.9491i | −0.594785 | − | 0.382402i | ||||
\(163\) | −141.258 | + | 141.258i | −0.866614 | + | 0.866614i | −0.992096 | − | 0.125482i | \(-0.959952\pi\) |
0.125482 | + | 0.992096i | \(0.459952\pi\) | |||||||
\(164\) | 34.6400 | + | 34.6400i | 0.211219 | + | 0.211219i | ||||
\(165\) | 61.6912 | + | 8.87279i | 0.373886 | + | 0.0537745i | ||||
\(166\) | −147.766 | −0.890155 | ||||||||
\(167\) | 156.347 | − | 156.347i | 0.936208 | − | 0.936208i | −0.0618761 | − | 0.998084i | \(-0.519708\pi\) |
0.998084 | + | 0.0618761i | \(0.0197084\pi\) | |||||||
\(168\) | 19.3749 | − | 14.5025i | 0.115327 | − | 0.0863243i | ||||
\(169\) | 345.079 | 2.04189 | ||||||||
\(170\) | −10.2222 | − | 41.6617i | −0.0601308 | − | 0.245069i | ||||
\(171\) | −49.6295 | + | 168.964i | −0.290231 | + | 0.988096i | ||||
\(172\) | − | 107.253i | − | 0.623567i | ||||||
\(173\) | −63.0996 | + | 63.0996i | −0.364737 | + | 0.364737i | −0.865554 | − | 0.500816i | \(-0.833033\pi\) |
0.500816 | + | 0.865554i | \(0.333033\pi\) | |||||||
\(174\) | 42.5564 | − | 31.8542i | 0.244577 | − | 0.183070i | ||||
\(175\) | 43.9988 | + | 43.9988i | 0.251422 | + | 0.251422i | ||||
\(176\) | 32.9326 | + | 32.9326i | 0.187117 | + | 0.187117i | ||||
\(177\) | 10.4621 | + | 1.50472i | 0.0591080 | + | 0.00850126i | ||||
\(178\) | − | 105.792i | − | 0.594339i | ||||||
\(179\) | −179.901 | −1.00503 | −0.502517 | − | 0.864567i | \(-0.667592\pi\) | ||||
−0.502517 | + | 0.864567i | \(0.667592\pi\) | |||||||
\(180\) | −28.1902 | + | 15.3896i | −0.156612 | + | 0.0854977i | ||||
\(181\) | 170.793 | − | 170.793i | 0.943606 | − | 0.943606i | −0.0548866 | − | 0.998493i | \(-0.517480\pi\) |
0.998493 | + | 0.0548866i | \(0.0174797\pi\) | |||||||
\(182\) | −64.6681 | + | 64.6681i | −0.355319 | + | 0.355319i | ||||
\(183\) | −72.2822 | + | 54.1045i | −0.394984 | + | 0.295653i | ||||
\(184\) | 19.3540 | + | 19.3540i | 0.105185 | + | 0.105185i | ||||
\(185\) | −58.3511 | −0.315411 | ||||||||
\(186\) | −59.9211 | − | 80.0530i | −0.322157 | − | 0.430393i | ||||
\(187\) | 192.236 | − | 47.1677i | 1.02800 | − | 0.252233i | ||||
\(188\) | 24.3183i | 0.129353i | ||||||||
\(189\) | −72.1569 | + | 26.9016i | −0.381782 | + | 0.142337i | ||||
\(190\) | 34.9133 | + | 34.9133i | 0.183754 | + | 0.183754i | ||||
\(191\) | 184.071i | 0.963725i | 0.876247 | + | 0.481862i | \(0.160039\pi\) | ||||
−0.876247 | + | 0.481862i | \(0.839961\pi\) | |||||||
\(192\) | −23.7556 | − | 3.41666i | −0.123727 | − | 0.0177951i | ||||
\(193\) | 16.0139 | − | 16.0139i | 0.0829738 | − | 0.0829738i | −0.664402 | − | 0.747376i | \(-0.731314\pi\) |
0.747376 | + | 0.664402i | \(0.231314\pi\) | |||||||
\(194\) | 137.286 | + | 137.286i | 0.707659 | + | 0.707659i | ||||
\(195\) | 97.1634 | − | 72.7285i | 0.498274 | − | 0.372967i | ||||
\(196\) | 81.7303i | 0.416991i | ||||||||
\(197\) | −101.238 | − | 101.238i | −0.513897 | − | 0.513897i | 0.401821 | − | 0.915718i | \(-0.368377\pi\) |
−0.915718 | + | 0.401821i | \(0.868377\pi\) | |||||||
\(198\) | −71.0109 | − | 130.076i | −0.358641 | − | 0.656948i | ||||
\(199\) | 52.7505 | + | 52.7505i | 0.265078 | + | 0.265078i | 0.827113 | − | 0.562035i | \(-0.189981\pi\) |
−0.562035 | + | 0.827113i | \(0.689981\pi\) | |||||||
\(200\) | − | 61.7058i | − | 0.308529i | ||||||
\(201\) | −87.6704 | − | 12.6093i | −0.436171 | − | 0.0627327i | ||||
\(202\) | 261.364i | 1.29388i | ||||||||
\(203\) | − | 35.7359i | − | 0.176039i | ||||||
\(204\) | −64.7405 | + | 78.8205i | −0.317356 | + | 0.386375i | ||||
\(205\) | −43.7049 | −0.213194 | ||||||||
\(206\) | 239.512 | 1.16268 | ||||||||
\(207\) | −41.7321 | − | 76.4435i | −0.201604 | − | 0.369292i | ||||
\(208\) | 90.6932 | 0.436025 | ||||||||
\(209\) | −161.097 | + | 161.097i | −0.770801 | + | 0.770801i | ||||
\(210\) | −3.07376 | + | 21.3714i | −0.0146369 | + | 0.101768i | ||||
\(211\) | −63.5331 | + | 63.5331i | −0.301105 | + | 0.301105i | −0.841446 | − | 0.540341i | \(-0.818295\pi\) |
0.540341 | + | 0.841446i | \(0.318295\pi\) | |||||||
\(212\) | 117.157 | 0.552626 | ||||||||
\(213\) | 216.873 | − | 162.333i | 1.01818 | − | 0.762128i | ||||
\(214\) | 178.447 | − | 178.447i | 0.833865 | − | 0.833865i | ||||
\(215\) | 67.6603 | + | 67.6603i | 0.314699 | + | 0.314699i | ||||
\(216\) | 69.4619 | + | 31.7339i | 0.321583 | + | 0.146916i | ||||
\(217\) | −67.2230 | −0.309783 | ||||||||
\(218\) | 156.715 | − | 156.715i | 0.718878 | − | 0.718878i | ||||
\(219\) | 138.236 | + | 184.680i | 0.631216 | + | 0.843287i | ||||
\(220\) | −41.5507 | −0.188867 | ||||||||
\(221\) | 199.753 | − | 329.648i | 0.903858 | − | 1.49162i | ||||
\(222\) | 83.1416 | + | 111.075i | 0.374512 | + | 0.500338i | ||||
\(223\) | − | 327.918i | − | 1.47048i | −0.677805 | − | 0.735242i | \(-0.737068\pi\) | ||
0.677805 | − | 0.735242i | \(-0.262932\pi\) | |||||||
\(224\) | −11.4087 | + | 11.4087i | −0.0509316 | + | 0.0509316i | ||||
\(225\) | −55.3348 | + | 188.388i | −0.245932 | + | 0.837280i | ||||
\(226\) | 144.493 | + | 144.493i | 0.639348 | + | 0.639348i | ||||
\(227\) | −68.8798 | − | 68.8798i | −0.303435 | − | 0.303435i | 0.538921 | − | 0.842356i | \(-0.318832\pi\) |
−0.842356 | + | 0.538921i | \(0.818832\pi\) | |||||||
\(228\) | 16.7134 | − | 116.206i | 0.0733044 | − | 0.509675i | ||||
\(229\) | 349.706i | 1.52710i | 0.645748 | + | 0.763550i | \(0.276545\pi\) | ||||
−0.645748 | + | 0.763550i | \(0.723455\pi\) | |||||||
\(230\) | −24.4187 | −0.106168 | ||||||||
\(231\) | −98.6122 | − | 14.1830i | −0.426893 | − | 0.0613982i | ||||
\(232\) | −25.0587 | + | 25.0587i | −0.108012 | + | 0.108012i | ||||
\(233\) | −150.583 | + | 150.583i | −0.646279 | + | 0.646279i | −0.952092 | − | 0.305813i | \(-0.901072\pi\) |
0.305813 | + | 0.952092i | \(0.401072\pi\) | |||||||
\(234\) | −276.887 | − | 81.3293i | −1.18328 | − | 0.347561i | ||||
\(235\) | −15.3411 | − | 15.3411i | −0.0652812 | − | 0.0652812i | ||||
\(236\) | −7.04651 | −0.0298581 | ||||||||
\(237\) | −108.186 | + | 80.9790i | −0.456480 | + | 0.341683i | ||||
\(238\) | 16.3401 | + | 66.5954i | 0.0686557 | + | 0.279813i | ||||
\(239\) | − | 50.7442i | − | 0.212319i | −0.994349 | − | 0.106159i | \(-0.966145\pi\) | ||
0.994349 | − | 0.106159i | \(-0.0338554\pi\) | |||||||
\(240\) | 17.1415 | − | 12.8307i | 0.0714227 | − | 0.0534612i | ||||
\(241\) | −313.072 | − | 313.072i | −1.29905 | − | 1.29905i | −0.929018 | − | 0.370035i | \(-0.879346\pi\) |
−0.370035 | − | 0.929018i | \(-0.620654\pi\) | |||||||
\(242\) | − | 20.6040i | − | 0.0851406i | ||||||
\(243\) | −183.610 | − | 159.174i | −0.755597 | − | 0.655037i | ||||
\(244\) | 42.5624 | − | 42.5624i | 0.174436 | − | 0.174436i | ||||
\(245\) | −51.5591 | − | 51.5591i | −0.210445 | − | 0.210445i | ||||
\(246\) | 62.2730 | + | 83.1950i | 0.253142 | + | 0.338191i | ||||
\(247\) | 443.647i | 1.79614i | ||||||||
\(248\) | 47.1382 | + | 47.1382i | 0.190073 | + | 0.190073i | ||||
\(249\) | −310.266 | − | 44.6243i | −1.24605 | − | 0.179214i | ||||
\(250\) | 83.5342 | + | 83.5342i | 0.334137 | + | 0.334137i | ||||
\(251\) | − | 169.441i | − | 0.675062i | −0.941314 | − | 0.337531i | \(-0.890408\pi\) | ||
0.941314 | − | 0.337531i | \(-0.109592\pi\) | |||||||
\(252\) | 45.0615 | − | 24.6000i | 0.178815 | − | 0.0976189i | ||||
\(253\) | − | 112.673i | − | 0.445349i | ||||||
\(254\) | − | 172.178i | − | 0.677866i | ||||||
\(255\) | −8.88224 | − | 90.5647i | −0.0348323 | − | 0.355156i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −485.571 | −1.88938 | −0.944691 | − | 0.327960i | \(-0.893639\pi\) | ||||
−0.944691 | + | 0.327960i | \(0.893639\pi\) | |||||||
\(258\) | 32.3898 | − | 225.202i | 0.125542 | − | 0.872874i | ||||
\(259\) | 93.2731 | 0.360128 | ||||||||
\(260\) | −57.2134 | + | 57.2134i | −0.220051 | + | 0.220051i | ||||
\(261\) | 98.9760 | − | 54.0330i | 0.379218 | − | 0.207023i | ||||
\(262\) | −211.422 | + | 211.422i | −0.806956 | + | 0.806956i | ||||
\(263\) | 330.182 | 1.25545 | 0.627723 | − | 0.778437i | \(-0.283987\pi\) | ||||
0.627723 | + | 0.778437i | \(0.283987\pi\) | |||||||
\(264\) | 59.2036 | + | 79.0944i | 0.224256 | + | 0.299600i | ||||
\(265\) | −73.9077 | + | 73.9077i | −0.278897 | + | 0.278897i | ||||
\(266\) | −55.8082 | − | 55.8082i | −0.209805 | − | 0.209805i | ||||
\(267\) | 31.9486 | − | 222.134i | 0.119658 | − | 0.831962i | ||||
\(268\) | 59.0483 | 0.220330 | ||||||||
\(269\) | −70.0262 | + | 70.0262i | −0.260321 | + | 0.260321i | −0.825184 | − | 0.564864i | \(-0.808929\pi\) |
0.564864 | + | 0.825184i | \(0.308929\pi\) | |||||||
\(270\) | −63.8389 | + | 23.8005i | −0.236440 | + | 0.0881500i | ||||
\(271\) | 310.083 | 1.14422 | 0.572109 | − | 0.820178i | \(-0.306125\pi\) | ||||
0.572109 | + | 0.820178i | \(0.306125\pi\) | |||||||
\(272\) | 35.2401 | − | 58.1561i | 0.129559 | − | 0.213809i | ||||
\(273\) | −155.314 | + | 116.255i | −0.568915 | + | 0.425843i | ||||
\(274\) | 114.477i | 0.417801i | ||||||||
\(275\) | −179.617 | + | 179.617i | −0.653151 | + | 0.653151i | ||||
\(276\) | 34.7931 | + | 46.4826i | 0.126062 | + | 0.168415i | ||||
\(277\) | −45.2033 | − | 45.2033i | −0.163189 | − | 0.163189i | 0.620789 | − | 0.783978i | \(-0.286812\pi\) |
−0.783978 | + | 0.620789i | \(0.786812\pi\) | |||||||
\(278\) | −20.1864 | − | 20.1864i | −0.0726130 | − | 0.0726130i | ||||
\(279\) | −101.642 | − | 186.184i | −0.364307 | − | 0.667327i | ||||
\(280\) | − | 14.3942i | − | 0.0514078i | ||||||
\(281\) | −492.144 | −1.75140 | −0.875700 | − | 0.482855i | \(-0.839600\pi\) | ||||
−0.875700 | + | 0.482855i | \(0.839600\pi\) | |||||||
\(282\) | −7.34397 | + | 51.0616i | −0.0260425 | + | 0.181069i | ||||
\(283\) | −170.438 | + | 170.438i | −0.602253 | + | 0.602253i | −0.940910 | − | 0.338657i | \(-0.890027\pi\) |
0.338657 | + | 0.940910i | \(0.390027\pi\) | |||||||
\(284\) | −127.703 | + | 127.703i | −0.449658 | + | 0.449658i | ||||
\(285\) | 62.7643 | + | 83.8514i | 0.220226 | + | 0.294216i | ||||
\(286\) | −263.995 | − | 263.995i | −0.923059 | − | 0.923059i | ||||
\(287\) | 69.8614 | 0.243419 | ||||||||
\(288\) | −48.8481 | − | 14.3480i | −0.169611 | − | 0.0498196i | ||||
\(289\) | −133.767 | − | 256.179i | −0.462861 | − | 0.886431i | ||||
\(290\) | − | 31.6164i | − | 0.109022i | ||||||
\(291\) | 246.802 | + | 329.721i | 0.848116 | + | 1.13306i | ||||
\(292\) | −108.746 | − | 108.746i | −0.372419 | − | 0.372419i | ||||
\(293\) | − | 119.260i | − | 0.407031i | −0.979072 | − | 0.203516i | \(-0.934763\pi\) | ||
0.979072 | − | 0.203516i | \(-0.0652368\pi\) | |||||||
\(294\) | −24.6820 | + | 171.610i | −0.0839524 | + | 0.583708i | ||||
\(295\) | 4.44526 | − | 4.44526i | 0.0150687 | − | 0.0150687i | ||||
\(296\) | −65.4050 | − | 65.4050i | −0.220963 | − | 0.220963i | ||||
\(297\) | −109.821 | − | 294.566i | −0.369767 | − | 0.991806i | ||||
\(298\) | − | 310.520i | − | 1.04201i | ||||||
\(299\) | −155.146 | − | 155.146i | −0.518883 | − | 0.518883i | ||||
\(300\) | 18.6347 | − | 129.564i | 0.0621157 | − | 0.431882i | ||||
\(301\) | −108.154 | − | 108.154i | −0.359314 | − | 0.359314i | ||||
\(302\) | 198.789i | 0.658240i | ||||||||
\(303\) | −78.9302 | + | 548.790i | −0.260496 | + | 1.81119i | ||||
\(304\) | 78.2678i | 0.257460i | ||||||||
\(305\) | 53.7005i | 0.176067i | ||||||||
\(306\) | −159.740 | + | 145.949i | −0.522026 | + | 0.476958i | ||||
\(307\) | −53.4322 | −0.174046 | −0.0870231 | − | 0.996206i | \(-0.527735\pi\) | ||||
−0.0870231 | + | 0.996206i | \(0.527735\pi\) | |||||||
\(308\) | 66.4180 | 0.215643 | ||||||||
\(309\) | 502.907 | + | 72.3311i | 1.62753 | + | 0.234081i | ||||
\(310\) | −59.4737 | −0.191851 | ||||||||
\(311\) | 379.691 | − | 379.691i | 1.22087 | − | 1.22087i | 0.253551 | − | 0.967322i | \(-0.418401\pi\) |
0.967322 | − | 0.253551i | \(-0.0815985\pi\) | |||||||
\(312\) | 190.430 | + | 27.3887i | 0.610352 | + | 0.0877844i | ||||
\(313\) | 179.390 | − | 179.390i | 0.573132 | − | 0.573132i | −0.359870 | − | 0.933002i | \(-0.617179\pi\) |
0.933002 | + | 0.359870i | \(0.117179\pi\) | |||||||
\(314\) | −41.1441 | −0.131032 | ||||||||
\(315\) | −12.9080 | + | 43.9455i | −0.0409779 | + | 0.139510i | ||||
\(316\) | 63.7037 | − | 63.7037i | 0.201594 | − | 0.201594i | ||||
\(317\) | 364.752 | + | 364.752i | 1.15064 | + | 1.15064i | 0.986425 | + | 0.164210i | \(0.0525076\pi\) |
0.164210 | + | 0.986425i | \(0.447492\pi\) | |||||||
\(318\) | 245.996 | + | 35.3805i | 0.773571 | + | 0.111259i | ||||
\(319\) | 145.885 | 0.457319 | ||||||||
\(320\) | −10.0935 | + | 10.0935i | −0.0315422 | + | 0.0315422i | ||||
\(321\) | 428.578 | − | 320.798i | 1.33513 | − | 0.999371i | ||||
\(322\) | 39.0329 | 0.121220 | ||||||||
\(323\) | 284.484 | + | 172.385i | 0.880756 | + | 0.533701i | ||||
\(324\) | 136.267 | + | 87.6092i | 0.420576 | + | 0.270399i | ||||
\(325\) | 494.647i | 1.52199i | ||||||||
\(326\) | 199.769 | − | 199.769i | 0.612788 | − | 0.612788i | ||||
\(327\) | 376.385 | − | 281.731i | 1.15102 | − | 0.861562i | ||||
\(328\) | −48.9883 | − | 48.9883i | −0.149355 | − | 0.149355i | ||||
\(329\) | 24.5224 | + | 24.5224i | 0.0745363 | + | 0.0745363i | ||||
\(330\) | −87.2445 | − | 12.5480i | −0.264377 | − | 0.0380243i | ||||
\(331\) | − | 135.363i | − | 0.408953i | −0.978871 | − | 0.204477i | \(-0.934451\pi\) | ||
0.978871 | − | 0.204477i | \(-0.0655492\pi\) | |||||||
\(332\) | 208.972 | 0.629435 | ||||||||
\(333\) | 141.030 | + | 258.334i | 0.423513 | + | 0.775778i | ||||
\(334\) | −221.108 | + | 221.108i | −0.661999 | + | 0.661999i | ||||
\(335\) | −37.2503 | + | 37.2503i | −0.111195 | + | 0.111195i | ||||
\(336\) | −27.4003 | + | 20.5096i | −0.0815485 | + | 0.0610405i | ||||
\(337\) | −162.370 | − | 162.370i | −0.481809 | − | 0.481809i | 0.423900 | − | 0.905709i | \(-0.360661\pi\) |
−0.905709 | + | 0.423900i | \(0.860661\pi\) | |||||||
\(338\) | −488.015 | −1.44383 | ||||||||
\(339\) | 259.757 | + | 347.029i | 0.766246 | + | 1.02368i | ||||
\(340\) | 14.4564 | + | 58.9185i | 0.0425189 | + | 0.173290i | ||||
\(341\) | − | 274.425i | − | 0.804765i | ||||||
\(342\) | 70.1868 | − | 238.952i | 0.205224 | − | 0.698690i | ||||
\(343\) | 181.239 | + | 181.239i | 0.528393 | + | 0.528393i | ||||
\(344\) | 151.679i | 0.440928i | ||||||||
\(345\) | −51.2723 | − | 7.37429i | −0.148615 | − | 0.0213748i | ||||
\(346\) | 89.2362 | − | 89.2362i | 0.257908 | − | 0.257908i | ||||
\(347\) | 318.311 | + | 318.311i | 0.917323 | + | 0.917323i | 0.996834 | − | 0.0795110i | \(-0.0253359\pi\) |
−0.0795110 | + | 0.996834i | \(0.525336\pi\) | |||||||
\(348\) | −60.1838 | + | 45.0486i | −0.172942 | + | 0.129450i | ||||
\(349\) | − | 134.199i | − | 0.384524i | −0.981344 | − | 0.192262i | \(-0.938418\pi\) | ||
0.981344 | − | 0.192262i | \(-0.0615823\pi\) | |||||||
\(350\) | −62.2237 | − | 62.2237i | −0.177782 | − | 0.177782i | ||||
\(351\) | −556.822 | − | 254.386i | −1.58639 | − | 0.724747i | ||||
\(352\) | −46.5737 | − | 46.5737i | −0.132312 | − | 0.132312i | ||||
\(353\) | 285.401i | 0.808502i | 0.914648 | + | 0.404251i | \(0.132468\pi\) | ||||
−0.914648 | + | 0.404251i | \(0.867532\pi\) | |||||||
\(354\) | −14.7957 | − | 2.12800i | −0.0417957 | − | 0.00601130i | ||||
\(355\) | − | 161.121i | − | 0.453863i | ||||||
\(356\) | 149.613i | 0.420261i | ||||||||
\(357\) | 14.1981 | + | 144.766i | 0.0397706 | + | 0.405507i | ||||
\(358\) | 254.418 | 0.710666 | ||||||||
\(359\) | 328.553 | 0.915188 | 0.457594 | − | 0.889161i | \(-0.348711\pi\) | ||||
0.457594 | + | 0.889161i | \(0.348711\pi\) | |||||||
\(360\) | 39.8669 | − | 21.7642i | 0.110741 | − | 0.0604560i | ||||
\(361\) | −21.8652 | −0.0605684 | ||||||||
\(362\) | −241.537 | + | 241.537i | −0.667230 | + | 0.667230i | ||||
\(363\) | 6.22227 | − | 43.2626i | 0.0171413 | − | 0.119181i | ||||
\(364\) | 91.4545 | − | 91.4545i | 0.251249 | − | 0.251249i | ||||
\(365\) | 137.204 | 0.375902 | ||||||||
\(366\) | 102.222 | − | 76.5153i | 0.279296 | − | 0.209058i | ||||
\(367\) | −84.2608 | + | 84.2608i | −0.229593 | + | 0.229593i | −0.812523 | − | 0.582929i | \(-0.801906\pi\) |
0.582929 | + | 0.812523i | \(0.301906\pi\) | |||||||
\(368\) | −27.3707 | − | 27.3707i | −0.0743768 | − | 0.0743768i | ||||
\(369\) | 105.631 | + | 193.492i | 0.286263 | + | 0.524368i | ||||
\(370\) | 82.5209 | 0.223029 | ||||||||
\(371\) | 118.140 | − | 118.140i | 0.318437 | − | 0.318437i | ||||
\(372\) | 84.7413 | + | 113.212i | 0.227799 | + | 0.304334i | ||||
\(373\) | 3.15815 | 0.00846690 | 0.00423345 | − | 0.999991i | \(-0.498652\pi\) | ||||
0.00423345 | + | 0.999991i | \(0.498652\pi\) | |||||||
\(374\) | −271.863 | + | 66.7051i | −0.726906 | + | 0.178356i | ||||
\(375\) | 150.171 | + | 200.625i | 0.400457 | + | 0.534999i | ||||
\(376\) | − | 34.3913i | − | 0.0914663i | ||||||
\(377\) | 200.877 | − | 200.877i | 0.532829 | − | 0.532829i | ||||
\(378\) | 102.045 | − | 38.0446i | 0.269961 | − | 0.100647i | ||||
\(379\) | −153.985 | − | 153.985i | −0.406292 | − | 0.406292i | 0.474151 | − | 0.880443i | \(-0.342755\pi\) |
−0.880443 | + | 0.474151i | \(0.842755\pi\) | |||||||
\(380\) | −49.3748 | − | 49.3748i | −0.129934 | − | 0.129934i | ||||
\(381\) | 51.9966 | − | 361.525i | 0.136474 | − | 0.948884i | ||||
\(382\) | − | 260.316i | − | 0.681456i | ||||||
\(383\) | 46.9418 | 0.122563 | 0.0612817 | − | 0.998121i | \(-0.480481\pi\) | ||||
0.0612817 | + | 0.998121i | \(0.480481\pi\) | |||||||
\(384\) | 33.5954 | + | 4.83189i | 0.0874881 | + | 0.0125831i | ||||
\(385\) | −41.8994 | + | 41.8994i | −0.108830 | + | 0.108830i | ||||
\(386\) | −22.6471 | + | 22.6471i | −0.0586713 | + | 0.0586713i | ||||
\(387\) | 136.019 | − | 463.077i | 0.351469 | − | 1.19658i | ||||
\(388\) | −194.152 | − | 194.152i | −0.500391 | − | 0.500391i | ||||
\(389\) | −224.195 | −0.576337 | −0.288168 | − | 0.957580i | \(-0.593046\pi\) | ||||
−0.288168 | + | 0.957580i | \(0.593046\pi\) | |||||||
\(390\) | −137.410 | + | 102.854i | −0.352333 | + | 0.263727i | ||||
\(391\) | −159.770 | + | 39.2016i | −0.408619 | + | 0.100260i | ||||
\(392\) | − | 115.584i | − | 0.294857i | ||||||
\(393\) | −507.775 | + | 380.079i | −1.29205 | + | 0.967121i | ||||
\(394\) | 143.172 | + | 143.172i | 0.363380 | + | 0.363380i | ||||
\(395\) | 80.3743i | 0.203479i | ||||||||
\(396\) | 100.425 | + | 183.955i | 0.253598 | + | 0.464532i | ||||
\(397\) | −401.965 | + | 401.965i | −1.01251 | + | 1.01251i | −0.0125843 | + | 0.999921i | \(0.504006\pi\) |
−0.999921 | + | 0.0125843i | \(0.995994\pi\) | |||||||
\(398\) | −74.6005 | − | 74.6005i | −0.187439 | − | 0.187439i | ||||
\(399\) | −100.328 | − | 134.035i | −0.251447 | − | 0.335927i | ||||
\(400\) | 87.2651i | 0.218163i | ||||||||
\(401\) | −143.103 | − | 143.103i | −0.356864 | − | 0.356864i | 0.505791 | − | 0.862656i | \(-0.331201\pi\) |
−0.862656 | + | 0.505791i | \(0.831201\pi\) | |||||||
\(402\) | 123.985 | + | 17.8322i | 0.308420 | + | 0.0443587i | ||||
\(403\) | −377.870 | − | 377.870i | −0.937643 | − | 0.937643i | ||||
\(404\) | − | 369.625i | − | 0.914913i | ||||||
\(405\) | −141.231 | + | 30.6953i | −0.348718 | + | 0.0757910i | ||||
\(406\) | 50.5382i | 0.124478i | ||||||||
\(407\) | 380.769i | 0.935551i | ||||||||
\(408\) | 91.5569 | − | 111.469i | 0.224404 | − | 0.273208i | ||||
\(409\) | 55.9919 | 0.136899 | 0.0684497 | − | 0.997655i | \(-0.478195\pi\) | ||||
0.0684497 | + | 0.997655i | \(0.478195\pi\) | |||||||
\(410\) | 61.8080 | 0.150751 | ||||||||
\(411\) | −34.5714 | + | 240.370i | −0.0841154 | + | 0.584842i | ||||
\(412\) | −338.721 | −0.822140 | ||||||||
\(413\) | −7.10566 | + | 7.10566i | −0.0172050 | + | 0.0172050i | ||||
\(414\) | 59.0181 | + | 108.107i | 0.142556 | + | 0.261129i | ||||
\(415\) | −131.829 | + | 131.829i | −0.317660 | + | 0.317660i | ||||
\(416\) | −128.260 | −0.308316 | ||||||||
\(417\) | −36.2895 | − | 48.4819i | −0.0870253 | − | 0.116263i | ||||
\(418\) | 227.826 | − | 227.826i | 0.545039 | − | 0.545039i | ||||
\(419\) | 239.758 | + | 239.758i | 0.572214 | + | 0.572214i | 0.932747 | − | 0.360532i | \(-0.117405\pi\) |
−0.360532 | + | 0.932747i | \(0.617405\pi\) | |||||||
\(420\) | 4.34695 | − | 30.2237i | 0.0103499 | − | 0.0719612i | ||||
\(421\) | 558.765 | 1.32723 | 0.663617 | − | 0.748073i | \(-0.269021\pi\) | ||||
0.663617 | + | 0.748073i | \(0.269021\pi\) | |||||||
\(422\) | 89.8494 | − | 89.8494i | 0.212913 | − | 0.212913i | ||||
\(423\) | −30.8405 | + | 104.997i | −0.0729089 | + | 0.248219i | ||||
\(424\) | −165.685 | −0.390765 | ||||||||
\(425\) | 317.188 | + | 192.202i | 0.746324 | + | 0.452240i | ||||
\(426\) | −306.705 | + | 229.574i | −0.719964 | + | 0.538906i | ||||
\(427\) | − | 85.8392i | − | 0.201029i | ||||||
\(428\) | −252.362 | + | 252.362i | −0.589632 | + | 0.589632i | ||||
\(429\) | −474.589 | − | 634.038i | −1.10627 | − | 1.47795i | ||||
\(430\) | −95.6861 | − | 95.6861i | −0.222526 | − | 0.222526i | ||||
\(431\) | −43.9049 | − | 43.9049i | −0.101868 | − | 0.101868i | 0.654336 | − | 0.756204i | \(-0.272948\pi\) |
−0.756204 | + | 0.654336i | \(0.772948\pi\) | |||||||
\(432\) | −98.2340 | − | 44.8786i | −0.227393 | − | 0.103886i | ||||
\(433\) | − | 327.439i | − | 0.756211i | −0.925763 | − | 0.378105i | \(-0.876576\pi\) | ||
0.925763 | − | 0.378105i | \(-0.123424\pi\) | |||||||
\(434\) | 95.0676 | 0.219050 | ||||||||
\(435\) | 9.54793 | − | 66.3853i | 0.0219493 | − | 0.152610i | ||||
\(436\) | −221.629 | + | 221.629i | −0.508324 | + | 0.508324i | ||||
\(437\) | 133.890 | − | 133.890i | 0.306385 | − | 0.306385i | ||||
\(438\) | −195.496 | − | 261.177i | −0.446337 | − | 0.596294i | ||||
\(439\) | 128.591 | + | 128.591i | 0.292918 | + | 0.292918i | 0.838232 | − | 0.545314i | \(-0.183590\pi\) |
−0.545314 | + | 0.838232i | \(0.683590\pi\) | |||||||
\(440\) | 58.7615 | 0.133549 | ||||||||
\(441\) | −103.650 | + | 352.879i | −0.235035 | + | 0.800178i | ||||
\(442\) | −282.493 | + | 466.193i | −0.639124 | + | 1.05473i | ||||
\(443\) | − | 644.845i | − | 1.45563i | −0.685773 | − | 0.727816i | \(-0.740536\pi\) | ||
0.685773 | − | 0.727816i | \(-0.259464\pi\) | |||||||
\(444\) | −117.580 | − | 157.084i | −0.264820 | − | 0.353792i | ||||
\(445\) | −94.3826 | − | 94.3826i | −0.212096 | − | 0.212096i | ||||
\(446\) | 463.746i | 1.03979i | ||||||||
\(447\) | 93.7749 | − | 652.003i | 0.209787 | − | 1.45862i | ||||
\(448\) | 16.1343 | − | 16.1343i | 0.0360140 | − | 0.0360140i | ||||
\(449\) | −211.164 | − | 211.164i | −0.470298 | − | 0.470298i | 0.431713 | − | 0.902011i | \(-0.357909\pi\) |
−0.902011 | + | 0.431713i | \(0.857909\pi\) | |||||||
\(450\) | 78.2552 | − | 266.421i | 0.173900 | − | 0.592046i | ||||
\(451\) | 285.196i | 0.632363i | ||||||||
\(452\) | −204.343 | − | 204.343i | −0.452087 | − | 0.452087i | ||||
\(453\) | −60.0328 | + | 417.399i | −0.132523 | + | 0.921411i | ||||
\(454\) | 97.4108 | + | 97.4108i | 0.214561 | + | 0.214561i | ||||
\(455\) | 115.387i | 0.253598i | ||||||||
\(456\) | −23.6363 | + | 164.340i | −0.0518341 | + | 0.360395i | ||||
\(457\) | 212.617i | 0.465244i | 0.972567 | + | 0.232622i | \(0.0747305\pi\) | ||||
−0.972567 | + | 0.232622i | \(0.925269\pi\) | |||||||
\(458\) | − | 494.559i | − | 1.07982i | ||||||
\(459\) | −379.484 | + | 258.211i | −0.826762 | + | 0.562552i | ||||
\(460\) | 34.5333 | 0.0750724 | ||||||||
\(461\) | 217.294 | 0.471354 | 0.235677 | − | 0.971831i | \(-0.424269\pi\) | ||||
0.235677 | + | 0.971831i | \(0.424269\pi\) | |||||||
\(462\) | 139.459 | + | 20.0578i | 0.301859 | + | 0.0434151i | ||||
\(463\) | −108.407 | −0.234140 | −0.117070 | − | 0.993124i | \(-0.537350\pi\) | ||||
−0.117070 | + | 0.993124i | \(0.537350\pi\) | |||||||
\(464\) | 35.4384 | − | 35.4384i | 0.0763759 | − | 0.0763759i | ||||
\(465\) | −124.878 | − | 17.9607i | −0.268554 | − | 0.0386251i | ||||
\(466\) | 212.956 | − | 212.956i | 0.456988 | − | 0.456988i | ||||
\(467\) | −623.962 | −1.33611 | −0.668054 | − | 0.744113i | \(-0.732872\pi\) | ||||
−0.668054 | + | 0.744113i | \(0.732872\pi\) | |||||||
\(468\) | 391.577 | + | 115.017i | 0.836703 | + | 0.245763i | ||||
\(469\) | 59.5440 | − | 59.5440i | 0.126959 | − | 0.126959i | ||||
\(470\) | 21.6956 | + | 21.6956i | 0.0461608 | + | 0.0461608i | ||||
\(471\) | −86.3909 | − | 12.4252i | −0.183420 | − | 0.0263806i | ||||
\(472\) | 9.96528 | 0.0211129 | ||||||||
\(473\) | 441.516 | − | 441.516i | 0.933438 | − | 0.933438i | ||||
\(474\) | 152.998 | − | 114.522i | 0.322780 | − | 0.241607i | ||||
\(475\) | −426.878 | −0.898690 | ||||||||
\(476\) | −23.1083 | − | 94.1801i | −0.0485469 | − | 0.197857i | ||||
\(477\) | 505.836 | + | 148.578i | 1.06045 | + | 0.311484i | ||||
\(478\) | 71.7631i | 0.150132i | ||||||||
\(479\) | −388.734 | + | 388.734i | −0.811553 | + | 0.811553i | −0.984867 | − | 0.173313i | \(-0.944553\pi\) |
0.173313 | + | 0.984867i | \(0.444553\pi\) | |||||||
\(480\) | −24.2417 | + | 18.1453i | −0.0505035 | + | 0.0378028i | ||||
\(481\) | 524.302 | + | 524.302i | 1.09002 | + | 1.09002i | ||||
\(482\) | 442.750 | + | 442.750i | 0.918569 | + | 0.918569i | ||||
\(483\) | 81.9579 | + | 11.7877i | 0.169685 | + | 0.0244051i | ||||
\(484\) | 29.1385i | 0.0602035i | ||||||||
\(485\) | 244.959 | 0.505070 | ||||||||
\(486\) | 259.664 | + | 225.106i | 0.534288 | + | 0.463181i | ||||
\(487\) | 257.620 | − | 257.620i | 0.528994 | − | 0.528994i | −0.391278 | − | 0.920272i | \(-0.627967\pi\) |
0.920272 | + | 0.391278i | \(0.127967\pi\) | |||||||
\(488\) | −60.1923 | + | 60.1923i | −0.123345 | + | 0.123345i | ||||
\(489\) | 479.787 | − | 359.129i | 0.981159 | − | 0.734415i | ||||
\(490\) | 72.9156 | + | 72.9156i | 0.148807 | + | 0.148807i | ||||
\(491\) | −935.607 | −1.90551 | −0.952757 | − | 0.303735i | \(-0.901766\pi\) | ||||
−0.952757 | + | 0.303735i | \(0.901766\pi\) | |||||||
\(492\) | −88.0673 | − | 117.656i | −0.178999 | − | 0.239137i | ||||
\(493\) | −50.7567 | − | 206.863i | −0.102955 | − | 0.419601i | ||||
\(494\) | − | 627.412i | − | 1.27006i | ||||||
\(495\) | −179.399 | − | 52.6945i | −0.362423 | − | 0.106454i | ||||
\(496\) | −66.6634 | − | 66.6634i | −0.134402 | − | 0.134402i | ||||
\(497\) | 257.549i | 0.518208i | ||||||||
\(498\) | 438.782 | + | 63.1082i | 0.881089 | + | 0.126723i | ||||
\(499\) | 93.6301 | − | 93.6301i | 0.187636 | − | 0.187636i | −0.607038 | − | 0.794673i | \(-0.707642\pi\) |
0.794673 | + | 0.607038i | \(0.207642\pi\) | |||||||
\(500\) | −118.135 | − | 118.135i | −0.236270 | − | 0.236270i | ||||
\(501\) | −531.036 | + | 397.490i | −1.05995 | + | 0.793393i | ||||
\(502\) | 239.625i | 0.477341i | ||||||||
\(503\) | −156.839 | − | 156.839i | −0.311807 | − | 0.311807i | 0.533803 | − | 0.845609i | \(-0.320763\pi\) |
−0.845609 | + | 0.533803i | \(0.820763\pi\) | |||||||
\(504\) | −63.7265 | + | 34.7896i | −0.126442 | + | 0.0690270i | ||||
\(505\) | 233.176 | + | 233.176i | 0.461734 | + | 0.461734i | ||||
\(506\) | 159.344i | 0.314909i | ||||||||
\(507\) | −1024.69 | − | 147.377i | −2.02109 | − | 0.290685i | ||||
\(508\) | 243.497i | 0.479324i | ||||||||
\(509\) | − | 378.401i | − | 0.743421i | −0.928349 | − | 0.371711i | \(-0.878771\pi\) | ||
0.928349 | − | 0.371711i | \(-0.121229\pi\) | |||||||
\(510\) | 12.5614 | + | 128.078i | 0.0246302 | + | 0.251133i | ||||
\(511\) | −219.318 | −0.429194 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 219.534 | − | 480.535i | 0.427942 | − | 0.936715i | ||||
\(514\) | 686.702 | 1.33600 | ||||||||
\(515\) | 213.681 | − | 213.681i | 0.414914 | − | 0.414914i | ||||
\(516\) | −45.8061 | + | 318.483i | −0.0887715 | + | 0.617215i | ||||
\(517\) | −100.108 | + | 100.108i | −0.193633 | + | 0.193633i | ||||
\(518\) | −131.908 | −0.254649 | ||||||||
\(519\) | 214.319 | − | 160.422i | 0.412947 | − | 0.309098i | ||||
\(520\) | 80.9119 | − | 80.9119i | 0.155600 | − | 0.155600i | ||||
\(521\) | 534.471 | + | 534.471i | 1.02586 | + | 1.02586i | 0.999657 | + | 0.0261996i | \(0.00834055\pi\) |
0.0261996 | + | 0.999657i | \(0.491659\pi\) | |||||||
\(522\) | −139.973 | + | 76.4142i | −0.268148 | + | 0.146387i | ||||
\(523\) | −272.068 | −0.520207 | −0.260103 | − | 0.965581i | \(-0.583757\pi\) | ||||
−0.260103 | + | 0.965581i | \(0.583757\pi\) | |||||||
\(524\) | 298.997 | − | 298.997i | 0.570604 | − | 0.570604i | ||||
\(525\) | −111.861 | − | 149.443i | −0.213068 | − | 0.284653i | ||||
\(526\) | −466.948 | −0.887734 | ||||||||
\(527\) | −389.132 | + | 95.4787i | −0.738391 | + | 0.181174i | ||||
\(528\) | −83.7265 | − | 111.856i | −0.158573 | − | 0.211849i | ||||
\(529\) | − | 435.356i | − | 0.822979i | ||||||
\(530\) | 104.521 | − | 104.521i | 0.197210 | − | 0.197210i | ||||
\(531\) | −30.4240 | − | 8.93638i | −0.0572957 | − | 0.0168293i | ||||
\(532\) | 78.9247 | + | 78.9247i | 0.148355 | + | 0.148355i | ||||
\(533\) | 392.701 | + | 392.701i | 0.736775 | + | 0.736775i | ||||
\(534\) | −45.1821 | + | 314.145i | −0.0846107 | + | 0.588286i | ||||
\(535\) | − | 318.403i | − | 0.595146i | ||||||
\(536\) | −83.5070 | −0.155797 | ||||||||
\(537\) | 534.206 | + | 76.8326i | 0.994797 | + | 0.143078i | ||||
\(538\) | 99.0320 | − | 99.0320i | 0.184074 | − | 0.184074i | ||||
\(539\) | −336.449 | + | 336.449i | −0.624209 | + | 0.624209i | ||||
\(540\) | 90.2818 | − | 33.6590i | 0.167189 | − | 0.0623315i | ||||
\(541\) | 522.103 | + | 522.103i | 0.965071 | + | 0.965071i | 0.999410 | − | 0.0343396i | \(-0.0109328\pi\) |
−0.0343396 | + | 0.999410i | \(0.510933\pi\) | |||||||
\(542\) | −438.524 | −0.809084 | ||||||||
\(543\) | −580.102 | + | 434.217i | −1.06833 | + | 0.799663i | ||||
\(544\) | −49.8371 | + | 82.2452i | −0.0916122 | + | 0.151186i | ||||
\(545\) | − | 279.627i | − | 0.513077i | ||||||
\(546\) | 219.647 | − | 164.410i | 0.402284 | − | 0.301116i | ||||
\(547\) | 630.656 | + | 630.656i | 1.15294 | + | 1.15294i | 0.985961 | + | 0.166976i | \(0.0534001\pi\) |
0.166976 | + | 0.985961i | \(0.446600\pi\) | |||||||
\(548\) | − | 161.896i | − | 0.295430i | ||||||
\(549\) | 237.745 | − | 129.790i | 0.433051 | − | 0.236411i | ||||
\(550\) | 254.016 | − | 254.016i | 0.461847 | − | 0.461847i | ||||
\(551\) | 173.355 | + | 173.355i | 0.314620 | + | 0.314620i | ||||
\(552\) | −49.2048 | − | 65.7363i | −0.0891392 | − | 0.119088i | ||||
\(553\) | − | 128.477i | − | 0.232327i | ||||||
\(554\) | 63.9271 | + | 63.9271i | 0.115392 | + | 0.115392i | ||||
\(555\) | 173.270 | + | 24.9207i | 0.312199 | + | 0.0449022i | ||||
\(556\) | 28.5479 | + | 28.5479i | 0.0513451 | + | 0.0513451i | ||||
\(557\) | 713.042i | 1.28015i | 0.768314 | + | 0.640073i | \(0.221096\pi\) | ||||
−0.768314 | + | 0.640073i | \(0.778904\pi\) | |||||||
\(558\) | 143.743 | + | 263.304i | 0.257604 | + | 0.471871i | ||||
\(559\) | − | 1215.90i | − | 2.17513i | ||||||
\(560\) | 20.3565i | 0.0363508i | ||||||||
\(561\) | −590.979 | + | 57.9610i | −1.05344 | + | 0.103317i | ||||
\(562\) | 695.996 | 1.23843 | ||||||||
\(563\) | −0.150683 | −0.000267643 | −0.000133821 | − | 1.00000i | \(-0.500043\pi\) | ||||
−0.000133821 | 1.00000i | \(0.500043\pi\) | ||||||||
\(564\) | 10.3859 | − | 72.2119i | 0.0184148 | − | 0.128035i | ||||
\(565\) | 257.818 | 0.456315 | ||||||||
\(566\) | 241.035 | − | 241.035i | 0.425857 | − | 0.425857i | ||||
\(567\) | 225.755 | − | 49.0659i | 0.398157 | − | 0.0865360i | ||||
\(568\) | 180.599 | − | 180.599i | 0.317956 | − | 0.317956i | ||||
\(569\) | −754.599 | −1.32618 | −0.663092 | − | 0.748538i | \(-0.730756\pi\) | ||||
−0.663092 | + | 0.748538i | \(0.730756\pi\) | |||||||
\(570\) | −88.7621 | − | 118.584i | −0.155723 | − | 0.208042i | ||||
\(571\) | 291.740 | − | 291.740i | 0.510929 | − | 0.510929i | −0.403882 | − | 0.914811i | \(-0.632339\pi\) |
0.914811 | + | 0.403882i | \(0.132339\pi\) | |||||||
\(572\) | 373.345 | + | 373.345i | 0.652701 | + | 0.652701i | ||||
\(573\) | 78.6138 | − | 546.590i | 0.137197 | − | 0.953909i | ||||
\(574\) | −98.7989 | −0.172124 | ||||||||
\(575\) | 149.282 | − | 149.282i | 0.259620 | − | 0.259620i | ||||
\(576\) | 69.0816 | + | 20.2912i | 0.119933 | + | 0.0352277i | ||||
\(577\) | −274.444 | −0.475639 | −0.237819 | − | 0.971309i | \(-0.576433\pi\) | ||||
−0.237819 | + | 0.971309i | \(0.576433\pi\) | |||||||
\(578\) | 189.175 | + | 362.291i | 0.327292 | + | 0.626801i | ||||
\(579\) | −54.3918 | + | 40.7132i | −0.0939409 | + | 0.0703164i | ||||
\(580\) | 44.7123i | 0.0770902i | ||||||||
\(581\) | 210.726 | − | 210.726i | 0.362696 | − | 0.362696i | ||||
\(582\) | −349.030 | − | 466.295i | −0.599709 | − | 0.801195i | ||||
\(583\) | 482.284 | + | 482.284i | 0.827245 | + | 0.827245i | ||||
\(584\) | 153.791 | + | 153.791i | 0.263340 | + | 0.263340i | ||||
\(585\) | −319.582 | + | 174.466i | −0.546295 | + | 0.298233i | ||||
\(586\) | 168.659i | 0.287815i | ||||||||
\(587\) | −307.536 | −0.523912 | −0.261956 | − | 0.965080i | \(-0.584368\pi\) | ||||
−0.261956 | + | 0.965080i | \(0.584368\pi\) | |||||||
\(588\) | 34.9056 | − | 242.694i | 0.0593633 | − | 0.412744i | ||||
\(589\) | 326.100 | − | 326.100i | 0.553650 | − | 0.553650i | ||||
\(590\) | −6.28654 | + | 6.28654i | −0.0106552 | + | 0.0106552i | ||||
\(591\) | 257.383 | + | 343.857i | 0.435504 | + | 0.581822i | ||||
\(592\) | 92.4967 | + | 92.4967i | 0.156244 | + | 0.156244i | ||||
\(593\) | −581.325 | −0.980312 | −0.490156 | − | 0.871635i | \(-0.663060\pi\) | ||||
−0.490156 | + | 0.871635i | \(0.663060\pi\) | |||||||
\(594\) | 155.310 | + | 416.580i | 0.261465 | + | 0.701313i | ||||
\(595\) | 73.9908 | + | 44.8353i | 0.124354 | + | 0.0753534i | ||||
\(596\) | 439.141i | 0.736814i | ||||||||
\(597\) | −134.111 | − | 179.169i | −0.224641 | − | 0.300115i | ||||
\(598\) | 219.409 | + | 219.409i | 0.366905 | + | 0.366905i | ||||
\(599\) | 216.818i | 0.361967i | 0.983486 | + | 0.180984i | \(0.0579281\pi\) | ||||
−0.983486 | + | 0.180984i | \(0.942072\pi\) | |||||||
\(600\) | −26.3535 | + | 183.232i | −0.0439225 | + | 0.305386i | ||||
\(601\) | −419.565 | + | 419.565i | −0.698111 | + | 0.698111i | −0.964003 | − | 0.265892i | \(-0.914334\pi\) |
0.265892 | + | 0.964003i | \(0.414334\pi\) | |||||||
\(602\) | 152.952 | + | 152.952i | 0.254074 | + | 0.254074i | ||||
\(603\) | 254.947 | + | 74.8850i | 0.422798 | + | 0.124187i | ||||
\(604\) | − | 281.129i | − | 0.465446i | ||||||
\(605\) | −18.3819 | − | 18.3819i | −0.0303832 | − | 0.0303832i | ||||
\(606\) | 111.624 | − | 776.106i | 0.184198 | − | 1.28070i | ||||
\(607\) | −187.790 | − | 187.790i | −0.309373 | − | 0.309373i | 0.535293 | − | 0.844666i | \(-0.320201\pi\) |
−0.844666 | + | 0.535293i | \(0.820201\pi\) | |||||||
\(608\) | − | 110.687i | − | 0.182052i | ||||||
\(609\) | −15.2622 | + | 106.116i | −0.0250610 | + | 0.174246i | ||||
\(610\) | − | 75.9440i | − | 0.124498i | ||||||
\(611\) | 275.689i | 0.451209i | ||||||||
\(612\) | 225.906 | − | 206.403i | 0.369128 | − | 0.337260i | ||||
\(613\) | 19.2663 | 0.0314296 | 0.0157148 | − | 0.999877i | \(-0.494998\pi\) | ||||
0.0157148 | + | 0.999877i | \(0.494998\pi\) | |||||||
\(614\) | 75.5645 | 0.123069 | ||||||||
\(615\) | 129.779 | + | 18.6656i | 0.211023 | + | 0.0303506i | ||||
\(616\) | −93.9292 | −0.152482 | ||||||||
\(617\) | 527.910 | − | 527.910i | 0.855608 | − | 0.855608i | −0.135209 | − | 0.990817i | \(-0.543171\pi\) |
0.990817 | + | 0.135209i | \(0.0431707\pi\) | |||||||
\(618\) | −711.218 | − | 102.292i | −1.15084 | − | 0.165520i | ||||
\(619\) | 482.168 | − | 482.168i | 0.778947 | − | 0.778947i | −0.200705 | − | 0.979652i | \(-0.564323\pi\) |
0.979652 | + | 0.200705i | \(0.0643231\pi\) | |||||||
\(620\) | 84.1085 | 0.135659 | ||||||||
\(621\) | 91.2734 | + | 244.818i | 0.146978 | + | 0.394232i | ||||
\(622\) | −536.965 | + | 536.965i | −0.863288 | + | 0.863288i | ||||
\(623\) | 150.869 | + | 150.869i | 0.242165 | + | 0.242165i | ||||
\(624\) | −269.309 | − | 38.7335i | −0.431584 | − | 0.0620730i | ||||
\(625\) | −396.357 | −0.634171 | ||||||||
\(626\) | −253.696 | + | 253.696i | −0.405266 | + | 0.405266i | ||||
\(627\) | 547.172 | − | 409.568i | 0.872682 | − | 0.653218i | ||||
\(628\) | 58.1866 | 0.0926538 | ||||||||
\(629\) | 539.928 | − | 132.478i | 0.858391 | − | 0.210617i | ||||
\(630\) | 18.2547 | − | 62.1484i | 0.0289757 | − | 0.0986482i | ||||
\(631\) | − | 68.3714i | − | 0.108354i | −0.998531 | − | 0.0541770i | \(-0.982746\pi\) | ||
0.998531 | − | 0.0541770i | \(-0.0172535\pi\) | |||||||
\(632\) | −90.0907 | + | 90.0907i | −0.142549 | + | 0.142549i | ||||
\(633\) | 215.792 | − | 161.524i | 0.340904 | − | 0.255173i | ||||
\(634\) | −515.837 | − | 515.837i | −0.813622 | − | 0.813622i | ||||
\(635\) | −153.609 | − | 153.609i | −0.241903 | − | 0.241903i | ||||
\(636\) | −347.890 | − | 50.0356i | −0.546997 | − | 0.0786723i | ||||
\(637\) | 926.548i | 1.45455i | ||||||||
\(638\) | −206.312 | −0.323373 | ||||||||
\(639\) | −713.322 | + | 389.417i | −1.11631 | + | 0.609416i | ||||
\(640\) | 14.2744 | − | 14.2744i | 0.0223037 | − | 0.0223037i | ||||
\(641\) | 48.9591 | − | 48.9591i | 0.0763793 | − | 0.0763793i | −0.667885 | − | 0.744264i | \(-0.732800\pi\) |
0.744264 | + | 0.667885i | \(0.232800\pi\) | |||||||
\(642\) | −606.100 | + | 453.677i | −0.944082 | + | 0.706662i | ||||
\(643\) | 813.584 | + | 813.584i | 1.26529 | + | 1.26529i | 0.948491 | + | 0.316803i | \(0.102609\pi\) |
0.316803 | + | 0.948491i | \(0.397391\pi\) | |||||||
\(644\) | −55.2008 | −0.0857155 | ||||||||
\(645\) | −172.017 | − | 229.810i | −0.266693 | − | 0.356295i | ||||
\(646\) | −402.322 | − | 243.790i | −0.622789 | − | 0.377383i | ||||
\(647\) | − | 774.097i | − | 1.19644i | −0.801332 | − | 0.598220i | \(-0.795875\pi\) | ||
0.801332 | − | 0.598220i | \(-0.204125\pi\) | |||||||
\(648\) | −192.710 | − | 123.898i | −0.297392 | − | 0.191201i | ||||
\(649\) | −29.0075 | − | 29.0075i | −0.0446957 | − | 0.0446957i | ||||
\(650\) | − | 699.537i | − | 1.07621i | ||||||
\(651\) | 199.615 | + | 28.7098i | 0.306628 | + | 0.0441010i | ||||
\(652\) | −282.516 | + | 282.516i | −0.433307 | + | 0.433307i | ||||
\(653\) | −256.085 | − | 256.085i | −0.392167 | − | 0.392167i | 0.483292 | − | 0.875459i | \(-0.339441\pi\) |
−0.875459 | + | 0.483292i | \(0.839441\pi\) | |||||||
\(654\) | −532.288 | + | 398.427i | −0.813897 | + | 0.609216i | ||||
\(655\) | 377.241i | 0.575940i | ||||||||
\(656\) | 69.2799 | + | 69.2799i | 0.105610 | + | 0.105610i | ||||
\(657\) | −331.611 | − | 607.435i | −0.504735 | − | 0.924559i | ||||
\(658\) | −34.6800 | − | 34.6800i | −0.0527051 | − | 0.0527051i | ||||
\(659\) | − | 599.982i | − | 0.910443i | −0.890378 | − | 0.455221i | \(-0.849560\pi\) | ||
0.890378 | − | 0.455221i | \(-0.150440\pi\) | |||||||
\(660\) | 123.382 | + | 17.7456i | 0.186943 | + | 0.0268872i | ||||
\(661\) | − | 492.163i | − | 0.744573i | −0.928118 | − | 0.372287i | \(-0.878574\pi\) | ||
0.928118 | − | 0.372287i | \(-0.121426\pi\) | |||||||
\(662\) | 191.433i | 0.289173i | ||||||||
\(663\) | −733.941 | + | 893.560i | −1.10700 | + | 1.34775i | ||||
\(664\) | −295.532 | −0.445078 | ||||||||
\(665\) | −99.5785 | −0.149742 | ||||||||
\(666\) | −199.446 | − | 365.339i | −0.299469 | − | 0.548558i | ||||
\(667\) | −121.247 | −0.181779 | ||||||||
\(668\) | 312.693 | − | 312.693i | 0.468104 | − | 0.468104i | ||||
\(669\) | −140.048 | + | 973.734i | −0.209340 | + | 1.45551i | ||||
\(670\) | 52.6799 | − | 52.6799i | 0.0786268 | − | 0.0786268i | ||||
\(671\) | 350.422 | 0.522239 | ||||||||
\(672\) | 38.7499 | − | 29.0050i | 0.0576635 | − | 0.0431621i | ||||
\(673\) | −532.410 | + | 532.410i | −0.791099 | + | 0.791099i | −0.981673 | − | 0.190574i | \(-0.938965\pi\) |
0.190574 | + | 0.981673i | \(0.438965\pi\) | |||||||
\(674\) | 229.625 | + | 229.625i | 0.340690 | + | 0.340690i | ||||
\(675\) | 244.771 | − | 535.775i | 0.362623 | − | 0.793741i | ||||
\(676\) | 690.158 | 1.02094 | ||||||||
\(677\) | 18.0380 | − | 18.0380i | 0.0266441 | − | 0.0266441i | −0.693659 | − | 0.720303i | \(-0.744003\pi\) |
0.720303 | + | 0.693659i | \(0.244003\pi\) | |||||||
\(678\) | −367.352 | − | 490.773i | −0.541818 | − | 0.723854i | ||||
\(679\) | −391.562 | −0.576675 | ||||||||
\(680\) | −20.4445 | − | 83.3234i | −0.0300654 | − | 0.122534i | ||||
\(681\) | 175.117 | + | 233.952i | 0.257147 | + | 0.343542i | ||||
\(682\) | 388.095i | 0.569054i | ||||||||
\(683\) | −384.931 | + | 384.931i | −0.563589 | + | 0.563589i | −0.930325 | − | 0.366736i | \(-0.880475\pi\) |
0.366736 | + | 0.930325i | \(0.380475\pi\) | |||||||
\(684\) | −99.2591 | + | 337.929i | −0.145116 | + | 0.494048i | ||||
\(685\) | 102.131 | + | 102.131i | 0.149096 | + | 0.149096i | ||||
\(686\) | −256.310 | − | 256.310i | −0.373630 | − | 0.373630i | ||||
\(687\) | 149.353 | − | 1038.43i | 0.217399 | − | 1.51155i | ||||
\(688\) | − | 214.507i | − | 0.311783i | ||||||
\(689\) | 1328.16 | 1.92767 | ||||||||
\(690\) | 72.5100 | + | 10.4288i | 0.105087 | + | 0.0151142i | ||||
\(691\) | −222.804 | + | 222.804i | −0.322437 | + | 0.322437i | −0.849701 | − | 0.527264i | \(-0.823218\pi\) |
0.527264 | + | 0.849701i | \(0.323218\pi\) | |||||||
\(692\) | −126.199 | + | 126.199i | −0.182369 | + | 0.182369i | ||||
\(693\) | 286.766 | + | 84.2312i | 0.413804 | + | 0.121546i | ||||
\(694\) | −450.160 | − | 450.160i | −0.648645 | − | 0.648645i | ||||
\(695\) | −36.0186 | −0.0518253 | ||||||||
\(696\) | 85.1127 | − | 63.7084i | 0.122288 | − | 0.0915351i | ||||
\(697\) | 404.405 | − | 99.2261i | 0.580208 | − | 0.142362i | ||||
\(698\) | 189.786i | 0.271899i | ||||||||
\(699\) | 511.459 | − | 382.836i | 0.731701 | − | 0.547691i | ||||
\(700\) | 87.9976 | + | 87.9976i | 0.125711 | + | 0.125711i | ||||
\(701\) | − | 213.935i | − | 0.305185i | −0.988289 | − | 0.152593i | \(-0.951238\pi\) | ||
0.988289 | − | 0.152593i | \(-0.0487623\pi\) | |||||||
\(702\) | 787.466 | + | 359.757i | 1.12175 | + | 0.512474i | ||||
\(703\) | −452.469 | + | 452.469i | −0.643626 | + | 0.643626i | ||||
\(704\) | 65.8651 | + | 65.8651i | 0.0935584 | + | 0.0935584i | ||||
\(705\) | 39.0026 | + | 52.1064i | 0.0553228 | + | 0.0739098i | ||||
\(706\) | − | 403.618i | − | 0.571697i | ||||||
\(707\) | −372.727 | − | 372.727i | −0.527195 | − | 0.527195i | ||||
\(708\) | 20.9242 | + | 3.00945i | 0.0295540 | + | 0.00425063i | ||||
\(709\) | −36.8068 | − | 36.8068i | −0.0519136 | − | 0.0519136i | 0.680673 | − | 0.732587i | \(-0.261687\pi\) |
−0.732587 | + | 0.680673i | \(0.761687\pi\) | |||||||
\(710\) | 227.860i | 0.320929i | ||||||||
\(711\) | 355.836 | − | 194.258i | 0.500473 | − | 0.273218i | ||||
\(712\) | − | 211.585i | − | 0.297170i | ||||||
\(713\) | 228.078i | 0.319885i | ||||||||
\(714\) | −20.0791 | − | 204.730i | −0.0281220 | − | 0.286737i | ||||
\(715\) | −471.046 | −0.658805 | ||||||||
\(716\) | −359.802 | −0.502517 | ||||||||
\(717\) | −21.6720 | + | 150.682i | −0.0302259 | + | 0.210156i | ||||
\(718\) | −464.643 | −0.647136 | ||||||||
\(719\) | 123.904 | − | 123.904i | 0.172328 | − | 0.172328i | −0.615674 | − | 0.788001i | \(-0.711116\pi\) |
0.788001 | + | 0.615674i | \(0.211116\pi\) | |||||||
\(720\) | −56.3804 | + | 30.7792i | −0.0783060 | + | 0.0427489i | ||||
\(721\) | −341.564 | + | 341.564i | −0.473737 | + | 0.473737i | ||||
\(722\) | 30.9220 | 0.0428283 | ||||||||
\(723\) | 795.942 | + | 1063.36i | 1.10089 | + | 1.47076i | ||||
\(724\) | 341.585 | − | 341.585i | 0.471803 | − | 0.471803i | ||||
\(725\) | 193.284 | + | 193.284i | 0.266598 | + | 0.266598i | ||||
\(726\) | −8.79962 | + | 61.1825i | −0.0121207 | + | 0.0842734i | ||||
\(727\) | −1434.30 | −1.97291 | −0.986454 | − | 0.164035i | \(-0.947549\pi\) | ||||
−0.986454 | + | 0.164035i | \(0.947549\pi\) | |||||||
\(728\) | −129.336 | + | 129.336i | −0.177660 | + | 0.177660i | ||||
\(729\) | 477.239 | + | 551.075i | 0.654649 | + | 0.755933i | ||||
\(730\) | −194.036 | −0.265803 | ||||||||
\(731\) | −779.680 | − | 472.453i | −1.06659 | − | 0.646311i | ||||
\(732\) | −144.564 | + | 108.209i | −0.197492 | + | 0.147826i | ||||
\(733\) | − | 1078.20i | − | 1.47094i | −0.677556 | − | 0.735471i | \(-0.736961\pi\) | ||
0.677556 | − | 0.735471i | \(-0.263039\pi\) | |||||||
\(734\) | 119.163 | − | 119.163i | 0.162347 | − | 0.162347i | ||||
\(735\) | 131.082 | + | 175.122i | 0.178343 | + | 0.238261i | ||||
\(736\) | 38.7080 | + | 38.7080i | 0.0525924 | + | 0.0525924i | ||||
\(737\) | 243.077 | + | 243.077i | 0.329819 | + | 0.329819i | ||||
\(738\) | −149.385 | − | 273.639i | −0.202419 | − | 0.370784i | ||||
\(739\) | − | 671.347i | − | 0.908453i | −0.890886 | − | 0.454227i | \(-0.849916\pi\) | ||
0.890886 | − | 0.454227i | \(-0.150084\pi\) | |||||||
\(740\) | −116.702 | −0.157706 | ||||||||
\(741\) | 189.474 | − | 1317.39i | 0.255701 | − | 1.77785i | ||||
\(742\) | −167.075 | + | 167.075i | −0.225169 | + | 0.225169i | ||||
\(743\) | −316.257 | + | 316.257i | −0.425649 | + | 0.425649i | −0.887143 | − | 0.461494i | \(-0.847314\pi\) |
0.461494 | + | 0.887143i | \(0.347314\pi\) | |||||||
\(744\) | −119.842 | − | 160.106i | −0.161078 | − | 0.215196i | ||||
\(745\) | −277.030 | − | 277.030i | −0.371852 | − | 0.371852i | ||||
\(746\) | −4.46630 | −0.00598700 | ||||||||
\(747\) | 902.259 | + | 265.018i | 1.20784 | + | 0.354777i | ||||
\(748\) | 384.472 | − | 94.3353i | 0.514000 | − | 0.126117i | ||||
\(749\) | 508.961i | 0.679521i | ||||||||
\(750\) | −212.374 | − | 283.726i | −0.283166 | − | 0.378302i | ||||
\(751\) | −518.315 | − | 518.315i | −0.690166 | − | 0.690166i | 0.272102 | − | 0.962268i | \(-0.412281\pi\) |
−0.962268 | + | 0.272102i | \(0.912281\pi\) | |||||||
\(752\) | 48.6367i | 0.0646764i | ||||||||
\(753\) | −72.3652 | + | 503.145i | −0.0961025 | + | 0.668187i | ||||
\(754\) | −284.082 | + | 284.082i | −0.376767 | + | 0.376767i | ||||
\(755\) | 177.349 | + | 177.349i | 0.234899 | + | 0.234899i | ||||
\(756\) | −144.314 | + | 53.8033i | −0.190891 | + | 0.0711683i | ||||
\(757\) | − | 476.672i | − | 0.629686i | −0.949144 | − | 0.314843i | \(-0.898048\pi\) | ||
0.949144 | − | 0.314843i | \(-0.101952\pi\) | |||||||
\(758\) | 217.767 | + | 217.767i | 0.287292 | + | 0.287292i | ||||
\(759\) | −48.1208 | + | 334.577i | −0.0634003 | + | 0.440813i | ||||
\(760\) | 69.8265 | + | 69.8265i | 0.0918770 | + | 0.0918770i | ||||
\(761\) | − | 530.851i | − | 0.697570i | −0.937203 | − | 0.348785i | \(-0.886594\pi\) | ||
0.937203 | − | 0.348785i | \(-0.113406\pi\) | |||||||
\(762\) | −73.5343 | + | 511.273i | −0.0965017 | + | 0.670962i | ||||
\(763\) | 446.979i | 0.585817i | ||||||||
\(764\) | 368.143i | 0.481862i | ||||||||
\(765\) | −12.3033 | + | 272.720i | −0.0160827 | + | 0.356497i | ||||
\(766\) | −66.3857 | −0.0866654 | ||||||||
\(767\) | −79.8839 | −0.104151 | ||||||||
\(768\) | −47.5111 | − | 6.83333i | −0.0618634 | − | 0.00889756i | ||||
\(769\) | −112.121 | −0.145801 | −0.0729006 | − | 0.997339i | \(-0.523226\pi\) | ||||
−0.0729006 | + | 0.997339i | \(0.523226\pi\) | |||||||
\(770\) | 59.2547 | − | 59.2547i | 0.0769542 | − | 0.0769542i | ||||
\(771\) | 1441.88 | + | 207.379i | 1.87014 | + | 0.268974i | ||||
\(772\) | 32.0279 | − | 32.0279i | 0.0414869 | − | 0.0414869i | ||||
\(773\) | −375.541 | −0.485823 | −0.242912 | − | 0.970048i | \(-0.578102\pi\) | ||||
−0.242912 | + | 0.970048i | \(0.578102\pi\) | |||||||
\(774\) | −192.359 | + | 654.890i | −0.248526 | + | 0.846112i | ||||
\(775\) | 363.587 | − | 363.587i | 0.469144 | − | 0.469144i | ||||
\(776\) | 274.572 | + | 274.572i | 0.353830 | + | 0.353830i | ||||
\(777\) | −276.969 | − | 39.8353i | −0.356460 | − | 0.0512681i | ||||
\(778\) | 317.060 | 0.407532 | ||||||||
\(779\) | −338.899 | + | 338.899i | −0.435044 | + | 0.435044i | ||||
\(780\) | 194.327 | − | 145.457i | 0.249137 | − | 0.186483i | ||||
\(781\) | −1051.40 | −1.34622 | ||||||||
\(782\) | 225.949 | − | 55.4395i | 0.288937 | − | 0.0708945i | ||||
\(783\) | −316.980 | + | 118.177i | −0.404828 | + | 0.150929i | ||||
\(784\) | 163.461i | 0.208496i | ||||||||
\(785\) | −36.7067 | + | 36.7067i | −0.0467601 | + | 0.0467601i | ||||
\(786\) | 718.102 | − | 537.512i | 0.913616 | − | 0.683858i | ||||
\(787\) | 394.268 | + | 394.268i | 0.500976 | + | 0.500976i | 0.911741 | − | 0.410765i | \(-0.134738\pi\) |
−0.410765 | + | 0.911741i | \(0.634738\pi\) | |||||||
\(788\) | −202.476 | − | 202.476i | −0.256949 | − | 0.256949i | ||||
\(789\) | −980.457 | − | 141.015i | −1.24266 | − | 0.178726i | ||||
\(790\) | − | 113.666i | − | 0.143882i | ||||||
\(791\) | −412.117 | −0.521008 | ||||||||
\(792\) | −142.022 | − | 260.151i | −0.179321 | − | 0.328474i | ||||
\(793\) | 482.515 | − | 482.515i | 0.608468 | − | 0.608468i | ||||
\(794\) | 568.464 | − | 568.464i | 0.715949 | − | 0.715949i | ||||
\(795\) | 251.029 | − | 187.900i | 0.315760 | − | 0.236352i | ||||
\(796\) | 105.501 | + | 105.501i | 0.132539 | + | 0.132539i | ||||
\(797\) | −784.524 | −0.984347 | −0.492173 | − | 0.870497i | \(-0.663797\pi\) | ||||
−0.492173 | + | 0.870497i | \(0.663797\pi\) | |||||||
\(798\) | 141.885 | + | 189.554i | 0.177800 | + | 0.237536i | ||||
\(799\) | 176.782 | + | 107.123i | 0.221255 | + | 0.134071i | ||||
\(800\) | − | 123.412i | − | 0.154264i | ||||||
\(801\) | −189.739 | + | 645.969i | −0.236878 | + | 0.806453i | ||||
\(802\) | 202.378 | + | 202.378i | 0.252341 | + | 0.252341i | ||||
\(803\) | − | 895.324i | − | 1.11497i | ||||||
\(804\) | −175.341 | − | 25.2185i | −0.218086 | − | 0.0313663i | ||||
\(805\) | 34.8231 | − | 34.8231i | 0.0432586 | − | 0.0432586i | ||||
\(806\) | 534.389 | + | 534.389i | 0.663014 | + | 0.663014i | ||||
\(807\) | 237.846 | − | 178.032i | 0.294729 | − | 0.220610i | ||||
\(808\) | 522.728i | 0.646941i | ||||||||
\(809\) | 154.504 | + | 154.504i | 0.190981 | + | 0.190981i | 0.796120 | − | 0.605139i | \(-0.206882\pi\) |
−0.605139 | + | 0.796120i | \(0.706882\pi\) | |||||||
\(810\) | 199.731 | − | 43.4098i | 0.246581 | − | 0.0535923i | ||||
\(811\) | 573.133 | + | 573.133i | 0.706699 | + | 0.706699i | 0.965840 | − | 0.259141i | \(-0.0834393\pi\) |
−0.259141 | + | 0.965840i | \(0.583439\pi\) | |||||||
\(812\) | − | 71.4717i | − | 0.0880194i | ||||||
\(813\) | −920.774 | − | 132.431i | −1.13256 | − | 0.162892i | ||||
\(814\) | − | 538.489i | − | 0.661534i | ||||||
\(815\) | − | 356.448i | − | 0.437359i | ||||||
\(816\) | −129.481 | + | 157.641i | −0.158678 | + | 0.193187i | ||||
\(817\) | 1049.31 | 1.28435 | ||||||||
\(818\) | −79.1845 | −0.0968025 | ||||||||
\(819\) | 510.846 | − | 278.881i | 0.623744 | − | 0.340514i | ||||
\(820\) | −87.4097 | −0.106597 | ||||||||
\(821\) | −701.659 | + | 701.659i | −0.854640 | + | 0.854640i | −0.990701 | − | 0.136061i | \(-0.956556\pi\) |
0.136061 | + | 0.990701i | \(0.456556\pi\) | |||||||
\(822\) | 48.8914 | − | 339.934i | 0.0594785 | − | 0.413546i | ||||
\(823\) | 298.479 | − | 298.479i | 0.362672 | − | 0.362672i | −0.502124 | − | 0.864796i | \(-0.667448\pi\) |
0.864796 | + | 0.502124i | \(0.167448\pi\) | |||||||
\(824\) | 479.025 | 0.581340 | ||||||||
\(825\) | 610.072 | − | 456.650i | 0.739482 | − | 0.553515i | ||||
\(826\) | 10.0489 | − | 10.0489i | 0.0121658 | − | 0.0121658i | ||||
\(827\) | −769.979 | − | 769.979i | −0.931051 | − | 0.931051i | 0.0667208 | − | 0.997772i | \(-0.478746\pi\) |
−0.997772 | + | 0.0667208i | \(0.978746\pi\) | |||||||
\(828\) | −83.4642 | − | 152.887i | −0.100802 | − | 0.184646i | ||||
\(829\) | −219.344 | −0.264588 | −0.132294 | − | 0.991211i | \(-0.542234\pi\) | ||||
−0.132294 | + | 0.991211i | \(0.542234\pi\) | |||||||
\(830\) | 186.435 | − | 186.435i | 0.224620 | − | 0.224620i | ||||
\(831\) | 114.923 | + | 153.534i | 0.138295 | + | 0.184758i | ||||
\(832\) | 181.386 | 0.218013 | ||||||||
\(833\) | 594.140 | + | 360.023i | 0.713253 | + | 0.432201i | ||||
\(834\) | 51.3212 | + | 68.5637i | 0.0615362 | + | 0.0822107i | ||||
\(835\) | 394.522i | 0.472481i | ||||||||
\(836\) | −322.195 | + | 322.195i | −0.385400 | + | 0.385400i | ||||
\(837\) | 222.303 | + | 596.273i | 0.265596 | + | 0.712393i | ||||
\(838\) | −339.069 | − | 339.069i | −0.404617 | − | 0.404617i | ||||
\(839\) | 939.794 | + | 939.794i | 1.12014 | + | 1.12014i | 0.991720 | + | 0.128415i | \(0.0409891\pi\) |
0.128415 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(840\) | −6.14752 | + | 42.7428i | −0.00731847 | + | 0.0508842i | ||||
\(841\) | 684.015i | 0.813335i | ||||||||
\(842\) | −790.214 | −0.938496 | ||||||||
\(843\) | 1461.39 | + | 210.186i | 1.73356 | + | 0.249331i | ||||
\(844\) | −127.066 | + | 127.066i | −0.150552 | + | 0.150552i | ||||
\(845\) | −435.383 | + | 435.383i | −0.515246 | + | 0.515246i | ||||
\(846\) | 43.6150 | − | 148.488i | 0.0515544 | − | 0.175518i | ||||
\(847\) | 29.3831 | + | 29.3831i | 0.0346907 | + | 0.0346907i | ||||
\(848\) | 234.313 | 0.276313 | ||||||||
\(849\) | 578.896 | − | 433.314i | 0.681856 | − | 0.510381i | ||||
\(850\) | −448.571 | − | 271.815i | −0.527730 | − | 0.319782i | ||||
\(851\) | − | 316.462i | − | 0.371871i | ||||||
\(852\) | 433.746 | − | 324.667i | 0.509092 | − | 0.381064i | ||||
\(853\) | −360.046 | − | 360.046i | −0.422094 | − | 0.422094i | 0.463830 | − | 0.885924i | \(-0.346475\pi\) |
−0.885924 | + | 0.463830i | \(0.846475\pi\) | |||||||
\(854\) | 121.395i | 0.142149i | ||||||||
\(855\) | −150.564 | − | 275.798i | −0.176098 | − | 0.322570i | ||||
\(856\) | 356.894 | − | 356.894i | 0.416932 | − | 0.416932i | ||||
\(857\) | 179.922 | + | 179.922i | 0.209944 | + | 0.209944i | 0.804244 | − | 0.594300i | \(-0.202571\pi\) |
−0.594300 | + | 0.804244i | \(0.702571\pi\) | |||||||
\(858\) | 671.170 | + | 896.666i | 0.782250 | + | 1.04507i | ||||
\(859\) | − | 1178.71i | − | 1.37219i | −0.727513 | − | 0.686093i | \(-0.759324\pi\) | ||
0.727513 | − | 0.686093i | \(-0.240676\pi\) | |||||||
\(860\) | 135.321 | + | 135.321i | 0.157349 | + | 0.157349i | ||||
\(861\) | −207.450 | − | 29.8366i | −0.240940 | − | 0.0346534i | ||||
\(862\) | 62.0910 | + | 62.0910i | 0.0720313 | + | 0.0720313i | ||||
\(863\) | 921.679i | 1.06799i | 0.845486 | + | 0.533997i | \(0.179311\pi\) | ||||
−0.845486 | + | 0.533997i | \(0.820689\pi\) | |||||||
\(864\) | 138.924 | + | 63.4679i | 0.160791 | + | 0.0734582i | ||||
\(865\) | − | 159.224i | − | 0.184074i | ||||||
\(866\) | 463.069i | 0.534722i | ||||||||
\(867\) | 287.803 | + | 817.838i | 0.331953 | + | 0.943296i | ||||
\(868\) | −134.446 | −0.154892 | ||||||||
\(869\) | 524.482 | 0.603547 | ||||||||
\(870\) | −13.5028 | + | 93.8830i | −0.0155205 | + | 0.107912i | ||||
\(871\) | 669.411 | 0.768554 | ||||||||
\(872\) | 313.431 | − | 313.431i | 0.359439 | − | 0.359439i | ||||
\(873\) | −592.046 | − | 1084.49i | −0.678174 | − | 1.24226i | ||||
\(874\) | −189.349 | + | 189.349i | −0.216647 | + | 0.216647i | ||||
\(875\) | −238.254 | −0.272290 | ||||||||
\(876\) | 276.472 | + | 369.360i | 0.315608 | + | 0.421644i | ||||
\(877\) | −246.709 | + | 246.709i | −0.281310 | + | 0.281310i | −0.833631 | − | 0.552321i | \(-0.813742\pi\) |
0.552321 | + | 0.833631i | \(0.313742\pi\) | |||||||
\(878\) | −181.855 | − | 181.855i | −0.207124 | − | 0.207124i | ||||
\(879\) | −50.9340 | + | 354.136i | −0.0579454 | + | 0.402886i | ||||
\(880\) | −83.1014 | −0.0944334 | ||||||||
\(881\) | 429.784 | − | 429.784i | 0.487837 | − | 0.487837i | −0.419786 | − | 0.907623i | \(-0.637895\pi\) |
0.907623 | + | 0.419786i | \(0.137895\pi\) | |||||||
\(882\) | 146.584 | − | 499.046i | 0.166195 | − | 0.565812i | ||||
\(883\) | −138.540 | −0.156897 | −0.0784484 | − | 0.996918i | \(-0.524997\pi\) | ||||
−0.0784484 | + | 0.996918i | \(0.524997\pi\) | |||||||
\(884\) | 399.505 | − | 659.296i | 0.451929 | − | 0.745810i | ||||
\(885\) | −15.0984 | + | 11.3015i | −0.0170604 | + | 0.0127700i | ||||
\(886\) | 911.948i | 1.02929i | ||||||||
\(887\) | 865.094 | − | 865.094i | 0.975303 | − | 0.975303i | −0.0243990 | − | 0.999702i | \(-0.507767\pi\) |
0.999702 | + | 0.0243990i | \(0.00776723\pi\) | |||||||
\(888\) | 166.283 | + | 222.150i | 0.187256 | + | 0.250169i | ||||
\(889\) | 245.540 | + | 245.540i | 0.276198 | + | 0.276198i | ||||
\(890\) | 133.477 | + | 133.477i | 0.149974 | + | 0.149974i | ||||
\(891\) | 200.302 | + | 921.601i | 0.224806 | + | 1.03434i | ||||
\(892\) | − | 655.836i | − | 0.735242i | ||||||
\(893\) | −237.918 | −0.266425 | ||||||||
\(894\) | −132.618 | + | 922.071i | −0.148342 | + | 1.03140i | ||||
\(895\) | 226.979 | − | 226.979i | 0.253608 | − | 0.253608i | ||||
\(896\) | −22.8173 | + | 22.8173i | −0.0254658 | + | 0.0254658i | ||||
\(897\) | 394.437 | + | 526.957i | 0.439729 | + | 0.587466i | ||||
\(898\) | 298.631 | + | 298.631i | 0.332551 | + | 0.332551i | ||||
\(899\) | −295.306 | −0.328483 | ||||||||
\(900\) | −110.670 | + | 376.776i | −0.122966 | + | 0.418640i | ||||
\(901\) | 516.077 | − | 851.672i | 0.572782 | − | 0.945252i | ||||
\(902\) | − | 403.328i | − | 0.447148i | ||||||
\(903\) | 274.966 | + | 367.347i | 0.304502 | + | 0.406807i | ||||
\(904\) | 288.985 | + | 288.985i | 0.319674 | + | 0.319674i | ||||
\(905\) | 430.975i | 0.476215i | ||||||||
\(906\) | 84.8992 | − | 590.292i | 0.0937077 | − | 0.651536i | ||||
\(907\) | 22.7933 | − | 22.7933i | 0.0251304 | − | 0.0251304i | −0.694430 | − | 0.719560i | \(-0.744343\pi\) |
0.719560 | + | 0.694430i | \(0.244343\pi\) | |||||||
\(908\) | −137.760 | − | 137.760i | −0.151718 | − | 0.151718i | ||||
\(909\) | 468.758 | − | 1595.89i | 0.515685 | − | 1.75566i | ||||
\(910\) | − | 163.182i | − | 0.179321i | ||||||
\(911\) | −101.819 | − | 101.819i | −0.111766 | − | 0.111766i | 0.649012 | − | 0.760778i | \(-0.275183\pi\) |
−0.760778 | + | 0.649012i | \(0.775183\pi\) | |||||||
\(912\) | 33.4268 | − | 232.412i | 0.0366522 | − | 0.254837i | ||||
\(913\) | 860.249 | + | 860.249i | 0.942223 | + | 0.942223i | ||||
\(914\) | − | 300.685i | − | 0.328977i | ||||||
\(915\) | 22.9346 | − | 159.461i | 0.0250651 | − | 0.174274i | ||||
\(916\) | 699.412i | 0.763550i | ||||||||
\(917\) | − | 603.012i | − | 0.657592i | ||||||
\(918\) | 536.671 | − | 365.166i | 0.584609 | − | 0.397784i | ||||
\(919\) | −319.385 | −0.347535 | −0.173768 | − | 0.984787i | \(-0.555594\pi\) | ||||
−0.173768 | + | 0.984787i | \(0.555594\pi\) | |||||||
\(920\) | −48.8374 | −0.0530842 | ||||||||
\(921\) | 158.664 | + | 22.8200i | 0.172274 | + | 0.0247774i | ||||
\(922\) | −307.300 | −0.333298 | ||||||||
\(923\) | −1447.72 | + | 1447.72i | −1.56850 | + | 1.56850i | ||||
\(924\) | −197.224 | − | 28.3660i | −0.213446 | − | 0.0306991i | ||||
\(925\) | −504.483 | + | 504.483i | −0.545388 | + | 0.545388i | ||||
\(926\) | 153.311 | 0.165562 | ||||||||
\(927\) | −1462.46 | − | 429.566i | −1.57763 | − | 0.463394i | ||||
\(928\) | −50.1175 | + | 50.1175i | −0.0540059 | + | 0.0540059i | ||||
\(929\) | −399.510 | − | 399.510i | −0.430044 | − | 0.430044i | 0.458600 | − | 0.888643i | \(-0.348351\pi\) |
−0.888643 | + | 0.458600i | \(0.848351\pi\) | |||||||
\(930\) | 176.604 | + | 25.4002i | 0.189897 | + | 0.0273121i | ||||
\(931\) | −799.606 | −0.858868 | ||||||||
\(932\) | −301.166 | + | 301.166i | −0.323139 | + | 0.323139i | ||||
\(933\) | −1289.63 | + | 965.313i | −1.38224 | + | 1.03463i | ||||
\(934\) | 882.416 | 0.944770 | ||||||||
\(935\) | −183.031 | + | 302.053i | −0.195755 | + | 0.323052i | ||||
\(936\) | −553.774 | − | 162.659i | −0.591639 | − | 0.173781i | ||||
\(937\) | − | 24.2514i | − | 0.0258819i | −0.999916 | − | 0.0129410i | \(-0.995881\pi\) | ||
0.999916 | − | 0.0129410i | \(-0.00411935\pi\) | |||||||
\(938\) | −84.2079 | + | 84.2079i | −0.0897738 | + | 0.0897738i | ||||
\(939\) | −609.305 | + | 456.075i | −0.648887 | + | 0.485703i | ||||
\(940\) | −30.6822 | − | 30.6822i | −0.0326406 | − | 0.0326406i | ||||
\(941\) | −1131.15 | − | 1131.15i | −1.20207 | − | 1.20207i | −0.973536 | − | 0.228532i | \(-0.926608\pi\) |
−0.228532 | − | 0.973536i | \(-0.573392\pi\) | |||||||
\(942\) | 122.175 | + | 17.5720i | 0.129698 | + | 0.0186539i | ||||
\(943\) | − | 237.030i | − | 0.251357i | ||||||
\(944\) | −14.0930 | −0.0149291 | ||||||||
\(945\) | 57.0981 | − | 124.981i | 0.0604212 | − | 0.132255i | ||||
\(946\) | −624.398 | + | 624.398i | −0.660041 | + | 0.660041i | ||||
\(947\) | 1188.15 | − | 1188.15i | 1.25464 | − | 1.25464i | 0.301028 | − | 0.953615i | \(-0.402670\pi\) |
0.953615 | − | 0.301028i | \(-0.0973299\pi\) | |||||||
\(948\) | −216.372 | + | 161.958i | −0.228240 | + | 0.170842i | ||||
\(949\) | −1232.82 | − | 1232.82i | −1.29907 | − | 1.29907i | ||||
\(950\) | 603.696 | 0.635470 | ||||||||
\(951\) | −927.330 | − | 1238.89i | −0.975111 | − | 1.30272i | ||||
\(952\) | 32.6801 | + | 133.191i | 0.0343279 | + | 0.139906i | ||||
\(953\) | 828.404i | 0.869259i | 0.900609 | + | 0.434629i | \(0.143121\pi\) | ||||
−0.900609 | + | 0.434629i | \(0.856879\pi\) | |||||||
\(954\) | −715.360 | − | 210.121i | −0.749853 | − | 0.220253i | ||||
\(955\) | −232.241 | − | 232.241i | −0.243184 | − | 0.243184i | ||||
\(956\) | − | 101.488i | − | 0.106159i | ||||||
\(957\) | −433.197 | − | 62.3049i | −0.452661 | − | 0.0651044i | ||||
\(958\) | 549.753 | − | 549.753i | 0.573855 | − | 0.573855i | ||||
\(959\) | −163.254 | − | 163.254i | −0.170234 | − | 0.170234i | ||||
\(960\) | 34.2829 | − | 25.6614i | 0.0357114 | − | 0.0267306i | ||||
\(961\) | − | 405.498i | − | 0.421955i | ||||||
\(962\) | −741.474 | − | 741.474i | −0.770763 | − | 0.770763i | ||||
\(963\) | −1409.65 | + | 769.554i | −1.46381 | + | 0.799121i | ||||
\(964\) | −626.143 | − | 626.143i | −0.649526 | − | 0.649526i | ||||
\(965\) | 40.4092i | 0.0418749i | ||||||||
\(966\) | −115.906 | − | 16.6703i | −0.119985 | − | 0.0172570i | ||||
\(967\) | 1825.79i | 1.88809i | 0.329813 | + | 0.944046i | \(0.393014\pi\) | ||||
−0.329813 | + | 0.944046i | \(0.606986\pi\) | |||||||
\(968\) | − | 41.2080i | − | 0.0425703i | ||||||
\(969\) | −771.138 | − | 633.387i | −0.795808 | − | 0.653650i | ||||
\(970\) | −346.424 | −0.357138 | ||||||||
\(971\) | −48.3021 | −0.0497447 | −0.0248723 | − | 0.999691i | \(-0.507918\pi\) | ||||
−0.0248723 | + | 0.999691i | \(0.507918\pi\) | |||||||
\(972\) | −367.220 | − | 318.348i | −0.377798 | − | 0.327518i | ||||
\(973\) | 57.5750 | 0.0591727 | ||||||||
\(974\) | −364.330 | + | 364.330i | −0.374055 | + | 0.374055i | ||||
\(975\) | 211.255 | − | 1468.83i | 0.216672 | − | 1.50649i | ||||
\(976\) | 85.1248 | − | 85.1248i | 0.0872180 | − | 0.0872180i | ||||
\(977\) | 72.2896 | 0.0739914 | 0.0369957 | − | 0.999315i | \(-0.488221\pi\) | ||||
0.0369957 | + | 0.999315i | \(0.488221\pi\) | |||||||
\(978\) | −678.521 | + | 507.885i | −0.693784 | + | 0.519310i | ||||
\(979\) | −615.892 | + | 615.892i | −0.629104 | + | 0.629104i | ||||
\(980\) | −103.118 | − | 103.118i | −0.105223 | − | 0.105223i | ||||
\(981\) | −1237.98 | + | 675.836i | −1.26195 | + | 0.688926i | ||||
\(982\) | 1323.15 | 1.34740 | ||||||||
\(983\) | 767.049 | − | 767.049i | 0.780314 | − | 0.780314i | −0.199570 | − | 0.979884i | \(-0.563954\pi\) |
0.979884 | + | 0.199570i | \(0.0639545\pi\) | |||||||
\(984\) | 124.546 | + | 166.390i | 0.126571 | + | 0.169096i | ||||
\(985\) | 255.461 | 0.259352 | ||||||||
\(986\) | 71.7808 | + | 292.549i | 0.0728000 | + | 0.296703i | ||||
\(987\) | −62.3449 | − | 83.2912i | −0.0631661 | − | 0.0843882i | ||||
\(988\) | 887.295i | 0.898071i | ||||||||
\(989\) | −366.950 | + | 366.950i | −0.371031 | + | 0.371031i | ||||
\(990\) | 253.709 | + | 74.5213i | 0.256272 | + | 0.0752740i | ||||
\(991\) | −964.155 | − | 964.155i | −0.972911 | − | 0.972911i | 0.0267316 | − | 0.999643i | \(-0.491490\pi\) |
−0.999643 | + | 0.0267316i | \(0.991490\pi\) | |||||||
\(992\) | 94.2763 | + | 94.2763i | 0.0950366 | + | 0.0950366i | ||||
\(993\) | −57.8114 | + | 401.954i | −0.0582189 | + | 0.404788i | ||||
\(994\) | − | 364.230i | − | 0.366428i | ||||||
\(995\) | −133.110 | −0.133779 | ||||||||
\(996\) | −620.532 | − | 89.2485i | −0.623024 | − | 0.0896069i | ||||
\(997\) | −773.432 | + | 773.432i | −0.775760 | + | 0.775760i | −0.979107 | − | 0.203347i | \(-0.934818\pi\) |
0.203347 | + | 0.979107i | \(0.434818\pi\) | |||||||
\(998\) | −132.413 | + | 132.413i | −0.132678 | + | 0.132678i | ||||
\(999\) | −308.450 | − | 827.340i | −0.308759 | − | 0.828168i |
(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 | 102.3.e.b.47.1 | ✓ | 20 | |
3.2 | odd | 2 | inner | 102.3.e.b.47.7 | yes | 20 | |
17.4 | even | 4 | inner | 102.3.e.b.89.7 | yes | 20 | |
51.38 | odd | 4 | inner | 102.3.e.b.89.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.3.e.b.47.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
102.3.e.b.47.7 | yes | 20 | 3.2 | odd | 2 | inner | |
102.3.e.b.89.1 | yes | 20 | 51.38 | odd | 4 | inner | |
102.3.e.b.89.7 | yes | 20 | 17.4 | even | 4 | inner |