Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(83,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.k (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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 83.7 | ||
Character | \(\chi\) | \(=\) | 210.83 |
Dual form | 210.3.k.a.167.7 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.282815 | + | 2.98664i | −0.0942716 | + | 0.995547i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −3.28357 | + | 3.77070i | −0.656714 | + | 0.754139i | ||||
\(6\) | 3.26945 | − | 2.70382i | 0.544909 | − | 0.450637i | ||||
\(7\) | −3.67639 | + | 5.95686i | −0.525199 | + | 0.850979i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | −8.84003 | − | 1.68933i | −0.982226 | − | 0.187704i | ||||
\(10\) | 7.05427 | − | 0.487124i | 0.705427 | − | 0.0487124i | ||||
\(11\) | − | 19.5576i | − | 1.77797i | −0.457939 | − | 0.888984i | \(-0.651412\pi\) | ||
0.457939 | − | 0.888984i | \(-0.348588\pi\) | |||||||
\(12\) | −5.97328 | − | 0.565630i | −0.497773 | − | 0.0471358i | ||||
\(13\) | −2.90656 | + | 2.90656i | −0.223582 | + | 0.223582i | −0.810005 | − | 0.586423i | \(-0.800536\pi\) |
0.586423 | + | 0.810005i | \(0.300536\pi\) | |||||||
\(14\) | 9.63325 | − | 2.28046i | 0.688089 | − | 0.162890i | ||||
\(15\) | −10.3331 | − | 10.8733i | −0.688871 | − | 0.724884i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 16.3194 | − | 16.3194i | 0.959967 | − | 0.959967i | −0.0392622 | − | 0.999229i | \(-0.512501\pi\) |
0.999229 | + | 0.0392622i | \(0.0125008\pi\) | |||||||
\(18\) | 7.15070 | + | 10.5294i | 0.397261 | + | 0.584965i | ||||
\(19\) | −8.66094 | −0.455839 | −0.227919 | − | 0.973680i | \(-0.573192\pi\) | ||||
−0.227919 | + | 0.973680i | \(0.573192\pi\) | |||||||
\(20\) | −7.54139 | − | 6.56714i | −0.377070 | − | 0.328357i | ||||
\(21\) | −16.7512 | − | 12.6647i | −0.797678 | − | 0.603083i | ||||
\(22\) | −19.5576 | + | 19.5576i | −0.888984 | + | 0.888984i | ||||
\(23\) | −6.73947 | + | 6.73947i | −0.293021 | + | 0.293021i | −0.838272 | − | 0.545252i | \(-0.816434\pi\) |
0.545252 | + | 0.838272i | \(0.316434\pi\) | |||||||
\(24\) | 5.40765 | + | 6.53891i | 0.225319 | + | 0.272455i | ||||
\(25\) | −3.43630 | − | 24.7627i | −0.137452 | − | 0.990508i | ||||
\(26\) | 5.81313 | 0.223582 | ||||||||
\(27\) | 7.54552 | − | 25.9242i | 0.279464 | − | 0.960156i | ||||
\(28\) | −11.9137 | − | 7.35279i | −0.425490 | − | 0.262600i | ||||
\(29\) | −31.3396 | −1.08067 | −0.540337 | − | 0.841449i | \(-0.681703\pi\) | ||||
−0.540337 | + | 0.841449i | \(0.681703\pi\) | |||||||
\(30\) | −0.540189 | + | 21.2063i | −0.0180063 | + | 0.706877i | ||||
\(31\) | 39.4508i | 1.27261i | 0.771439 | + | 0.636304i | \(0.219537\pi\) | ||||
−0.771439 | + | 0.636304i | \(0.780463\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 58.4116 | + | 5.53119i | 1.77005 | + | 0.167612i | ||||
\(34\) | −32.6389 | −0.959967 | ||||||||
\(35\) | −10.3898 | − | 33.4223i | −0.296851 | − | 0.954924i | ||||
\(36\) | 3.37866 | − | 17.6801i | 0.0938518 | − | 0.491113i | ||||
\(37\) | −25.1721 | + | 25.1721i | −0.680326 | + | 0.680326i | −0.960074 | − | 0.279747i | \(-0.909749\pi\) |
0.279747 | + | 0.960074i | \(0.409749\pi\) | |||||||
\(38\) | 8.66094 | + | 8.66094i | 0.227919 | + | 0.227919i | ||||
\(39\) | −7.85884 | − | 9.50288i | −0.201509 | − | 0.243664i | ||||
\(40\) | 0.974248 | + | 14.1085i | 0.0243562 | + | 0.352713i | ||||
\(41\) | −58.9348 | −1.43743 | −0.718717 | − | 0.695303i | \(-0.755270\pi\) | ||||
−0.718717 | + | 0.695303i | \(0.755270\pi\) | |||||||
\(42\) | 4.08649 | + | 29.4160i | 0.0972974 | + | 0.700381i | ||||
\(43\) | 10.5096 | + | 10.5096i | 0.244409 | + | 0.244409i | 0.818671 | − | 0.574262i | \(-0.194711\pi\) |
−0.574262 | + | 0.818671i | \(0.694711\pi\) | |||||||
\(44\) | 39.1153 | 0.888984 | ||||||||
\(45\) | 35.3968 | − | 27.7860i | 0.786597 | − | 0.617467i | ||||
\(46\) | 13.4789 | 0.293021 | ||||||||
\(47\) | −29.2211 | + | 29.2211i | −0.621725 | + | 0.621725i | −0.945972 | − | 0.324247i | \(-0.894889\pi\) |
0.324247 | + | 0.945972i | \(0.394889\pi\) | |||||||
\(48\) | 1.13126 | − | 11.9466i | 0.0235679 | − | 0.248887i | ||||
\(49\) | −21.9683 | − | 43.7995i | −0.448332 | − | 0.893867i | ||||
\(50\) | −21.3264 | + | 28.1990i | −0.426528 | + | 0.563980i | ||||
\(51\) | 44.1249 | + | 53.3556i | 0.865194 | + | 1.04619i | ||||
\(52\) | −5.81313 | − | 5.81313i | −0.111791 | − | 0.111791i | ||||
\(53\) | −10.3554 | + | 10.3554i | −0.195386 | + | 0.195386i | −0.798019 | − | 0.602633i | \(-0.794118\pi\) |
0.602633 | + | 0.798019i | \(0.294118\pi\) | |||||||
\(54\) | −33.4697 | + | 18.3787i | −0.619810 | + | 0.340346i | ||||
\(55\) | 73.7459 | + | 64.2189i | 1.34084 | + | 1.16762i | ||||
\(56\) | 4.56092 | + | 19.2665i | 0.0814451 | + | 0.344045i | ||||
\(57\) | 2.44944 | − | 25.8671i | 0.0429727 | − | 0.453809i | ||||
\(58\) | 31.3396 | + | 31.3396i | 0.540337 | + | 0.540337i | ||||
\(59\) | 42.5598i | 0.721353i | 0.932691 | + | 0.360676i | \(0.117454\pi\) | ||||
−0.932691 | + | 0.360676i | \(0.882546\pi\) | |||||||
\(60\) | 21.7465 | − | 20.6661i | 0.362442 | − | 0.344436i | ||||
\(61\) | − | 45.1131i | − | 0.739559i | −0.929120 | − | 0.369779i | \(-0.879433\pi\) | ||
0.929120 | − | 0.369779i | \(-0.120567\pi\) | |||||||
\(62\) | 39.4508 | − | 39.4508i | 0.636304 | − | 0.636304i | ||||
\(63\) | 42.5625 | − | 46.4481i | 0.675596 | − | 0.737272i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −1.41586 | − | 20.5037i | −0.0217824 | − | 0.315441i | ||||
\(66\) | −52.8804 | − | 63.9428i | −0.801219 | − | 0.968831i | ||||
\(67\) | 89.3559 | − | 89.3559i | 1.33367 | − | 1.33367i | 0.431611 | − | 0.902060i | \(-0.357945\pi\) |
0.902060 | − | 0.431611i | \(-0.142055\pi\) | |||||||
\(68\) | 32.6389 | + | 32.6389i | 0.479983 | + | 0.479983i | ||||
\(69\) | −18.2224 | − | 22.0344i | −0.264092 | − | 0.319339i | ||||
\(70\) | −23.0325 | + | 43.8121i | −0.329036 | + | 0.625887i | ||||
\(71\) | − | 47.3026i | − | 0.666233i | −0.942886 | − | 0.333117i | \(-0.891900\pi\) | ||
0.942886 | − | 0.333117i | \(-0.108100\pi\) | |||||||
\(72\) | −21.0587 | + | 14.3014i | −0.292482 | + | 0.198631i | ||||
\(73\) | −89.3562 | + | 89.3562i | −1.22406 | + | 1.22406i | −0.257880 | + | 0.966177i | \(0.583024\pi\) |
−0.966177 | + | 0.257880i | \(0.916976\pi\) | |||||||
\(74\) | 50.3442 | 0.680326 | ||||||||
\(75\) | 74.9291 | − | 3.25974i | 0.999055 | − | 0.0434631i | ||||
\(76\) | − | 17.3219i | − | 0.227919i | ||||||
\(77\) | 116.502 | + | 71.9016i | 1.51301 | + | 0.933787i | ||||
\(78\) | −1.64404 | + | 17.3617i | −0.0210774 | + | 0.222586i | ||||
\(79\) | − | 41.4668i | − | 0.524896i | −0.964946 | − | 0.262448i | \(-0.915470\pi\) | ||
0.964946 | − | 0.262448i | \(-0.0845298\pi\) | |||||||
\(80\) | 13.1343 | − | 15.0828i | 0.164179 | − | 0.188535i | ||||
\(81\) | 75.2923 | + | 29.8675i | 0.929535 | + | 0.368735i | ||||
\(82\) | 58.9348 | + | 58.9348i | 0.718717 | + | 0.718717i | ||||
\(83\) | 44.9271 | + | 44.9271i | 0.541290 | + | 0.541290i | 0.923907 | − | 0.382617i | \(-0.124977\pi\) |
−0.382617 | + | 0.923907i | \(0.624977\pi\) | |||||||
\(84\) | 25.3295 | − | 33.5025i | 0.301542 | − | 0.398839i | ||||
\(85\) | 7.94959 | + | 115.122i | 0.0935246 | + | 1.35437i | ||||
\(86\) | − | 21.0192i | − | 0.244409i | ||||||
\(87\) | 8.86329 | − | 93.6000i | 0.101877 | − | 1.07586i | ||||
\(88\) | −39.1153 | − | 39.1153i | −0.444492 | − | 0.444492i | ||||
\(89\) | − | 4.80429i | − | 0.0539807i | −0.999636 | − | 0.0269904i | \(-0.991408\pi\) | ||
0.999636 | − | 0.0269904i | \(-0.00859234\pi\) | |||||||
\(90\) | −63.1829 | − | 7.61081i | −0.702032 | − | 0.0845646i | ||||
\(91\) | −6.62831 | − | 27.9997i | −0.0728386 | − | 0.307689i | ||||
\(92\) | −13.4789 | − | 13.4789i | −0.146510 | − | 0.146510i | ||||
\(93\) | −117.825 | − | 11.1573i | −1.26694 | − | 0.119971i | ||||
\(94\) | 58.4422 | 0.621725 | ||||||||
\(95\) | 28.4388 | − | 32.6578i | 0.299356 | − | 0.343766i | ||||
\(96\) | −13.0778 | + | 10.8153i | −0.136227 | + | 0.112659i | ||||
\(97\) | −2.01325 | − | 2.01325i | −0.0207551 | − | 0.0207551i | 0.696653 | − | 0.717408i | \(-0.254672\pi\) |
−0.717408 | + | 0.696653i | \(0.754672\pi\) | |||||||
\(98\) | −21.8312 | + | 65.7678i | −0.222768 | + | 0.671100i | ||||
\(99\) | −33.0394 | + | 172.890i | −0.333731 | + | 1.74637i | ||||
\(100\) | 49.5254 | − | 6.87261i | 0.495254 | − | 0.0687261i | ||||
\(101\) | −152.563 | −1.51052 | −0.755262 | − | 0.655423i | \(-0.772491\pi\) | ||||
−0.755262 | + | 0.655423i | \(0.772491\pi\) | |||||||
\(102\) | 9.23076 | − | 97.4805i | 0.0904976 | − | 0.955691i | ||||
\(103\) | −58.4473 | + | 58.4473i | −0.567450 | + | 0.567450i | −0.931413 | − | 0.363963i | \(-0.881423\pi\) |
0.363963 | + | 0.931413i | \(0.381423\pi\) | |||||||
\(104\) | 11.6263i | 0.111791i | ||||||||
\(105\) | 102.759 | − | 21.5782i | 0.978656 | − | 0.205507i | ||||
\(106\) | 20.7109 | 0.195386 | ||||||||
\(107\) | −31.9911 | − | 31.9911i | −0.298982 | − | 0.298982i | 0.541633 | − | 0.840615i | \(-0.317806\pi\) |
−0.840615 | + | 0.541633i | \(0.817806\pi\) | |||||||
\(108\) | 51.8484 | + | 15.0910i | 0.480078 | + | 0.139732i | ||||
\(109\) | − | 0.710351i | − | 0.00651698i | −0.999995 | − | 0.00325849i | \(-0.998963\pi\) | ||
0.999995 | − | 0.00325849i | \(-0.00103721\pi\) | |||||||
\(110\) | −9.52700 | − | 137.965i | −0.0866090 | − | 1.25423i | ||||
\(111\) | −68.0609 | − | 82.2990i | −0.613161 | − | 0.741432i | ||||
\(112\) | 14.7056 | − | 23.8274i | 0.131300 | − | 0.212745i | ||||
\(113\) | −59.6020 | + | 59.6020i | −0.527451 | + | 0.527451i | −0.919812 | − | 0.392360i | \(-0.871659\pi\) |
0.392360 | + | 0.919812i | \(0.371659\pi\) | |||||||
\(114\) | −28.3165 | + | 23.4177i | −0.248391 | + | 0.205418i | ||||
\(115\) | −3.28296 | − | 47.5421i | −0.0285475 | − | 0.413409i | ||||
\(116\) | − | 62.6791i | − | 0.540337i | ||||||
\(117\) | 30.6043 | − | 20.7840i | 0.261575 | − | 0.177641i | ||||
\(118\) | 42.5598 | − | 42.5598i | 0.360676 | − | 0.360676i | ||||
\(119\) | 37.2159 | + | 157.209i | 0.312738 | + | 1.32109i | ||||
\(120\) | −42.4126 | − | 1.08038i | −0.353439 | − | 0.00900315i | ||||
\(121\) | −261.501 | −2.16117 | ||||||||
\(122\) | −45.1131 | + | 45.1131i | −0.369779 | + | 0.369779i | ||||
\(123\) | 16.6676 | − | 176.017i | 0.135509 | − | 1.43103i | ||||
\(124\) | −78.9016 | −0.636304 | ||||||||
\(125\) | 104.656 | + | 68.3529i | 0.837248 | + | 0.546823i | ||||
\(126\) | −89.0107 | + | 3.88560i | −0.706434 | + | 0.0308381i | ||||
\(127\) | −116.358 | + | 116.358i | −0.916202 | + | 0.916202i | −0.996751 | − | 0.0805491i | \(-0.974333\pi\) |
0.0805491 | + | 0.996751i | \(0.474333\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −34.3606 | + | 28.4161i | −0.266361 | + | 0.220280i | ||||
\(130\) | −19.0878 | + | 21.9195i | −0.146829 | + | 0.168612i | ||||
\(131\) | −67.9862 | −0.518978 | −0.259489 | − | 0.965746i | \(-0.583554\pi\) | ||||
−0.259489 | + | 0.965746i | \(0.583554\pi\) | |||||||
\(132\) | −11.0624 | + | 116.823i | −0.0838059 | + | 0.885025i | ||||
\(133\) | 31.8410 | − | 51.5920i | 0.239406 | − | 0.387909i | ||||
\(134\) | −178.712 | −1.33367 | ||||||||
\(135\) | 72.9761 | + | 113.576i | 0.540564 | + | 0.841303i | ||||
\(136\) | − | 65.2777i | − | 0.479983i | ||||||
\(137\) | 43.2163 | + | 43.2163i | 0.315448 | + | 0.315448i | 0.847016 | − | 0.531568i | \(-0.178397\pi\) |
−0.531568 | + | 0.847016i | \(0.678397\pi\) | |||||||
\(138\) | −3.81205 | + | 40.2568i | −0.0276235 | + | 0.291716i | ||||
\(139\) | −16.4136 | −0.118083 | −0.0590417 | − | 0.998256i | \(-0.518804\pi\) | ||||
−0.0590417 | + | 0.998256i | \(0.518804\pi\) | |||||||
\(140\) | 66.8447 | − | 20.7796i | 0.477462 | − | 0.148426i | ||||
\(141\) | −79.0087 | − | 95.5370i | −0.560345 | − | 0.677567i | ||||
\(142\) | −47.3026 | + | 47.3026i | −0.333117 | + | 0.333117i | ||||
\(143\) | 56.8456 | + | 56.8456i | 0.397521 | + | 0.397521i | ||||
\(144\) | 35.3601 | + | 6.75733i | 0.245556 | + | 0.0469259i | ||||
\(145\) | 102.906 | − | 118.172i | 0.709695 | − | 0.814979i | ||||
\(146\) | 178.712 | 1.22406 | ||||||||
\(147\) | 137.026 | − | 53.2241i | 0.932151 | − | 0.362069i | ||||
\(148\) | −50.3442 | − | 50.3442i | −0.340163 | − | 0.340163i | ||||
\(149\) | −63.8210 | −0.428329 | −0.214165 | − | 0.976798i | \(-0.568703\pi\) | ||||
−0.214165 | + | 0.976798i | \(0.568703\pi\) | |||||||
\(150\) | −78.1889 | − | 71.6694i | −0.521259 | − | 0.477796i | ||||
\(151\) | 100.225 | 0.663739 | 0.331869 | − | 0.943325i | \(-0.392321\pi\) | ||||
0.331869 | + | 0.943325i | \(0.392321\pi\) | |||||||
\(152\) | −17.3219 | + | 17.3219i | −0.113960 | + | 0.113960i | ||||
\(153\) | −171.833 | + | 116.695i | −1.12309 | + | 0.762715i | ||||
\(154\) | −44.6005 | − | 188.404i | −0.289613 | − | 1.22340i | ||||
\(155\) | −148.757 | − | 129.540i | −0.959723 | − | 0.835740i | ||||
\(156\) | 19.0058 | − | 15.7177i | 0.121832 | − | 0.100754i | ||||
\(157\) | 157.532 | + | 157.532i | 1.00339 | + | 1.00339i | 0.999994 | + | 0.00339453i | \(0.00108051\pi\) |
0.00339453 | + | 0.999994i | \(0.498919\pi\) | |||||||
\(158\) | −41.4668 | + | 41.4668i | −0.262448 | + | 0.262448i | ||||
\(159\) | −27.9993 | − | 33.8567i | −0.176096 | − | 0.212935i | ||||
\(160\) | −28.2171 | + | 1.94850i | −0.176357 | + | 0.0121781i | ||||
\(161\) | −15.3691 | − | 64.9230i | −0.0954604 | − | 0.403249i | ||||
\(162\) | −45.4248 | − | 105.160i | −0.280400 | − | 0.649135i | ||||
\(163\) | 130.800 | + | 130.800i | 0.802457 | + | 0.802457i | 0.983479 | − | 0.181022i | \(-0.0579405\pi\) |
−0.181022 | + | 0.983479i | \(0.557941\pi\) | |||||||
\(164\) | − | 117.870i | − | 0.718717i | ||||||
\(165\) | −212.655 | + | 202.090i | −1.28882 | + | 1.22479i | ||||
\(166\) | − | 89.8542i | − | 0.541290i | ||||||
\(167\) | 35.0842 | − | 35.0842i | 0.210085 | − | 0.210085i | −0.594219 | − | 0.804304i | \(-0.702539\pi\) |
0.804304 | + | 0.594219i | \(0.202539\pi\) | |||||||
\(168\) | −58.8320 | + | 8.17299i | −0.350190 | + | 0.0486487i | ||||
\(169\) | 152.104i | 0.900022i | ||||||||
\(170\) | 107.172 | − | 123.071i | 0.630424 | − | 0.723949i | ||||
\(171\) | 76.5630 | + | 14.6312i | 0.447737 | + | 0.0855626i | ||||
\(172\) | −21.0192 | + | 21.0192i | −0.122204 | + | 0.122204i | ||||
\(173\) | −224.736 | − | 224.736i | −1.29905 | − | 1.29905i | −0.929019 | − | 0.370032i | \(-0.879347\pi\) |
−0.370032 | − | 0.929019i | \(-0.620653\pi\) | |||||||
\(174\) | −102.463 | + | 84.7367i | −0.588869 | + | 0.486992i | ||||
\(175\) | 160.141 | + | 70.5679i | 0.915092 | + | 0.403245i | ||||
\(176\) | 78.2306i | 0.444492i | ||||||||
\(177\) | −127.111 | − | 12.0366i | −0.718140 | − | 0.0680031i | ||||
\(178\) | −4.80429 | + | 4.80429i | −0.0269904 | + | 0.0269904i | ||||
\(179\) | 209.136 | 1.16836 | 0.584179 | − | 0.811625i | \(-0.301417\pi\) | ||||
0.584179 | + | 0.811625i | \(0.301417\pi\) | |||||||
\(180\) | 55.5721 | + | 70.7937i | 0.308734 | + | 0.393298i | ||||
\(181\) | − | 227.999i | − | 1.25966i | −0.776731 | − | 0.629832i | \(-0.783124\pi\) | ||
0.776731 | − | 0.629832i | \(-0.216876\pi\) | |||||||
\(182\) | −21.3714 | + | 34.6280i | −0.117425 | + | 0.190264i | ||||
\(183\) | 134.737 | + | 12.7587i | 0.736265 | + | 0.0697194i | ||||
\(184\) | 26.9579i | 0.146510i | ||||||||
\(185\) | −12.2619 | − | 177.571i | −0.0662807 | − | 0.959841i | ||||
\(186\) | 106.668 | + | 128.983i | 0.573484 | + | 0.693455i | ||||
\(187\) | −319.170 | − | 319.170i | −1.70679 | − | 1.70679i | ||||
\(188\) | −58.4422 | − | 58.4422i | −0.310863 | − | 0.310863i | ||||
\(189\) | 126.687 | + | 140.255i | 0.670299 | + | 0.742091i | ||||
\(190\) | −61.0966 | + | 4.21895i | −0.321561 | + | 0.0222050i | ||||
\(191\) | − | 24.3448i | − | 0.127460i | −0.997967 | − | 0.0637298i | \(-0.979700\pi\) | ||
0.997967 | − | 0.0637298i | \(-0.0202996\pi\) | |||||||
\(192\) | 23.8931 | + | 2.26252i | 0.124443 | + | 0.0117840i | ||||
\(193\) | −119.177 | − | 119.177i | −0.617497 | − | 0.617497i | 0.327392 | − | 0.944889i | \(-0.393830\pi\) |
−0.944889 | + | 0.327392i | \(0.893830\pi\) | |||||||
\(194\) | 4.02649i | 0.0207551i | ||||||||
\(195\) | 61.6376 | + | 1.57009i | 0.316090 | + | 0.00805176i | ||||
\(196\) | 87.5990 | − | 43.9365i | 0.446934 | − | 0.224166i | ||||
\(197\) | 24.0000 | + | 24.0000i | 0.121827 | + | 0.121827i | 0.765392 | − | 0.643565i | \(-0.222545\pi\) |
−0.643565 | + | 0.765392i | \(0.722545\pi\) | |||||||
\(198\) | 205.930 | − | 139.851i | 1.04005 | − | 0.706317i | ||||
\(199\) | 146.804 | 0.737706 | 0.368853 | − | 0.929488i | \(-0.379751\pi\) | ||||
0.368853 | + | 0.929488i | \(0.379751\pi\) | |||||||
\(200\) | −56.3980 | − | 42.6528i | −0.281990 | − | 0.213264i | ||||
\(201\) | 241.603 | + | 292.145i | 1.20200 | + | 1.45346i | ||||
\(202\) | 152.563 | + | 152.563i | 0.755262 | + | 0.755262i | ||||
\(203\) | 115.217 | − | 186.685i | 0.567569 | − | 0.919632i | ||||
\(204\) | −106.711 | + | 88.2498i | −0.523095 | + | 0.432597i | ||||
\(205\) | 193.517 | − | 222.225i | 0.943984 | − | 1.08403i | ||||
\(206\) | 116.895 | 0.567450 | ||||||||
\(207\) | 70.9624 | − | 48.1919i | 0.342813 | − | 0.232811i | ||||
\(208\) | 11.6263 | − | 11.6263i | 0.0558955 | − | 0.0558955i | ||||
\(209\) | 169.388i | 0.810467i | ||||||||
\(210\) | −124.337 | − | 81.1806i | −0.592081 | − | 0.386574i | ||||
\(211\) | 123.187 | 0.583825 | 0.291912 | − | 0.956445i | \(-0.405708\pi\) | ||||
0.291912 | + | 0.956445i | \(0.405708\pi\) | |||||||
\(212\) | −20.7109 | − | 20.7109i | −0.0976929 | − | 0.0976929i | ||||
\(213\) | 141.276 | + | 13.3779i | 0.663266 | + | 0.0628069i | ||||
\(214\) | 63.9822i | 0.298982i | ||||||||
\(215\) | −74.1374 | + | 5.11947i | −0.344825 | + | 0.0238115i | ||||
\(216\) | −36.7574 | − | 66.9395i | −0.170173 | − | 0.309905i | ||||
\(217\) | −235.003 | − | 145.037i | −1.08296 | − | 0.668372i | ||||
\(218\) | −0.710351 | + | 0.710351i | −0.00325849 | + | 0.00325849i | ||||
\(219\) | −241.603 | − | 292.146i | −1.10321 | − | 1.33400i | ||||
\(220\) | −128.438 | + | 147.492i | −0.583808 | + | 0.670418i | ||||
\(221\) | 94.8670i | 0.429262i | ||||||||
\(222\) | −14.2381 | + | 150.360i | −0.0641355 | + | 0.677297i | ||||
\(223\) | −88.3904 | + | 88.3904i | −0.396369 | + | 0.396369i | −0.876950 | − | 0.480581i | \(-0.840426\pi\) |
0.480581 | + | 0.876950i | \(0.340426\pi\) | |||||||
\(224\) | −38.5330 | + | 9.12185i | −0.172022 | + | 0.0407225i | ||||
\(225\) | −11.4554 | + | 224.708i | −0.0509130 | + | 0.998703i | ||||
\(226\) | 119.204 | 0.527451 | ||||||||
\(227\) | 19.9546 | − | 19.9546i | 0.0879055 | − | 0.0879055i | −0.661787 | − | 0.749692i | \(-0.730202\pi\) |
0.749692 | + | 0.661787i | \(0.230202\pi\) | |||||||
\(228\) | 51.7342 | + | 4.89888i | 0.226904 | + | 0.0214863i | ||||
\(229\) | 291.903 | 1.27468 | 0.637342 | − | 0.770581i | \(-0.280034\pi\) | ||||
0.637342 | + | 0.770581i | \(0.280034\pi\) | |||||||
\(230\) | −44.2591 | + | 50.8250i | −0.192431 | + | 0.220978i | ||||
\(231\) | −247.693 | + | 327.615i | −1.07226 | + | 1.41825i | ||||
\(232\) | −62.6791 | + | 62.6791i | −0.270169 | + | 0.270169i | ||||
\(233\) | −263.920 | + | 263.920i | −1.13270 | + | 1.13270i | −0.142978 | + | 0.989726i | \(0.545668\pi\) |
−0.989726 | + | 0.142978i | \(0.954332\pi\) | |||||||
\(234\) | −51.3883 | − | 9.82031i | −0.219608 | − | 0.0419671i | ||||
\(235\) | −14.2343 | − | 206.133i | −0.0605714 | − | 0.877163i | ||||
\(236\) | −85.1196 | −0.360676 | ||||||||
\(237\) | 123.846 | + | 11.7274i | 0.522558 | + | 0.0494828i | ||||
\(238\) | 119.993 | − | 194.425i | 0.504174 | − | 0.816912i | ||||
\(239\) | 407.365 | 1.70446 | 0.852228 | − | 0.523171i | \(-0.175251\pi\) | ||||
0.852228 | + | 0.523171i | \(0.175251\pi\) | |||||||
\(240\) | 41.3323 | + | 43.4930i | 0.172218 | + | 0.181221i | ||||
\(241\) | 311.118i | 1.29095i | 0.763783 | + | 0.645474i | \(0.223340\pi\) | ||||
−0.763783 | + | 0.645474i | \(0.776660\pi\) | |||||||
\(242\) | 261.501 | + | 261.501i | 1.08058 | + | 1.08058i | ||||
\(243\) | −110.497 | + | 216.424i | −0.454721 | + | 0.890634i | ||||
\(244\) | 90.2262 | 0.369779 | ||||||||
\(245\) | 237.289 | + | 60.9832i | 0.968526 | + | 0.248911i | ||||
\(246\) | −192.685 | + | 159.349i | −0.783271 | + | 0.647761i | ||||
\(247\) | 25.1736 | − | 25.1736i | 0.101917 | − | 0.101917i | ||||
\(248\) | 78.9016 | + | 78.9016i | 0.318152 | + | 0.318152i | ||||
\(249\) | −146.887 | + | 121.475i | −0.589908 | + | 0.487851i | ||||
\(250\) | −36.3031 | − | 173.009i | −0.145212 | − | 0.692036i | ||||
\(251\) | 91.1631 | 0.363200 | 0.181600 | − | 0.983373i | \(-0.441872\pi\) | ||||
0.181600 | + | 0.983373i | \(0.441872\pi\) | |||||||
\(252\) | 92.8963 | + | 85.1251i | 0.368636 | + | 0.337798i | ||||
\(253\) | 131.808 | + | 131.808i | 0.520981 | + | 0.520981i | ||||
\(254\) | 232.715 | 0.916202 | ||||||||
\(255\) | −346.075 | − | 8.81557i | −1.35716 | − | 0.0345709i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −221.675 | + | 221.675i | −0.862547 | + | 0.862547i | −0.991633 | − | 0.129086i | \(-0.958796\pi\) |
0.129086 | + | 0.991633i | \(0.458796\pi\) | |||||||
\(258\) | 62.7767 | + | 5.94453i | 0.243320 | + | 0.0230408i | ||||
\(259\) | −57.4040 | − | 242.489i | −0.221637 | − | 0.936251i | ||||
\(260\) | 41.0074 | − | 2.83171i | 0.157721 | − | 0.0108912i | ||||
\(261\) | 277.043 | + | 52.9429i | 1.06147 | + | 0.202846i | ||||
\(262\) | 67.9862 | + | 67.9862i | 0.259489 | + | 0.259489i | ||||
\(263\) | −258.162 | + | 258.162i | −0.981603 | + | 0.981603i | −0.999834 | − | 0.0182309i | \(-0.994197\pi\) |
0.0182309 | + | 0.999834i | \(0.494197\pi\) | |||||||
\(264\) | 127.886 | − | 105.761i | 0.484415 | − | 0.400609i | ||||
\(265\) | −5.04439 | − | 73.0501i | −0.0190354 | − | 0.275661i | ||||
\(266\) | −83.4330 | + | 19.7509i | −0.313658 | + | 0.0742517i | ||||
\(267\) | 14.3487 | + | 1.35872i | 0.0537403 | + | 0.00508885i | ||||
\(268\) | 178.712 | + | 178.712i | 0.666835 | + | 0.666835i | ||||
\(269\) | − | 138.071i | − | 0.513275i | −0.966508 | − | 0.256637i | \(-0.917385\pi\) | ||
0.966508 | − | 0.256637i | \(-0.0826146\pi\) | |||||||
\(270\) | 40.5998 | − | 186.552i | 0.150370 | − | 0.690933i | ||||
\(271\) | 95.9122i | 0.353920i | 0.984218 | + | 0.176960i | \(0.0566263\pi\) | ||||
−0.984218 | + | 0.176960i | \(0.943374\pi\) | |||||||
\(272\) | −65.2777 | + | 65.2777i | −0.239992 | + | 0.239992i | ||||
\(273\) | 85.4995 | − | 11.8777i | 0.313185 | − | 0.0435079i | ||||
\(274\) | − | 86.4327i | − | 0.315448i | ||||||
\(275\) | −484.300 | + | 67.2060i | −1.76109 | + | 0.244385i | ||||
\(276\) | 44.0688 | − | 36.4447i | 0.159670 | − | 0.132046i | ||||
\(277\) | 105.512 | − | 105.512i | 0.380910 | − | 0.380910i | −0.490520 | − | 0.871430i | \(-0.663193\pi\) |
0.871430 | + | 0.490520i | \(0.163193\pi\) | |||||||
\(278\) | 16.4136 | + | 16.4136i | 0.0590417 | + | 0.0590417i | ||||
\(279\) | 66.6456 | − | 348.747i | 0.238873 | − | 1.24999i | ||||
\(280\) | −87.6242 | − | 46.0651i | −0.312944 | − | 0.164518i | ||||
\(281\) | − | 237.031i | − | 0.843525i | −0.906706 | − | 0.421762i | \(-0.861412\pi\) | ||
0.906706 | − | 0.421762i | \(-0.138588\pi\) | |||||||
\(282\) | −16.5283 | + | 174.546i | −0.0586111 | + | 0.618956i | ||||
\(283\) | 286.765 | − | 286.765i | 1.01330 | − | 1.01330i | 0.0133925 | − | 0.999910i | \(-0.495737\pi\) |
0.999910 | − | 0.0133925i | \(-0.00426309\pi\) | |||||||
\(284\) | 94.6051 | 0.333117 | ||||||||
\(285\) | 89.4941 | + | 94.1726i | 0.314014 | + | 0.330430i | ||||
\(286\) | − | 113.691i | − | 0.397521i | ||||||
\(287\) | 216.667 | − | 351.066i | 0.754939 | − | 1.22323i | ||||
\(288\) | −28.6028 | − | 42.1175i | −0.0993153 | − | 0.146241i | ||||
\(289\) | − | 243.648i | − | 0.843072i | ||||||
\(290\) | −221.078 | + | 15.2662i | −0.762337 | + | 0.0526422i | ||||
\(291\) | 6.58222 | − | 5.44346i | 0.0226193 | − | 0.0187061i | ||||
\(292\) | −178.712 | − | 178.712i | −0.612029 | − | 0.612029i | ||||
\(293\) | −353.346 | − | 353.346i | −1.20596 | − | 1.20596i | −0.972324 | − | 0.233635i | \(-0.924938\pi\) |
−0.233635 | − | 0.972324i | \(-0.575062\pi\) | |||||||
\(294\) | −190.250 | − | 83.8021i | −0.647110 | − | 0.285041i | ||||
\(295\) | −160.480 | − | 139.748i | −0.544001 | − | 0.473723i | ||||
\(296\) | 100.688i | 0.340163i | ||||||||
\(297\) | −507.017 | − | 147.573i | −1.70713 | − | 0.496877i | ||||
\(298\) | 63.8210 | + | 63.8210i | 0.214165 | + | 0.214165i | ||||
\(299\) | − | 39.1774i | − | 0.131028i | ||||||
\(300\) | 6.51947 | + | 149.858i | 0.0217316 | + | 0.499528i | ||||
\(301\) | −101.241 | + | 23.9667i | −0.336350 | + | 0.0796236i | ||||
\(302\) | −100.225 | − | 100.225i | −0.331869 | − | 0.331869i | ||||
\(303\) | 43.1471 | − | 455.651i | 0.142400 | − | 1.50380i | ||||
\(304\) | 34.6437 | 0.113960 | ||||||||
\(305\) | 170.108 | + | 148.132i | 0.557730 | + | 0.485679i | ||||
\(306\) | 288.529 | + | 55.1379i | 0.942904 | + | 0.180189i | ||||
\(307\) | 268.995 | + | 268.995i | 0.876204 | + | 0.876204i | 0.993140 | − | 0.116935i | \(-0.0373069\pi\) |
−0.116935 | + | 0.993140i | \(0.537307\pi\) | |||||||
\(308\) | −143.803 | + | 233.004i | −0.466893 | + | 0.756507i | ||||
\(309\) | −158.031 | − | 191.091i | −0.511428 | − | 0.618417i | ||||
\(310\) | 19.2174 | + | 278.297i | 0.0619917 | + | 0.897731i | ||||
\(311\) | 93.5888 | 0.300929 | 0.150464 | − | 0.988615i | \(-0.451923\pi\) | ||||
0.150464 | + | 0.988615i | \(0.451923\pi\) | |||||||
\(312\) | −34.7234 | − | 3.28808i | −0.111293 | − | 0.0105387i | ||||
\(313\) | −65.0697 | + | 65.0697i | −0.207890 | + | 0.207890i | −0.803370 | − | 0.595480i | \(-0.796962\pi\) |
0.595480 | + | 0.803370i | \(0.296962\pi\) | |||||||
\(314\) | − | 315.064i | − | 1.00339i | ||||||
\(315\) | 35.3847 | + | 313.006i | 0.112332 | + | 0.993671i | ||||
\(316\) | 82.9336 | 0.262448 | ||||||||
\(317\) | 183.110 | + | 183.110i | 0.577633 | + | 0.577633i | 0.934251 | − | 0.356617i | \(-0.116070\pi\) |
−0.356617 | + | 0.934251i | \(0.616070\pi\) | |||||||
\(318\) | −5.85735 | + | 61.8560i | −0.0184193 | + | 0.194516i | ||||
\(319\) | 612.928i | 1.92140i | ||||||||
\(320\) | 30.1656 | + | 26.2686i | 0.0942674 | + | 0.0820893i | ||||
\(321\) | 104.593 | − | 86.4983i | 0.325836 | − | 0.269465i | ||||
\(322\) | −49.5539 | + | 80.2921i | −0.153894 | + | 0.249354i | ||||
\(323\) | −141.342 | + | 141.342i | −0.437590 | + | 0.437590i | ||||
\(324\) | −59.7350 | + | 150.585i | −0.184367 | + | 0.464767i | ||||
\(325\) | 81.9623 | + | 61.9866i | 0.252192 | + | 0.190728i | ||||
\(326\) | − | 261.601i | − | 0.802457i | ||||||
\(327\) | 2.12156 | + | 0.200898i | 0.00648796 | + | 0.000614367i | ||||
\(328\) | −117.870 | + | 117.870i | −0.359358 | + | 0.359358i | ||||
\(329\) | −66.6376 | − | 281.494i | −0.202546 | − | 0.855605i | ||||
\(330\) | 414.746 | + | 10.5648i | 1.25681 | + | 0.0320146i | ||||
\(331\) | −389.930 | −1.17804 | −0.589018 | − | 0.808120i | \(-0.700485\pi\) | ||||
−0.589018 | + | 0.808120i | \(0.700485\pi\) | |||||||
\(332\) | −89.8542 | + | 89.8542i | −0.270645 | + | 0.270645i | ||||
\(333\) | 265.046 | − | 179.998i | 0.795934 | − | 0.540534i | ||||
\(334\) | −70.1684 | −0.210085 | ||||||||
\(335\) | 43.5274 | + | 630.341i | 0.129933 | + | 1.88161i | ||||
\(336\) | 67.0050 | + | 50.6590i | 0.199420 | + | 0.150771i | ||||
\(337\) | 201.311 | − | 201.311i | 0.597362 | − | 0.597362i | −0.342248 | − | 0.939610i | \(-0.611188\pi\) |
0.939610 | + | 0.342248i | \(0.111188\pi\) | |||||||
\(338\) | 152.104 | − | 152.104i | 0.450011 | − | 0.450011i | ||||
\(339\) | −161.153 | − | 194.866i | −0.475379 | − | 0.574826i | ||||
\(340\) | −230.243 | + | 15.8992i | −0.677186 | + | 0.0467623i | ||||
\(341\) | 771.565 | 2.26265 | ||||||||
\(342\) | −61.9318 | − | 91.1942i | −0.181087 | − | 0.266650i | ||||
\(343\) | 341.671 | + | 30.1624i | 0.996126 | + | 0.0879370i | ||||
\(344\) | 42.0383 | 0.122204 | ||||||||
\(345\) | 142.919 | + | 3.64059i | 0.414259 | + | 0.0105524i | ||||
\(346\) | 449.472i | 1.29905i | ||||||||
\(347\) | −373.074 | − | 373.074i | −1.07514 | − | 1.07514i | −0.996938 | − | 0.0782023i | \(-0.975082\pi\) |
−0.0782023 | − | 0.996938i | \(-0.524918\pi\) | |||||||
\(348\) | 187.200 | + | 17.7266i | 0.537931 | + | 0.0509385i | ||||
\(349\) | −413.538 | −1.18492 | −0.592461 | − | 0.805599i | \(-0.701843\pi\) | ||||
−0.592461 | + | 0.805599i | \(0.701843\pi\) | |||||||
\(350\) | −89.5732 | − | 230.709i | −0.255923 | − | 0.659169i | ||||
\(351\) | 53.4189 | + | 97.2820i | 0.152191 | + | 0.277157i | ||||
\(352\) | 78.2306 | − | 78.2306i | 0.222246 | − | 0.222246i | ||||
\(353\) | 7.52215 | + | 7.52215i | 0.0213092 | + | 0.0213092i | 0.717681 | − | 0.696372i | \(-0.245204\pi\) |
−0.696372 | + | 0.717681i | \(0.745204\pi\) | |||||||
\(354\) | 115.074 | + | 139.147i | 0.325069 | + | 0.393072i | ||||
\(355\) | 178.364 | + | 155.321i | 0.502433 | + | 0.437525i | ||||
\(356\) | 9.60857 | 0.0269904 | ||||||||
\(357\) | −480.052 | + | 66.6892i | −1.34468 | + | 0.186805i | ||||
\(358\) | −209.136 | − | 209.136i | −0.584179 | − | 0.584179i | ||||
\(359\) | 166.966 | 0.465085 | 0.232543 | − | 0.972586i | \(-0.425295\pi\) | ||||
0.232543 | + | 0.972586i | \(0.425295\pi\) | |||||||
\(360\) | 15.2216 | − | 126.366i | 0.0422823 | − | 0.351016i | ||||
\(361\) | −285.988 | −0.792211 | ||||||||
\(362\) | −227.999 | + | 227.999i | −0.629832 | + | 0.629832i | ||||
\(363\) | 73.9565 | − | 781.010i | 0.203737 | − | 2.15154i | ||||
\(364\) | 55.9993 | − | 13.2566i | 0.153844 | − | 0.0364193i | ||||
\(365\) | −43.5275 | − | 630.342i | −0.119254 | − | 1.72697i | ||||
\(366\) | −121.978 | − | 147.495i | −0.333273 | − | 0.402992i | ||||
\(367\) | −216.400 | − | 216.400i | −0.589646 | − | 0.589646i | 0.347890 | − | 0.937535i | \(-0.386898\pi\) |
−0.937535 | + | 0.347890i | \(0.886898\pi\) | |||||||
\(368\) | 26.9579 | − | 26.9579i | 0.0732551 | − | 0.0732551i | ||||
\(369\) | 520.985 | + | 99.5604i | 1.41188 | + | 0.269811i | ||||
\(370\) | −165.309 | + | 189.833i | −0.446780 | + | 0.513061i | ||||
\(371\) | −23.6152 | − | 99.7566i | −0.0636529 | − | 0.268886i | ||||
\(372\) | 22.3146 | − | 235.651i | 0.0599854 | − | 0.633470i | ||||
\(373\) | −64.8753 | − | 64.8753i | −0.173928 | − | 0.173928i | 0.614775 | − | 0.788703i | \(-0.289247\pi\) |
−0.788703 | + | 0.614775i | \(0.789247\pi\) | |||||||
\(374\) | 638.339i | 1.70679i | ||||||||
\(375\) | −233.744 | + | 293.239i | −0.623317 | + | 0.781970i | ||||
\(376\) | 116.884i | 0.310863i | ||||||||
\(377\) | 91.0905 | − | 91.0905i | 0.241619 | − | 0.241619i | ||||
\(378\) | 13.5687 | − | 266.942i | 0.0358959 | − | 0.706195i | ||||
\(379\) | 44.8235i | 0.118268i | 0.998250 | + | 0.0591339i | \(0.0188339\pi\) | ||||
−0.998250 | + | 0.0591339i | \(0.981166\pi\) | |||||||
\(380\) | 65.3155 | + | 56.8776i | 0.171883 | + | 0.149678i | ||||
\(381\) | −314.611 | − | 380.426i | −0.825749 | − | 0.998493i | ||||
\(382\) | −24.3448 | + | 24.3448i | −0.0637298 | + | 0.0637298i | ||||
\(383\) | 465.824 | + | 465.824i | 1.21625 | + | 1.21625i | 0.968935 | + | 0.247315i | \(0.0795483\pi\) |
0.247315 | + | 0.968935i | \(0.420452\pi\) | |||||||
\(384\) | −21.6306 | − | 26.1556i | −0.0563297 | − | 0.0681136i | ||||
\(385\) | −653.662 | + | 203.200i | −1.69782 | + | 0.527792i | ||||
\(386\) | 238.354i | 0.617497i | ||||||||
\(387\) | −75.1509 | − | 110.659i | −0.194188 | − | 0.285941i | ||||
\(388\) | 4.02649 | − | 4.02649i | 0.0103776 | − | 0.0103776i | ||||
\(389\) | −341.962 | −0.879079 | −0.439540 | − | 0.898223i | \(-0.644858\pi\) | ||||
−0.439540 | + | 0.898223i | \(0.644858\pi\) | |||||||
\(390\) | −60.0675 | − | 63.2077i | −0.154019 | − | 0.162071i | ||||
\(391\) | 219.969i | 0.562580i | ||||||||
\(392\) | −131.536 | − | 43.6625i | −0.335550 | − | 0.111384i | ||||
\(393\) | 19.2275 | − | 203.050i | 0.0489249 | − | 0.516667i | ||||
\(394\) | − | 48.0000i | − | 0.121827i | ||||||
\(395\) | 156.359 | + | 136.159i | 0.395845 | + | 0.344707i | ||||
\(396\) | −345.780 | − | 66.0787i | −0.873183 | − | 0.166865i | ||||
\(397\) | −214.201 | − | 214.201i | −0.539549 | − | 0.539549i | 0.383847 | − | 0.923397i | \(-0.374599\pi\) |
−0.923397 | + | 0.383847i | \(0.874599\pi\) | |||||||
\(398\) | −146.804 | − | 146.804i | −0.368853 | − | 0.368853i | ||||
\(399\) | 145.081 | + | 109.689i | 0.363613 | + | 0.274909i | ||||
\(400\) | 13.7452 | + | 99.0508i | 0.0343630 | + | 0.247627i | ||||
\(401\) | − | 278.216i | − | 0.693806i | −0.937901 | − | 0.346903i | \(-0.887233\pi\) | ||
0.937901 | − | 0.346903i | \(-0.112767\pi\) | |||||||
\(402\) | 50.5424 | − | 533.748i | 0.125727 | − | 1.32773i | ||||
\(403\) | −114.666 | − | 114.666i | −0.284532 | − | 0.284532i | ||||
\(404\) | − | 305.126i | − | 0.755262i | ||||||
\(405\) | −359.849 | + | 185.832i | −0.888516 | + | 0.458845i | ||||
\(406\) | −301.902 | + | 71.4687i | −0.743600 | + | 0.176031i | ||||
\(407\) | 492.307 | + | 492.307i | 1.20960 | + | 1.20960i | ||||
\(408\) | 194.961 | + | 18.4615i | 0.477846 | + | 0.0452488i | ||||
\(409\) | 481.543 | 1.17737 | 0.588684 | − | 0.808364i | \(-0.299646\pi\) | ||||
0.588684 | + | 0.808364i | \(0.299646\pi\) | |||||||
\(410\) | −415.742 | + | 28.7085i | −1.01400 | + | 0.0700208i | ||||
\(411\) | −141.294 | + | 116.849i | −0.343781 | + | 0.284305i | ||||
\(412\) | −116.895 | − | 116.895i | −0.283725 | − | 0.283725i | ||||
\(413\) | −253.523 | − | 156.467i | −0.613856 | − | 0.378854i | ||||
\(414\) | −119.154 | − | 22.7704i | −0.287812 | − | 0.0550010i | ||||
\(415\) | −316.928 | + | 21.8851i | −0.763682 | + | 0.0527351i | ||||
\(416\) | −23.2525 | −0.0558955 | ||||||||
\(417\) | 4.64201 | − | 49.0215i | 0.0111319 | − | 0.117557i | ||||
\(418\) | 169.388 | − | 169.388i | 0.405233 | − | 0.405233i | ||||
\(419\) | 12.3613i | 0.0295020i | 0.999891 | + | 0.0147510i | \(0.00469556\pi\) | ||||
−0.999891 | + | 0.0147510i | \(0.995304\pi\) | |||||||
\(420\) | 43.1565 | + | 205.518i | 0.102753 | + | 0.489328i | ||||
\(421\) | 10.9249 | 0.0259498 | 0.0129749 | − | 0.999916i | \(-0.495870\pi\) | ||||
0.0129749 | + | 0.999916i | \(0.495870\pi\) | |||||||
\(422\) | −123.187 | − | 123.187i | −0.291912 | − | 0.291912i | ||||
\(423\) | 307.679 | − | 208.951i | 0.727375 | − | 0.493974i | ||||
\(424\) | 41.4218i | 0.0976929i | ||||||||
\(425\) | −460.192 | − | 348.035i | −1.08280 | − | 0.818906i | ||||
\(426\) | −127.898 | − | 154.654i | −0.300230 | − | 0.363036i | ||||
\(427\) | 268.732 | + | 165.853i | 0.629349 | + | 0.388416i | ||||
\(428\) | 63.9822 | − | 63.9822i | 0.149491 | − | 0.149491i | ||||
\(429\) | −185.854 | + | 153.700i | −0.433226 | + | 0.358276i | ||||
\(430\) | 79.2569 | + | 69.0180i | 0.184318 | + | 0.160507i | ||||
\(431\) | 7.70570i | 0.0178786i | 0.999960 | + | 0.00893932i | \(0.00284551\pi\) | ||||
−0.999960 | + | 0.00893932i | \(0.997154\pi\) | |||||||
\(432\) | −30.1821 | + | 103.697i | −0.0698659 | + | 0.240039i | ||||
\(433\) | −16.6929 | + | 16.6929i | −0.0385516 | + | 0.0385516i | −0.726120 | − | 0.687568i | \(-0.758678\pi\) |
0.687568 | + | 0.726120i | \(0.258678\pi\) | |||||||
\(434\) | 89.9661 | + | 380.040i | 0.207295 | + | 0.875667i | ||||
\(435\) | 323.834 | + | 340.763i | 0.744445 | + | 0.783363i | ||||
\(436\) | 1.42070 | 0.00325849 | ||||||||
\(437\) | 58.3702 | − | 58.3702i | 0.133570 | − | 0.133570i | ||||
\(438\) | −50.5425 | + | 533.749i | −0.115394 | + | 1.21861i | ||||
\(439\) | −717.592 | −1.63461 | −0.817303 | − | 0.576208i | \(-0.804532\pi\) | ||||
−0.817303 | + | 0.576208i | \(0.804532\pi\) | |||||||
\(440\) | 275.930 | − | 19.0540i | 0.627113 | − | 0.0433045i | ||||
\(441\) | 120.208 | + | 424.301i | 0.272581 | + | 0.962133i | ||||
\(442\) | 94.8670 | − | 94.8670i | 0.214631 | − | 0.214631i | ||||
\(443\) | −163.039 | + | 163.039i | −0.368035 | + | 0.368035i | −0.866760 | − | 0.498725i | \(-0.833802\pi\) |
0.498725 | + | 0.866760i | \(0.333802\pi\) | |||||||
\(444\) | 164.598 | − | 136.122i | 0.370716 | − | 0.306581i | ||||
\(445\) | 18.1155 | + | 15.7752i | 0.0407090 | + | 0.0354499i | ||||
\(446\) | 176.781 | 0.396369 | ||||||||
\(447\) | 18.0495 | − | 190.610i | 0.0403793 | − | 0.426422i | ||||
\(448\) | 47.6548 | + | 29.4111i | 0.106372 | + | 0.0656499i | ||||
\(449\) | 681.871 | 1.51864 | 0.759322 | − | 0.650715i | \(-0.225531\pi\) | ||||
0.759322 | + | 0.650715i | \(0.225531\pi\) | |||||||
\(450\) | 236.164 | − | 213.253i | 0.524808 | − | 0.473895i | ||||
\(451\) | 1152.63i | 2.55571i | ||||||||
\(452\) | −119.204 | − | 119.204i | −0.263726 | − | 0.263726i | ||||
\(453\) | −28.3450 | + | 299.335i | −0.0625717 | + | 0.660783i | ||||
\(454\) | −39.9091 | −0.0879055 | ||||||||
\(455\) | 127.343 | + | 66.9456i | 0.279874 | + | 0.147133i | ||||
\(456\) | −46.8353 | − | 56.6331i | −0.102709 | − | 0.124195i | ||||
\(457\) | 201.532 | − | 201.532i | 0.440990 | − | 0.440990i | −0.451355 | − | 0.892345i | \(-0.649059\pi\) |
0.892345 | + | 0.451355i | \(0.149059\pi\) | |||||||
\(458\) | −291.903 | − | 291.903i | −0.637342 | − | 0.637342i | ||||
\(459\) | −299.930 | − | 546.207i | −0.653442 | − | 1.18999i | ||||
\(460\) | 95.0841 | − | 6.56592i | 0.206705 | − | 0.0142737i | ||||
\(461\) | 205.599 | 0.445985 | 0.222993 | − | 0.974820i | \(-0.428417\pi\) | ||||
0.222993 | + | 0.974820i | \(0.428417\pi\) | |||||||
\(462\) | 575.307 | − | 79.9222i | 1.24525 | − | 0.172992i | ||||
\(463\) | −172.047 | − | 172.047i | −0.371592 | − | 0.371592i | 0.496465 | − | 0.868057i | \(-0.334631\pi\) |
−0.868057 | + | 0.496465i | \(0.834631\pi\) | |||||||
\(464\) | 125.358 | 0.270169 | ||||||||
\(465\) | 428.959 | − | 407.648i | 0.922492 | − | 0.876662i | ||||
\(466\) | 527.840 | 1.13270 | ||||||||
\(467\) | −331.816 | + | 331.816i | −0.710527 | + | 0.710527i | −0.966645 | − | 0.256118i | \(-0.917556\pi\) |
0.256118 | + | 0.966645i | \(0.417556\pi\) | |||||||
\(468\) | 41.5679 | + | 61.2086i | 0.0888204 | + | 0.130788i | ||||
\(469\) | 203.773 | + | 860.788i | 0.434484 | + | 1.83537i | ||||
\(470\) | −191.899 | + | 220.368i | −0.408296 | + | 0.468867i | ||||
\(471\) | −515.044 | + | 425.939i | −1.09351 | + | 0.904329i | ||||
\(472\) | 85.1196 | + | 85.1196i | 0.180338 | + | 0.180338i | ||||
\(473\) | 205.543 | − | 205.543i | 0.434551 | − | 0.434551i | ||||
\(474\) | −112.119 | − | 135.574i | −0.236538 | − | 0.286021i | ||||
\(475\) | 29.7616 | + | 214.468i | 0.0626560 | + | 0.451512i | ||||
\(476\) | −314.418 | + | 74.4317i | −0.660543 | + | 0.156369i | ||||
\(477\) | 109.036 | − | 74.0487i | 0.228588 | − | 0.155238i | ||||
\(478\) | −407.365 | − | 407.365i | −0.852228 | − | 0.852228i | ||||
\(479\) | − | 449.861i | − | 0.939167i | −0.882888 | − | 0.469584i | \(-0.844404\pi\) | ||
0.882888 | − | 0.469584i | \(-0.155596\pi\) | |||||||
\(480\) | 2.16076 | − | 84.8253i | 0.00450157 | − | 0.176719i | ||||
\(481\) | − | 146.329i | − | 0.304217i | ||||||
\(482\) | 311.118 | − | 311.118i | 0.645474 | − | 0.645474i | ||||
\(483\) | 198.248 | − | 27.5408i | 0.410452 | − | 0.0570203i | ||||
\(484\) | − | 523.003i | − | 1.08058i | ||||||
\(485\) | 14.2020 | − | 0.980700i | 0.0292824 | − | 0.00202206i | ||||
\(486\) | 326.921 | − | 105.927i | 0.672678 | − | 0.217956i | ||||
\(487\) | −281.676 | + | 281.676i | −0.578391 | + | 0.578391i | −0.934460 | − | 0.356069i | \(-0.884117\pi\) |
0.356069 | + | 0.934460i | \(0.384117\pi\) | |||||||
\(488\) | −90.2262 | − | 90.2262i | −0.184890 | − | 0.184890i | ||||
\(489\) | −427.646 | + | 353.662i | −0.874532 | + | 0.723234i | ||||
\(490\) | −176.306 | − | 298.272i | −0.359808 | − | 0.608719i | ||||
\(491\) | 896.974i | 1.82683i | 0.407029 | + | 0.913415i | \(0.366565\pi\) | ||||
−0.407029 | + | 0.913415i | \(0.633435\pi\) | |||||||
\(492\) | 352.034 | + | 33.3353i | 0.715516 | + | 0.0677546i | ||||
\(493\) | −511.444 | + | 511.444i | −1.03741 | + | 1.03741i | ||||
\(494\) | −50.3472 | −0.101917 | ||||||||
\(495\) | −543.429 | − | 692.279i | −1.09784 | − | 1.39854i | ||||
\(496\) | − | 157.803i | − | 0.318152i | ||||||
\(497\) | 281.774 | + | 173.903i | 0.566951 | + | 0.349905i | ||||
\(498\) | 268.362 | + | 25.4121i | 0.538880 | + | 0.0510283i | ||||
\(499\) | 0.286254i | 0.000573655i | 1.00000 | 0.000286827i | \(9.13000e-5\pi\) | |||||
−1.00000 | 0.000286827i | \(0.999909\pi\) | ||||||||
\(500\) | −136.706 | + | 209.312i | −0.273412 | + | 0.418624i | ||||
\(501\) | 94.8615 | + | 114.706i | 0.189344 | + | 0.228954i | ||||
\(502\) | −91.1631 | − | 91.1631i | −0.181600 | − | 0.181600i | ||||
\(503\) | 167.300 | + | 167.300i | 0.332605 | + | 0.332605i | 0.853575 | − | 0.520970i | \(-0.174430\pi\) |
−0.520970 | + | 0.853575i | \(0.674430\pi\) | |||||||
\(504\) | −7.77120 | − | 178.021i | −0.0154190 | − | 0.353217i | ||||
\(505\) | 500.952 | − | 575.269i | 0.991983 | − | 1.13915i | ||||
\(506\) | − | 263.616i | − | 0.520981i | ||||||
\(507\) | −454.279 | − | 43.0172i | −0.896014 | − | 0.0848466i | ||||
\(508\) | −232.715 | − | 232.715i | −0.458101 | − | 0.458101i | ||||
\(509\) | − | 480.263i | − | 0.943543i | −0.881721 | − | 0.471771i | \(-0.843615\pi\) | ||
0.881721 | − | 0.471771i | \(-0.156385\pi\) | |||||||
\(510\) | 337.260 | + | 354.891i | 0.661293 | + | 0.695864i | ||||
\(511\) | −203.773 | − | 860.790i | −0.398774 | − | 1.68452i | ||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −65.3513 | + | 224.528i | −0.127390 | + | 0.437676i | ||||
\(514\) | 443.349 | 0.862547 | ||||||||
\(515\) | −28.4711 | − | 412.303i | −0.0552837 | − | 0.800589i | ||||
\(516\) | −56.8321 | − | 68.7212i | −0.110140 | − | 0.133181i | ||||
\(517\) | 571.496 | + | 571.496i | 1.10541 | + | 1.10541i | ||||
\(518\) | −185.085 | + | 299.893i | −0.357307 | + | 0.578944i | ||||
\(519\) | 734.764 | − | 607.646i | 1.41573 | − | 1.17080i | ||||
\(520\) | −43.8391 | − | 38.1757i | −0.0843060 | − | 0.0734147i | ||||
\(521\) | −168.144 | −0.322733 | −0.161366 | − | 0.986895i | \(-0.551590\pi\) | ||||
−0.161366 | + | 0.986895i | \(0.551590\pi\) | |||||||
\(522\) | −224.100 | − | 329.986i | −0.429310 | − | 0.632156i | ||||
\(523\) | −4.84540 | + | 4.84540i | −0.00926463 | + | 0.00926463i | −0.711724 | − | 0.702459i | \(-0.752085\pi\) |
0.702459 | + | 0.711724i | \(0.252085\pi\) | |||||||
\(524\) | − | 135.972i | − | 0.259489i | ||||||
\(525\) | −256.051 | + | 458.326i | −0.487717 | + | 0.873002i | ||||
\(526\) | 516.323 | 0.981603 | ||||||||
\(527\) | 643.815 | + | 643.815i | 1.22166 | + | 1.22166i | ||||
\(528\) | −233.646 | − | 22.1248i | −0.442512 | − | 0.0419030i | ||||
\(529\) | 438.159i | 0.828278i | ||||||||
\(530\) | −68.0057 | + | 78.0945i | −0.128313 | + | 0.147348i | ||||
\(531\) | 71.8977 | − | 376.230i | 0.135401 | − | 0.708531i | ||||
\(532\) | 103.184 | + | 63.6820i | 0.193955 | + | 0.119703i | ||||
\(533\) | 171.298 | − | 171.298i | 0.321384 | − | 0.321384i | ||||
\(534\) | −12.9899 | − | 15.7074i | −0.0243257 | − | 0.0294146i | ||||
\(535\) | 225.674 | − | 15.5836i | 0.421820 | − | 0.0291283i | ||||
\(536\) | − | 357.424i | − | 0.666835i | ||||||
\(537\) | −59.1468 | + | 624.614i | −0.110143 | + | 1.16315i | ||||
\(538\) | −138.071 | + | 138.071i | −0.256637 | + | 0.256637i | ||||
\(539\) | −856.615 | + | 429.647i | −1.58927 | + | 0.797119i | ||||
\(540\) | −227.152 | + | 145.952i | −0.420652 | + | 0.270282i | ||||
\(541\) | 664.777 | 1.22879 | 0.614397 | − | 0.788997i | \(-0.289400\pi\) | ||||
0.614397 | + | 0.788997i | \(0.289400\pi\) | |||||||
\(542\) | 95.9122 | − | 95.9122i | 0.176960 | − | 0.176960i | ||||
\(543\) | 680.952 | + | 64.4816i | 1.25405 | + | 0.118751i | ||||
\(544\) | 130.555 | 0.239992 | ||||||||
\(545\) | 2.67852 | + | 2.33249i | 0.00491471 | + | 0.00427980i | ||||
\(546\) | −97.3771 | − | 73.6218i | −0.178346 | − | 0.134839i | ||||
\(547\) | 367.452 | − | 367.452i | 0.671758 | − | 0.671758i | −0.286363 | − | 0.958121i | \(-0.592446\pi\) |
0.958121 | + | 0.286363i | \(0.0924464\pi\) | |||||||
\(548\) | −86.4327 | + | 86.4327i | −0.157724 | + | 0.157724i | ||||
\(549\) | −76.2110 | + | 398.801i | −0.138818 | + | 0.726414i | ||||
\(550\) | 551.506 | + | 417.094i | 1.00274 | + | 0.758353i | ||||
\(551\) | 271.430 | 0.492613 | ||||||||
\(552\) | −80.5135 | − | 7.62409i | −0.145858 | − | 0.0138118i | ||||
\(553\) | 247.012 | + | 152.448i | 0.446676 | + | 0.275675i | ||||
\(554\) | −211.024 | −0.380910 | ||||||||
\(555\) | 533.807 | + | 13.5977i | 0.961815 | + | 0.0245003i | ||||
\(556\) | − | 32.8272i | − | 0.0590417i | ||||||
\(557\) | 83.3059 | + | 83.3059i | 0.149562 | + | 0.149562i | 0.777922 | − | 0.628361i | \(-0.216274\pi\) |
−0.628361 | + | 0.777922i | \(0.716274\pi\) | |||||||
\(558\) | −415.392 | + | 282.101i | −0.744430 | + | 0.505557i | ||||
\(559\) | −61.0936 | −0.109291 | ||||||||
\(560\) | 41.5592 | + | 133.689i | 0.0742128 | + | 0.238731i | ||||
\(561\) | 1043.51 | − | 862.979i | 1.86009 | − | 1.53829i | ||||
\(562\) | −237.031 | + | 237.031i | −0.421762 | + | 0.421762i | ||||
\(563\) | −52.8031 | − | 52.8031i | −0.0937889 | − | 0.0937889i | 0.658656 | − | 0.752445i | \(-0.271125\pi\) |
−0.752445 | + | 0.658656i | \(0.771125\pi\) | |||||||
\(564\) | 191.074 | − | 158.017i | 0.338784 | − | 0.280173i | ||||
\(565\) | −29.0336 | − | 420.448i | −0.0513868 | − | 0.744157i | ||||
\(566\) | −573.529 | −1.01330 | ||||||||
\(567\) | −454.721 | + | 338.701i | −0.801976 | + | 0.597356i | ||||
\(568\) | −94.6051 | − | 94.6051i | −0.166558 | − | 0.166558i | ||||
\(569\) | 354.050 | 0.622233 | 0.311116 | − | 0.950372i | \(-0.399297\pi\) | ||||
0.311116 | + | 0.950372i | \(0.399297\pi\) | |||||||
\(570\) | 4.67854 | − | 183.667i | 0.00820797 | − | 0.322222i | ||||
\(571\) | 490.557 | 0.859119 | 0.429559 | − | 0.903039i | \(-0.358669\pi\) | ||||
0.429559 | + | 0.903039i | \(0.358669\pi\) | |||||||
\(572\) | −113.691 | + | 113.691i | −0.198761 | + | 0.198761i | ||||
\(573\) | 72.7090 | + | 6.88506i | 0.126892 | + | 0.0120158i | ||||
\(574\) | −567.733 | + | 134.399i | −0.989083 | + | 0.234144i | ||||
\(575\) | 190.047 | + | 143.729i | 0.330516 | + | 0.249963i | ||||
\(576\) | −13.5147 | + | 70.7203i | −0.0234629 | + | 0.122778i | ||||
\(577\) | 677.908 | + | 677.908i | 1.17488 | + | 1.17488i | 0.981031 | + | 0.193852i | \(0.0620983\pi\) |
0.193852 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(578\) | −243.648 | + | 243.648i | −0.421536 | + | 0.421536i | ||||
\(579\) | 389.643 | − | 322.233i | 0.672959 | − | 0.556534i | ||||
\(580\) | 236.344 | + | 205.811i | 0.407489 | + | 0.354847i | ||||
\(581\) | −432.794 | + | 102.455i | −0.744912 | + | 0.176342i | ||||
\(582\) | −12.0257 | − | 1.13875i | −0.0206627 | − | 0.00195662i | ||||
\(583\) | 202.528 | + | 202.528i | 0.347390 | + | 0.347390i | ||||
\(584\) | 357.425i | 0.612029i | ||||||||
\(585\) | −22.1213 | + | 183.645i | −0.0378142 | + | 0.313923i | ||||
\(586\) | 706.692i | 1.20596i | ||||||||
\(587\) | −130.869 | + | 130.869i | −0.222946 | + | 0.222946i | −0.809738 | − | 0.586792i | \(-0.800391\pi\) |
0.586792 | + | 0.809738i | \(0.300391\pi\) | |||||||
\(588\) | 106.448 | + | 274.052i | 0.181034 | + | 0.466076i | ||||
\(589\) | − | 341.681i | − | 0.580104i | ||||||
\(590\) | 20.7319 | + | 300.228i | 0.0351388 | + | 0.508862i | ||||
\(591\) | −78.4668 | + | 64.8917i | −0.132770 | + | 0.109800i | ||||
\(592\) | 100.688 | − | 100.688i | 0.170082 | − | 0.170082i | ||||
\(593\) | 35.4197 | + | 35.4197i | 0.0597296 | + | 0.0597296i | 0.736341 | − | 0.676611i | \(-0.236552\pi\) |
−0.676611 | + | 0.736341i | \(0.736552\pi\) | |||||||
\(594\) | 359.444 | + | 654.589i | 0.605125 | + | 1.10200i | ||||
\(595\) | −714.989 | − | 375.878i | −1.20166 | − | 0.631728i | ||||
\(596\) | − | 127.642i | − | 0.214165i | ||||||
\(597\) | −41.5182 | + | 438.449i | −0.0695448 | + | 0.734421i | ||||
\(598\) | −39.1774 | + | 39.1774i | −0.0655141 | + | 0.0655141i | ||||
\(599\) | −442.029 | −0.737946 | −0.368973 | − | 0.929440i | \(-0.620290\pi\) | ||||
−0.368973 | + | 0.929440i | \(0.620290\pi\) | |||||||
\(600\) | 143.339 | − | 156.378i | 0.238898 | − | 0.260630i | ||||
\(601\) | − | 468.548i | − | 0.779614i | −0.920897 | − | 0.389807i | \(-0.872542\pi\) | ||
0.920897 | − | 0.389807i | \(-0.127458\pi\) | |||||||
\(602\) | 125.208 | + | 77.2747i | 0.207987 | + | 0.128363i | ||||
\(603\) | −940.861 | + | 638.957i | −1.56030 | + | 1.05963i | ||||
\(604\) | 200.449i | 0.331869i | ||||||||
\(605\) | 858.659 | − | 986.042i | 1.41927 | − | 1.62982i | ||||
\(606\) | −498.798 | + | 412.504i | −0.823099 | + | 0.680699i | ||||
\(607\) | −622.632 | − | 622.632i | −1.02575 | − | 1.02575i | −0.999660 | − | 0.0260927i | \(-0.991694\pi\) |
−0.0260927 | − | 0.999660i | \(-0.508306\pi\) | |||||||
\(608\) | −34.6437 | − | 34.6437i | −0.0569798 | − | 0.0569798i | ||||
\(609\) | 524.976 | + | 396.908i | 0.862030 | + | 0.651737i | ||||
\(610\) | −21.9757 | − | 318.240i | −0.0360257 | − | 0.521705i | ||||
\(611\) | − | 169.866i | − | 0.278013i | ||||||
\(612\) | −233.391 | − | 343.667i | −0.381357 | − | 0.561547i | ||||
\(613\) | 140.330 | + | 140.330i | 0.228923 | + | 0.228923i | 0.812243 | − | 0.583319i | \(-0.198246\pi\) |
−0.583319 | + | 0.812243i | \(0.698246\pi\) | |||||||
\(614\) | − | 537.990i | − | 0.876204i | ||||||
\(615\) | 608.977 | + | 640.813i | 0.990207 | + | 1.04197i | ||||
\(616\) | 376.807 | − | 89.2009i | 0.611700 | − | 0.144807i | ||||
\(617\) | −354.668 | − | 354.668i | −0.574826 | − | 0.574826i | 0.358647 | − | 0.933473i | \(-0.383238\pi\) |
−0.933473 | + | 0.358647i | \(0.883238\pi\) | |||||||
\(618\) | −33.0596 | + | 349.122i | −0.0534944 | + | 0.564923i | ||||
\(619\) | −802.714 | −1.29679 | −0.648396 | − | 0.761304i | \(-0.724560\pi\) | ||||
−0.648396 | + | 0.761304i | \(0.724560\pi\) | |||||||
\(620\) | 259.079 | − | 297.514i | 0.417870 | − | 0.479862i | ||||
\(621\) | 123.863 | + | 225.568i | 0.199457 | + | 0.363234i | ||||
\(622\) | −93.5888 | − | 93.5888i | −0.150464 | − | 0.150464i | ||||
\(623\) | 28.6184 | + | 17.6624i | 0.0459365 | + | 0.0283506i | ||||
\(624\) | 31.4354 | + | 38.0115i | 0.0503772 | + | 0.0609159i | ||||
\(625\) | −601.384 | + | 170.184i | −0.962214 | + | 0.272295i | ||||
\(626\) | 130.139 | 0.207890 | ||||||||
\(627\) | −505.899 | − | 47.9053i | −0.806857 | − | 0.0764040i | ||||
\(628\) | −315.064 | + | 315.064i | −0.501694 | + | 0.501694i | ||||
\(629\) | 821.588i | 1.30618i | ||||||||
\(630\) | 277.622 | − | 348.391i | 0.440669 | − | 0.553001i | ||||
\(631\) | −1193.86 | −1.89202 | −0.946010 | − | 0.324137i | \(-0.894926\pi\) | ||||
−0.946010 | + | 0.324137i | \(0.894926\pi\) | |||||||
\(632\) | −82.9336 | − | 82.9336i | −0.131224 | − | 0.131224i | ||||
\(633\) | −34.8391 | + | 367.915i | −0.0550381 | + | 0.581225i | ||||
\(634\) | − | 366.220i | − | 0.577633i | ||||||
\(635\) | −56.6806 | − | 820.818i | −0.0892607 | − | 1.29263i | ||||
\(636\) | 67.7133 | − | 55.9986i | 0.106467 | − | 0.0880482i | ||||
\(637\) | 191.158 | + | 63.4539i | 0.300091 | + | 0.0996136i | ||||
\(638\) | 612.928 | − | 612.928i | 0.960702 | − | 0.960702i | ||||
\(639\) | −79.9097 | + | 418.156i | −0.125054 | + | 0.654391i | ||||
\(640\) | −3.89699 | − | 56.4342i | −0.00608905 | − | 0.0881784i | ||||
\(641\) | − | 542.970i | − | 0.847067i | −0.905881 | − | 0.423533i | \(-0.860790\pi\) | ||
0.905881 | − | 0.423533i | \(-0.139210\pi\) | |||||||
\(642\) | −191.092 | − | 18.0951i | −0.297651 | − | 0.0281855i | ||||
\(643\) | 487.269 | − | 487.269i | 0.757806 | − | 0.757806i | −0.218117 | − | 0.975923i | \(-0.569991\pi\) |
0.975923 | + | 0.218117i | \(0.0699913\pi\) | |||||||
\(644\) | 129.846 | − | 30.7382i | 0.201624 | − | 0.0477302i | ||||
\(645\) | 5.67716 | − | 222.870i | 0.00880180 | − | 0.345534i | ||||
\(646\) | 282.683 | 0.437590 | ||||||||
\(647\) | −431.186 | + | 431.186i | −0.666439 | + | 0.666439i | −0.956890 | − | 0.290451i | \(-0.906195\pi\) |
0.290451 | + | 0.956890i | \(0.406195\pi\) | |||||||
\(648\) | 210.320 | − | 90.8496i | 0.324567 | − | 0.140200i | ||||
\(649\) | 832.370 | 1.28254 | ||||||||
\(650\) | −19.9757 | − | 143.949i | −0.0307318 | − | 0.221460i | ||||
\(651\) | 499.635 | − | 660.850i | 0.767488 | − | 1.01513i | ||||
\(652\) | −261.601 | + | 261.601i | −0.401229 | + | 0.401229i | ||||
\(653\) | 698.488 | − | 698.488i | 1.06966 | − | 1.06966i | 0.0722752 | − | 0.997385i | \(-0.476974\pi\) |
0.997385 | − | 0.0722752i | \(-0.0230260\pi\) | |||||||
\(654\) | −1.92067 | − | 2.32246i | −0.00293680 | − | 0.00355116i | ||||
\(655\) | 223.238 | − | 256.355i | 0.340821 | − | 0.391382i | ||||
\(656\) | 235.739 | 0.359358 | ||||||||
\(657\) | 940.864 | − | 638.959i | 1.43206 | − | 0.972541i | ||||
\(658\) | −214.856 | + | 348.132i | −0.326530 | + | 0.529075i | ||||
\(659\) | −433.424 | −0.657699 | −0.328850 | − | 0.944382i | \(-0.606661\pi\) | ||||
−0.328850 | + | 0.944382i | \(0.606661\pi\) | |||||||
\(660\) | −404.181 | − | 425.311i | −0.612395 | − | 0.644410i | ||||
\(661\) | − | 797.271i | − | 1.20616i | −0.797681 | − | 0.603079i | \(-0.793940\pi\) | ||
0.797681 | − | 0.603079i | \(-0.206060\pi\) | |||||||
\(662\) | 389.930 | + | 389.930i | 0.589018 | + | 0.589018i | ||||
\(663\) | −283.334 | − | 26.8298i | −0.427351 | − | 0.0404673i | ||||
\(664\) | 179.708 | 0.270645 | ||||||||
\(665\) | 89.9853 | + | 289.469i | 0.135316 | + | 0.435291i | ||||
\(666\) | −445.044 | − | 85.0480i | −0.668234 | − | 0.127700i | ||||
\(667\) | 211.212 | − | 211.212i | 0.316660 | − | 0.316660i | ||||
\(668\) | 70.1684 | + | 70.1684i | 0.105043 | + | 0.105043i | ||||
\(669\) | −238.992 | − | 288.988i | −0.357238 | − | 0.431971i | ||||
\(670\) | 586.813 | − | 673.868i | 0.875841 | − | 1.00577i | ||||
\(671\) | −882.305 | −1.31491 | ||||||||
\(672\) | −16.3460 | − | 117.664i | −0.0243244 | − | 0.175095i | ||||
\(673\) | 369.528 | + | 369.528i | 0.549076 | + | 0.549076i | 0.926174 | − | 0.377098i | \(-0.123078\pi\) |
−0.377098 | + | 0.926174i | \(0.623078\pi\) | |||||||
\(674\) | −402.622 | −0.597362 | ||||||||
\(675\) | −667.883 | − | 97.7640i | −0.989456 | − | 0.144836i | ||||
\(676\) | −304.208 | −0.450011 | ||||||||
\(677\) | −238.013 | + | 238.013i | −0.351570 | + | 0.351570i | −0.860694 | − | 0.509123i | \(-0.829970\pi\) |
0.509123 | + | 0.860694i | \(0.329970\pi\) | |||||||
\(678\) | −33.7127 | + | 356.019i | −0.0497237 | + | 0.525102i | ||||
\(679\) | 19.3941 | − | 4.59113i | 0.0285627 | − | 0.00676161i | ||||
\(680\) | 246.143 | + | 214.344i | 0.361974 | + | 0.315212i | ||||
\(681\) | 53.9536 | + | 65.2405i | 0.0792270 | + | 0.0958010i | ||||
\(682\) | −771.565 | − | 771.565i | −1.13133 | − | 1.13133i | ||||
\(683\) | −399.484 | + | 399.484i | −0.584896 | + | 0.584896i | −0.936245 | − | 0.351349i | \(-0.885723\pi\) |
0.351349 | + | 0.936245i | \(0.385723\pi\) | |||||||
\(684\) | −29.2624 | + | 153.126i | −0.0427813 | + | 0.223868i | ||||
\(685\) | −304.860 | + | 21.0517i | −0.445051 | + | 0.0307324i | ||||
\(686\) | −311.509 | − | 371.834i | −0.454095 | − | 0.542032i | ||||
\(687\) | −82.5544 | + | 871.808i | −0.120167 | + | 1.26901i | ||||
\(688\) | −42.0383 | − | 42.0383i | −0.0611022 | − | 0.0611022i | ||||
\(689\) | − | 60.1976i | − | 0.0873695i | ||||||
\(690\) | −139.279 | − | 146.560i | −0.201853 | − | 0.212406i | ||||
\(691\) | − | 964.818i | − | 1.39626i | −0.715969 | − | 0.698132i | \(-0.754015\pi\) | ||
0.715969 | − | 0.698132i | \(-0.245985\pi\) | |||||||
\(692\) | 449.472 | − | 449.472i | 0.649526 | − | 0.649526i | ||||
\(693\) | −908.416 | − | 832.423i | −1.31085 | − | 1.20119i | ||||
\(694\) | 746.147i | 1.07514i | ||||||||
\(695\) | 53.8952 | − | 61.8907i | 0.0775471 | − | 0.0890513i | ||||
\(696\) | −169.473 | − | 204.927i | −0.243496 | − | 0.294435i | ||||
\(697\) | −961.782 | + | 961.782i | −1.37989 | + | 1.37989i | ||||
\(698\) | 413.538 | + | 413.538i | 0.592461 | + | 0.592461i | ||||
\(699\) | −713.594 | − | 862.875i | −1.02088 | − | 1.23444i | ||||
\(700\) | −141.136 | + | 320.282i | −0.201623 | + | 0.457546i | ||||
\(701\) | 256.614i | 0.366069i | 0.983106 | + | 0.183035i | \(0.0585920\pi\) | ||||
−0.983106 | + | 0.183035i | \(0.941408\pi\) | |||||||
\(702\) | 43.8631 | − | 150.701i | 0.0624830 | − | 0.214674i | ||||
\(703\) | 218.014 | − | 218.014i | 0.310119 | − | 0.310119i | ||||
\(704\) | −156.461 | −0.222246 | ||||||||
\(705\) | 619.672 | + | 15.7849i | 0.878967 | + | 0.0223899i | ||||
\(706\) | − | 15.0443i | − | 0.0213092i | ||||||
\(707\) | 560.882 | − | 908.796i | 0.793326 | − | 1.28543i | ||||
\(708\) | 24.0731 | − | 254.222i | 0.0340016 | − | 0.359070i | ||||
\(709\) | − | 271.653i | − | 0.383149i | −0.981478 | − | 0.191575i | \(-0.938641\pi\) | ||
0.981478 | − | 0.191575i | \(-0.0613594\pi\) | |||||||
\(710\) | −23.0422 | − | 333.685i | −0.0324538 | − | 0.469979i | ||||
\(711\) | −70.0512 | + | 366.568i | −0.0985249 | + | 0.515566i | ||||
\(712\) | −9.60857 | − | 9.60857i | −0.0134952 | − | 0.0134952i | ||||
\(713\) | −265.878 | − | 265.878i | −0.372900 | − | 0.372900i | ||||
\(714\) | 546.742 | + | 413.363i | 0.765745 | + | 0.578940i | ||||
\(715\) | −401.004 | + | 27.6908i | −0.560845 | + | 0.0387284i | ||||
\(716\) | 418.272i | 0.584179i | ||||||||
\(717\) | −115.209 | + | 1216.65i | −0.160682 | + | 1.69686i | ||||
\(718\) | −166.966 | − | 166.966i | −0.232543 | − | 0.232543i | ||||
\(719\) | 648.915i | 0.902524i | 0.892391 | + | 0.451262i | \(0.149026\pi\) | ||||
−0.892391 | + | 0.451262i | \(0.850974\pi\) | |||||||
\(720\) | −141.587 | + | 111.144i | −0.196649 | + | 0.154367i | ||||
\(721\) | −133.287 | − | 563.038i | −0.184864 | − | 0.780912i | ||||
\(722\) | 285.988 | + | 285.988i | 0.396105 | + | 0.396105i | ||||
\(723\) | −929.198 | − | 87.9889i | −1.28520 | − | 0.121700i | ||||
\(724\) | 455.999 | 0.629832 | ||||||||
\(725\) | 107.692 | + | 776.052i | 0.148541 | + | 1.07042i | ||||
\(726\) | −854.967 | + | 707.054i | −1.17764 | + | 0.973903i | ||||
\(727\) | 165.102 | + | 165.102i | 0.227100 | + | 0.227100i | 0.811480 | − | 0.584380i | \(-0.198662\pi\) |
−0.584380 | + | 0.811480i | \(0.698662\pi\) | |||||||
\(728\) | −69.2560 | − | 42.7427i | −0.0951318 | − | 0.0587125i | ||||
\(729\) | −615.130 | − | 391.223i | −0.843800 | − | 0.536658i | ||||
\(730\) | −586.815 | + | 673.870i | −0.803856 | + | 0.923110i | ||||
\(731\) | 343.021 | 0.469249 | ||||||||
\(732\) | −25.5173 | + | 269.473i | −0.0348597 | + | 0.368133i | ||||
\(733\) | −927.909 | + | 927.909i | −1.26591 | + | 1.26591i | −0.317721 | + | 0.948184i | \(0.602918\pi\) |
−0.948184 | + | 0.317721i | \(0.897082\pi\) | |||||||
\(734\) | 432.800i | 0.589646i | ||||||||
\(735\) | −249.244 | + | 691.450i | −0.339107 | + | 0.940748i | ||||
\(736\) | −53.9158 | −0.0732551 | ||||||||
\(737\) | −1747.59 | − | 1747.59i | −2.37122 | − | 2.37122i | ||||
\(738\) | −421.425 | − | 620.546i | −0.571036 | − | 0.840848i | ||||
\(739\) | − | 960.261i | − | 1.29941i | −0.760188 | − | 0.649703i | \(-0.774893\pi\) | ||
0.760188 | − | 0.649703i | \(-0.225107\pi\) | |||||||
\(740\) | 355.141 | − | 24.5238i | 0.479921 | − | 0.0331403i | ||||
\(741\) | 68.0649 | + | 82.3039i | 0.0918555 | + | 0.111071i | ||||
\(742\) | −76.1414 | + | 123.372i | −0.102616 | + | 0.166269i | ||||
\(743\) | 197.378 | − | 197.378i | 0.265650 | − | 0.265650i | −0.561695 | − | 0.827345i | \(-0.689850\pi\) |
0.827345 | + | 0.561695i | \(0.189850\pi\) | |||||||
\(744\) | −257.965 | + | 213.336i | −0.346728 | + | 0.286742i | ||||
\(745\) | 209.561 | − | 240.650i | 0.281290 | − | 0.323020i | ||||
\(746\) | 129.751i | 0.173928i | ||||||||
\(747\) | −321.260 | − | 473.054i | −0.430067 | − | 0.633271i | ||||
\(748\) | 638.339 | − | 638.339i | 0.853395 | − | 0.853395i | ||||
\(749\) | 308.178 | − | 72.9545i | 0.411453 | − | 0.0974026i | ||||
\(750\) | 526.982 | − | 59.4948i | 0.702643 | − | 0.0793264i | ||||
\(751\) | 1038.60 | 1.38295 | 0.691477 | − | 0.722398i | \(-0.256960\pi\) | ||||
0.691477 | + | 0.722398i | \(0.256960\pi\) | |||||||
\(752\) | 116.884 | − | 116.884i | 0.155431 | − | 0.155431i | ||||
\(753\) | −25.7823 | + | 272.271i | −0.0342394 | + | 0.361582i | ||||
\(754\) | −182.181 | −0.241619 | ||||||||
\(755\) | −329.095 | + | 377.916i | −0.435887 | + | 0.500552i | ||||
\(756\) | −280.510 | + | 253.373i | −0.371046 | + | 0.335150i | ||||
\(757\) | 230.964 | − | 230.964i | 0.305105 | − | 0.305105i | −0.537902 | − | 0.843007i | \(-0.680783\pi\) |
0.843007 | + | 0.537902i | \(0.180783\pi\) | |||||||
\(758\) | 44.8235 | − | 44.8235i | 0.0591339 | − | 0.0591339i | ||||
\(759\) | −430.941 | + | 356.386i | −0.567775 | + | 0.469547i | ||||
\(760\) | −8.43790 | − | 122.193i | −0.0111025 | − | 0.160780i | ||||
\(761\) | −34.8617 | −0.0458103 | −0.0229052 | − | 0.999738i | \(-0.507292\pi\) | ||||
−0.0229052 | + | 0.999738i | \(0.507292\pi\) | |||||||
\(762\) | −65.8153 | + | 695.036i | −0.0863718 | + | 0.912121i | ||||
\(763\) | 4.23146 | + | 2.61153i | 0.00554582 | + | 0.00342271i | ||||
\(764\) | 48.6895 | 0.0637298 | ||||||||
\(765\) | 124.204 | − | 1031.11i | 0.162358 | − | 1.34785i | ||||
\(766\) | − | 931.648i | − | 1.21625i | ||||||
\(767\) | −123.703 | − | 123.703i | −0.161281 | − | 0.161281i | ||||
\(768\) | −4.52504 | + | 47.7862i | −0.00589198 | + | 0.0622217i | ||||
\(769\) | −378.987 | −0.492830 | −0.246415 | − | 0.969164i | \(-0.579253\pi\) | ||||
−0.246415 | + | 0.969164i | \(0.579253\pi\) | |||||||
\(770\) | 856.862 | + | 450.462i | 1.11281 | + | 0.585016i | ||||
\(771\) | −599.369 | − | 724.755i | −0.777392 | − | 0.940019i | ||||
\(772\) | 238.354 | − | 238.354i | 0.308748 | − | 0.308748i | ||||
\(773\) | 579.682 | + | 579.682i | 0.749912 | + | 0.749912i | 0.974462 | − | 0.224551i | \(-0.0720915\pi\) |
−0.224551 | + | 0.974462i | \(0.572091\pi\) | |||||||
\(774\) | −35.5084 | + | 185.810i | −0.0458764 | + | 0.240065i | ||||
\(775\) | 976.909 | − | 135.565i | 1.26053 | − | 0.174923i | ||||
\(776\) | −8.05298 | −0.0103776 | ||||||||
\(777\) | 740.462 | − | 102.866i | 0.952975 | − | 0.132388i | ||||
\(778\) | 341.962 | + | 341.962i | 0.439540 | + | 0.439540i | ||||
\(779\) | 510.430 | 0.655238 | ||||||||
\(780\) | −3.14019 | + | 123.275i | −0.00402588 | + | 0.158045i | ||||
\(781\) | −925.126 | −1.18454 | ||||||||
\(782\) | 219.969 | − | 219.969i | 0.281290 | − | 0.281290i | ||||
\(783\) | −236.473 | + | 812.454i | −0.302009 | + | 1.03762i | ||||
\(784\) | 87.8731 | + | 175.198i | 0.112083 | + | 0.223467i | ||||
\(785\) | −1111.27 | + | 76.7376i | −1.41563 | + | 0.0977549i | ||||
\(786\) | −222.278 | + | 183.823i | −0.282796 | + | 0.233871i | ||||
\(787\) | 755.283 | + | 755.283i | 0.959699 | + | 0.959699i | 0.999219 | − | 0.0395194i | \(-0.0125827\pi\) |
−0.0395194 | + | 0.999219i | \(0.512583\pi\) | |||||||
\(788\) | −48.0000 | + | 48.0000i | −0.0609136 | + | 0.0609136i | ||||
\(789\) | −698.024 | − | 844.047i | −0.884694 | − | 1.06977i | ||||
\(790\) | −20.1995 | − | 292.518i | −0.0255689 | − | 0.370276i | ||||
\(791\) | −135.920 | − | 574.161i | −0.171833 | − | 0.725867i | ||||
\(792\) | 279.702 | + | 411.859i | 0.353159 | + | 0.520024i | ||||
\(793\) | 131.124 | + | 131.124i | 0.165352 | + | 0.165352i | ||||
\(794\) | 428.402i | 0.539549i | ||||||||
\(795\) | 219.601 | + | 5.59390i | 0.276228 | + | 0.00703635i | ||||
\(796\) | 293.607i | 0.368853i | ||||||||
\(797\) | −420.714 | + | 420.714i | −0.527872 | + | 0.527872i | −0.919937 | − | 0.392066i | \(-0.871761\pi\) |
0.392066 | + | 0.919937i | \(0.371761\pi\) | |||||||
\(798\) | −35.3929 | − | 254.770i | −0.0443520 | − | 0.319261i | ||||
\(799\) | 953.743i | 1.19367i | ||||||||
\(800\) | 85.3056 | − | 112.796i | 0.106632 | − | 0.140995i | ||||
\(801\) | −8.11603 | + | 42.4700i | −0.0101324 | + | 0.0530213i | ||||
\(802\) | −278.216 | + | 278.216i | −0.346903 | + | 0.346903i | ||||
\(803\) | 1747.60 | + | 1747.60i | 2.17633 | + | 2.17633i | ||||
\(804\) | −584.290 | + | 483.206i | −0.726729 | + | 0.601002i | ||||
\(805\) | 295.271 | + | 155.227i | 0.366796 | + | 0.192829i | ||||
\(806\) | 229.333i | 0.284532i | ||||||||
\(807\) | 412.368 | + | 39.0485i | 0.510989 | + | 0.0483872i | ||||
\(808\) | −305.126 | + | 305.126i | −0.377631 | + | 0.377631i | ||||
\(809\) | 563.269 | 0.696253 | 0.348127 | − | 0.937448i | \(-0.386818\pi\) | ||||
0.348127 | + | 0.937448i | \(0.386818\pi\) | |||||||
\(810\) | 545.681 | + | 174.017i | 0.673681 | + | 0.214835i | ||||
\(811\) | − | 1284.84i | − | 1.58427i | −0.610346 | − | 0.792135i | \(-0.708970\pi\) | ||
0.610346 | − | 0.792135i | \(-0.291030\pi\) | |||||||
\(812\) | 373.370 | + | 230.433i | 0.459816 | + | 0.283785i | ||||
\(813\) | −286.455 | − | 27.1254i | −0.352343 | − | 0.0333646i | ||||
\(814\) | − | 984.613i | − | 1.20960i | ||||||
\(815\) | −922.702 | + | 63.7161i | −1.13215 | + | 0.0781792i | ||||
\(816\) | −176.500 | − | 213.423i | −0.216298 | − | 0.261547i | ||||
\(817\) | −91.0228 | − | 91.0228i | −0.111411 | − | 0.111411i | ||||
\(818\) | −481.543 | − | 481.543i | −0.588684 | − | 0.588684i | ||||
\(819\) | 11.2937 | + | 258.715i | 0.0137897 | + | 0.315892i | ||||
\(820\) | 444.450 | + | 387.033i | 0.542013 | + | 0.471992i | ||||
\(821\) | 611.792i | 0.745179i | 0.927996 | + | 0.372589i | \(0.121530\pi\) | ||||
−0.927996 | + | 0.372589i | \(0.878470\pi\) | |||||||
\(822\) | 258.143 | + | 24.4444i | 0.314043 | + | 0.0297378i | ||||
\(823\) | −49.6982 | − | 49.6982i | −0.0603866 | − | 0.0603866i | 0.676269 | − | 0.736655i | \(-0.263596\pi\) |
−0.736655 | + | 0.676269i | \(0.763596\pi\) | |||||||
\(824\) | 233.789i | 0.283725i | ||||||||
\(825\) | −63.7527 | − | 1465.44i | −0.0772761 | − | 1.77629i | ||||
\(826\) | 97.0561 | + | 409.989i | 0.117501 | + | 0.496355i | ||||
\(827\) | −312.887 | − | 312.887i | −0.378340 | − | 0.378340i | 0.492163 | − | 0.870503i | \(-0.336206\pi\) |
−0.870503 | + | 0.492163i | \(0.836206\pi\) | |||||||
\(828\) | 96.3839 | + | 141.925i | 0.116406 | + | 0.171407i | ||||
\(829\) | −1348.53 | −1.62670 | −0.813348 | − | 0.581778i | \(-0.802357\pi\) | ||||
−0.813348 | + | 0.581778i | \(0.802357\pi\) | |||||||
\(830\) | 338.813 | + | 295.043i | 0.408208 | + | 0.355473i | ||||
\(831\) | 285.286 | + | 344.967i | 0.343305 | + | 0.415123i | ||||
\(832\) | 23.2525 | + | 23.2525i | 0.0279477 | + | 0.0279477i | ||||
\(833\) | −1073.29 | − | 356.273i | −1.28847 | − | 0.427699i | ||||
\(834\) | −53.6635 | + | 44.3795i | −0.0643447 | + | 0.0532128i | ||||
\(835\) | 17.0904 | + | 247.493i | 0.0204675 | + | 0.296399i | ||||
\(836\) | −338.775 | −0.405233 | ||||||||
\(837\) | 1022.73 | + | 297.677i | 1.22190 | + | 0.355647i | ||||
\(838\) | 12.3613 | − | 12.3613i | 0.0147510 | − | 0.0147510i | ||||
\(839\) | − | 297.070i | − | 0.354076i | −0.984204 | − | 0.177038i | \(-0.943348\pi\) | ||
0.984204 | − | 0.177038i | \(-0.0566515\pi\) | |||||||
\(840\) | 162.361 | − | 248.674i | 0.193287 | − | 0.296041i | ||||
\(841\) | 141.168 | 0.167857 | ||||||||
\(842\) | −10.9249 | − | 10.9249i | −0.0129749 | − | 0.0129749i | ||||
\(843\) | 707.925 | + | 67.0358i | 0.839768 | + | 0.0795205i | ||||
\(844\) | 246.374i | 0.291912i | ||||||||
\(845\) | −573.537 | − | 499.444i | −0.678742 | − | 0.591058i | ||||
\(846\) | −516.631 | − | 98.7282i | −0.610674 | − | 0.116700i | ||||
\(847\) | 961.382 | − | 1557.73i | 1.13504 | − | 1.83911i | ||||
\(848\) | 41.4218 | − | 41.4218i | 0.0488465 | − | 0.0488465i | ||||
\(849\) | 775.361 | + | 937.564i | 0.913264 | + | 1.10432i | ||||
\(850\) | 112.157 | + | 808.227i | 0.131949 | + | 0.950855i | ||||
\(851\) | − | 339.293i | − | 0.398699i | ||||||
\(852\) | −26.7557 | + | 282.551i | −0.0314034 | + | 0.331633i | ||||
\(853\) | 153.624 | − | 153.624i | 0.180098 | − | 0.180098i | −0.611301 | − | 0.791399i | \(-0.709353\pi\) |
0.791399 | + | 0.611301i | \(0.209353\pi\) | |||||||
\(854\) | −102.879 | − | 434.586i | −0.120467 | − | 0.508882i | ||||
\(855\) | −306.570 | + | 240.653i | −0.358561 | + | 0.281466i | ||||
\(856\) | −127.964 | −0.149491 | ||||||||
\(857\) | −275.201 | + | 275.201i | −0.321121 | + | 0.321121i | −0.849197 | − | 0.528076i | \(-0.822914\pi\) |
0.528076 | + | 0.849197i | \(0.322914\pi\) | |||||||
\(858\) | 339.554 | + | 32.1535i | 0.395751 | + | 0.0374750i | ||||
\(859\) | 1008.84 | 1.17444 | 0.587218 | − | 0.809429i | \(-0.300223\pi\) | ||||
0.587218 | + | 0.809429i | \(0.300223\pi\) | |||||||
\(860\) | −10.2389 | − | 148.275i | −0.0119057 | − | 0.172413i | ||||
\(861\) | 987.231 | + | 746.394i | 1.14661 | + | 0.866892i | ||||
\(862\) | 7.70570 | − | 7.70570i | 0.00893932 | − | 0.00893932i | ||||
\(863\) | −255.798 | + | 255.798i | −0.296405 | + | 0.296405i | −0.839604 | − | 0.543199i | \(-0.817213\pi\) |
0.543199 | + | 0.839604i | \(0.317213\pi\) | |||||||
\(864\) | 133.879 | − | 73.5148i | 0.154952 | − | 0.0850866i | ||||
\(865\) | 1585.35 | − | 109.474i | 1.83277 | − | 0.126560i | ||||
\(866\) | 33.3857 | 0.0385516 | ||||||||
\(867\) | 727.688 | + | 68.9072i | 0.839317 | + | 0.0794778i | ||||
\(868\) | 290.073 | − | 470.006i | 0.334186 | − | 0.541481i | ||||
\(869\) | −810.993 | −0.933248 | ||||||||
\(870\) | 16.9293 | − | 664.597i | 0.0194589 | − | 0.763904i | ||||
\(871\) | 519.438i | 0.596369i | ||||||||
\(872\) | −1.42070 | − | 1.42070i | −0.00162925 | − | 0.00162925i | ||||
\(873\) | 14.3961 | + | 21.1982i | 0.0164904 | + | 0.0242820i | ||||
\(874\) | −116.740 | −0.133570 | ||||||||
\(875\) | −791.925 | + | 372.129i | −0.905057 | + | 0.425290i | ||||
\(876\) | 584.292 | − | 483.207i | 0.667000 | − | 0.551606i | ||||
\(877\) | −100.445 | + | 100.445i | −0.114532 | + | 0.114532i | −0.762050 | − | 0.647518i | \(-0.775807\pi\) |
0.647518 | + | 0.762050i | \(0.275807\pi\) | |||||||
\(878\) | 717.592 | + | 717.592i | 0.817303 | + | 0.817303i | ||||
\(879\) | 1155.25 | − | 955.386i | 1.31428 | − | 1.08690i | ||||
\(880\) | −294.984 | − | 256.876i | −0.335209 | − | 0.291904i | ||||
\(881\) | −1255.66 | −1.42526 | −0.712631 | − | 0.701539i | \(-0.752497\pi\) | ||||
−0.712631 | + | 0.701539i | \(0.752497\pi\) | |||||||
\(882\) | 304.092 | − | 544.509i | 0.344776 | − | 0.617357i | ||||
\(883\) | −230.612 | − | 230.612i | −0.261169 | − | 0.261169i | 0.564360 | − | 0.825529i | \(-0.309123\pi\) |
−0.825529 | + | 0.564360i | \(0.809123\pi\) | |||||||
\(884\) | −189.734 | −0.214631 | ||||||||
\(885\) | 462.764 | − | 439.774i | 0.522897 | − | 0.496919i | ||||
\(886\) | 326.079 | 0.368035 | ||||||||
\(887\) | 261.714 | − | 261.714i | 0.295055 | − | 0.295055i | −0.544018 | − | 0.839073i | \(-0.683098\pi\) |
0.839073 | + | 0.544018i | \(0.183098\pi\) | |||||||
\(888\) | −300.720 | − | 28.4762i | −0.338648 | − | 0.0320677i | ||||
\(889\) | −265.349 | − | 1120.90i | −0.298480 | − | 1.26086i | ||||
\(890\) | −2.34028 | − | 33.8907i | −0.00262953 | − | 0.0380795i | ||||
\(891\) | 584.138 | − | 1472.54i | 0.655598 | − | 1.65268i | ||||
\(892\) | −176.781 | − | 176.781i | −0.198185 | − | 0.198185i | ||||
\(893\) | 253.082 | − | 253.082i | 0.283406 | − | 0.283406i | ||||
\(894\) | −208.660 | + | 172.561i | −0.233400 | + | 0.193021i | ||||
\(895\) | −686.713 | + | 788.588i | −0.767277 | + | 0.881104i | ||||
\(896\) | −18.2437 | − | 77.0660i | −0.0203613 | − | 0.0860112i | ||||
\(897\) | 117.009 | + | 11.0800i | 0.130445 | + | 0.0123522i | ||||
\(898\) | −681.871 | − | 681.871i | −0.759322 | − | 0.759322i | ||||
\(899\) | − | 1236.37i | − | 1.37527i | ||||||
\(900\) | −449.416 | − | 22.9108i | −0.499352 | − | 0.0254565i | ||||
\(901\) | 337.990i | 0.375128i | ||||||||
\(902\) | 1152.63 | − | 1152.63i | 1.27786 | − | 1.27786i | ||||
\(903\) | −42.9473 | − | 309.150i | −0.0475607 | − | 0.342359i | ||||
\(904\) | 238.408i | 0.263726i | ||||||||
\(905\) | 859.716 | + | 748.652i | 0.949962 | + | 0.827240i | ||||
\(906\) | 327.680 | − | 270.990i | 0.361677 | − | 0.299106i | ||||
\(907\) | 475.338 | − | 475.338i | 0.524077 | − | 0.524077i | −0.394723 | − | 0.918800i | \(-0.629159\pi\) |
0.918800 | + | 0.394723i | \(0.129159\pi\) | |||||||
\(908\) | 39.9091 | + | 39.9091i | 0.0439528 | + | 0.0439528i | ||||
\(909\) | 1348.66 | + | 257.730i | 1.48368 | + | 0.283531i | ||||
\(910\) | −60.3972 | − | 194.288i | −0.0663706 | − | 0.213504i | ||||
\(911\) | 648.228i | 0.711556i | 0.934570 | + | 0.355778i | \(0.115784\pi\) | ||||
−0.934570 | + | 0.355778i | \(0.884216\pi\) | |||||||
\(912\) | −9.79777 | + | 103.468i | −0.0107432 | + | 0.113452i | ||||
\(913\) | 878.668 | − | 878.668i | 0.962397 | − | 0.962397i | ||||
\(914\) | −403.064 | −0.440990 | ||||||||
\(915\) | −490.526 | + | 466.157i | −0.536094 | + | 0.509461i | ||||
\(916\) | 583.805i | 0.637342i | ||||||||
\(917\) | 249.944 | − | 404.984i | 0.272567 | − | 0.441640i | ||||
\(918\) | −246.277 | + | 846.137i | −0.268276 | + | 0.921718i | ||||
\(919\) | 1609.03i | 1.75085i | 0.483354 | + | 0.875425i | \(0.339418\pi\) | ||||
−0.483354 | + | 0.875425i | \(0.660582\pi\) | |||||||
\(920\) | −101.650 | − | 88.5182i | −0.110489 | − | 0.0962154i | ||||
\(921\) | −879.466 | + | 727.315i | −0.954904 | + | 0.789701i | ||||
\(922\) | −205.599 | − | 205.599i | −0.222993 | − | 0.222993i | ||||
\(923\) | 137.488 | + | 137.488i | 0.148958 | + | 0.148958i | ||||
\(924\) | −655.230 | − | 495.385i | −0.709123 | − | 0.536131i | ||||
\(925\) | 709.828 | + | 536.830i | 0.767381 | + | 0.580357i | ||||
\(926\) | 344.094i | 0.371592i | ||||||||
\(927\) | 615.413 | − | 417.939i | 0.663876 | − | 0.450851i | ||||
\(928\) | −125.358 | − | 125.358i | −0.135084 | − | 0.135084i | ||||
\(929\) | 1737.48i | 1.87027i | 0.354289 | + | 0.935136i | \(0.384723\pi\) | ||||
−0.354289 | + | 0.935136i | \(0.615277\pi\) | |||||||
\(930\) | −836.607 | − | 21.3109i | −0.899577 | − | 0.0229149i | ||||
\(931\) | 190.266 | + | 379.345i | 0.204367 | + | 0.407459i | ||||
\(932\) | −527.840 | − | 527.840i | −0.566352 | − | 0.566352i | ||||
\(933\) | −26.4683 | + | 279.516i | −0.0283690 | + | 0.299588i | ||||
\(934\) | 663.632 | 0.710527 | ||||||||
\(935\) | 2251.51 | − | 155.475i | 2.40803 | − | 0.166284i | ||||
\(936\) | 19.6406 | − | 102.777i | 0.0209836 | − | 0.109804i | ||||
\(937\) | 333.838 | + | 333.838i | 0.356283 | + | 0.356283i | 0.862441 | − | 0.506158i | \(-0.168935\pi\) |
−0.506158 | + | 0.862441i | \(0.668935\pi\) | |||||||
\(938\) | 657.015 | − | 1064.56i | 0.700443 | − | 1.13493i | ||||
\(939\) | −175.937 | − | 212.742i | −0.187366 | − | 0.226563i | ||||
\(940\) | 412.267 | − | 28.4686i | 0.438582 | − | 0.0302857i | ||||
\(941\) | 705.893 | 0.750152 | 0.375076 | − | 0.926994i | \(-0.377617\pi\) | ||||
0.375076 | + | 0.926994i | \(0.377617\pi\) | |||||||
\(942\) | 940.983 | + | 89.1048i | 0.998920 | + | 0.0945911i | ||||
\(943\) | 397.189 | − | 397.189i | 0.421198 | − | 0.421198i | ||||
\(944\) | − | 170.239i | − | 0.180338i | ||||||
\(945\) | −944.844 | + | 17.1584i | −0.999835 | + | 0.0181570i | ||||
\(946\) | −411.085 | −0.434551 | ||||||||
\(947\) | 226.136 | + | 226.136i | 0.238792 | + | 0.238792i | 0.816350 | − | 0.577558i | \(-0.195994\pi\) |
−0.577558 | + | 0.816350i | \(0.695994\pi\) | |||||||
\(948\) | −23.4549 | + | 247.693i | −0.0247414 | + | 0.261279i | ||||
\(949\) | − | 519.439i | − | 0.547354i | ||||||
\(950\) | 184.707 | − | 244.230i | 0.194428 | − | 0.257084i | ||||
\(951\) | −598.669 | + | 495.097i | −0.629515 | + | 0.520606i | ||||
\(952\) | 388.850 | + | 239.987i | 0.408456 | + | 0.252087i | ||||
\(953\) | 74.5492 | − | 74.5492i | 0.0782258 | − | 0.0782258i | −0.666911 | − | 0.745137i | \(-0.732384\pi\) |
0.745137 | + | 0.666911i | \(0.232384\pi\) | |||||||
\(954\) | −183.085 | − | 34.9876i | −0.191913 | − | 0.0366746i | ||||
\(955\) | 91.7967 | + | 79.9378i | 0.0961222 | + | 0.0837045i | ||||
\(956\) | 814.730i | 0.852228i | ||||||||
\(957\) | −1830.59 | − | 173.345i | −1.91285 | − | 0.181134i | ||||
\(958\) | −449.861 | + | 449.861i | −0.469584 | + | 0.469584i | ||||
\(959\) | −416.314 | + | 98.5532i | −0.434112 | + | 0.102767i | ||||
\(960\) | −86.9861 | + | 82.6645i | −0.0906105 | + | 0.0861089i | ||||
\(961\) | −595.367 | −0.619529 | ||||||||
\(962\) | −146.329 | + | 146.329i | −0.152109 | + | 0.152109i | ||||
\(963\) | 228.759 | + | 336.846i | 0.237548 | + | 0.349788i | ||||
\(964\) | −622.236 | −0.645474 | ||||||||
\(965\) | 840.706 | − | 58.0539i | 0.871197 | − | 0.0601595i | ||||
\(966\) | −225.789 | − | 170.707i | −0.233736 | − | 0.176716i | ||||
\(967\) | −910.300 | + | 910.300i | −0.941365 | + | 0.941365i | −0.998374 | − | 0.0570084i | \(-0.981844\pi\) |
0.0570084 | + | 0.998374i | \(0.481844\pi\) | |||||||
\(968\) | −523.003 | + | 523.003i | −0.540292 | + | 0.540292i | ||||
\(969\) | −382.163 | − | 462.110i | −0.394389 | − | 0.476894i | ||||
\(970\) | −15.1827 | − | 13.2213i | −0.0156522 | − | 0.0136302i | ||||
\(971\) | 168.309 | 0.173336 | 0.0866680 | − | 0.996237i | \(-0.472378\pi\) | ||||
0.0866680 | + | 0.996237i | \(0.472378\pi\) | |||||||
\(972\) | −432.848 | − | 220.995i | −0.445317 | − | 0.227361i | ||||
\(973\) | 60.3428 | − | 97.7734i | 0.0620173 | − | 0.100487i | ||||
\(974\) | 563.353 | 0.578391 | ||||||||
\(975\) | −208.312 | + | 227.261i | −0.213653 | + | 0.233088i | ||||
\(976\) | 180.452i | 0.184890i | ||||||||
\(977\) | 1091.06 | + | 1091.06i | 1.11674 | + | 1.11674i | 0.992216 | + | 0.124526i | \(0.0397409\pi\) |
0.124526 | + | 0.992216i | \(0.460259\pi\) | |||||||
\(978\) | 781.308 | + | 73.9847i | 0.798883 | + | 0.0756489i | ||||
\(979\) | −93.9605 | −0.0959760 | ||||||||
\(980\) | −121.966 | + | 474.578i | −0.124455 | + | 0.484263i | ||||
\(981\) | −1.20002 | + | 6.27953i | −0.00122326 | + | 0.00640115i | ||||
\(982\) | 896.974 | − | 896.974i | 0.913415 | − | 0.913415i | ||||
\(983\) | −236.326 | − | 236.326i | −0.240413 | − | 0.240413i | 0.576608 | − | 0.817021i | \(-0.304376\pi\) |
−0.817021 | + | 0.576608i | \(0.804376\pi\) | |||||||
\(984\) | −318.699 | − | 385.369i | −0.323881 | − | 0.391635i | ||||
\(985\) | −169.302 | + | 11.6910i | −0.171880 | + | 0.0118690i | ||||
\(986\) | 1022.89 | 1.03741 | ||||||||
\(987\) | 859.567 | − | 119.412i | 0.870889 | − | 0.120985i | ||||
\(988\) | 50.3472 | + | 50.3472i | 0.0509587 | + | 0.0509587i | ||||
\(989\) | −141.658 | −0.143234 | ||||||||
\(990\) | −148.850 | + | 1235.71i | −0.150353 | + | 1.24819i | ||||
\(991\) | −178.507 | −0.180128 | −0.0900638 | − | 0.995936i | \(-0.528707\pi\) | ||||
−0.0900638 | + | 0.995936i | \(0.528707\pi\) | |||||||
\(992\) | −157.803 | + | 157.803i | −0.159076 | + | 0.159076i | ||||
\(993\) | 110.278 | − | 1164.58i | 0.111055 | − | 1.17279i | ||||
\(994\) | −107.872 | − | 455.677i | −0.108523 | − | 0.458428i | ||||
\(995\) | −482.040 | + | 553.552i | −0.484462 | + | 0.556333i | ||||
\(996\) | −242.950 | − | 293.774i | −0.243926 | − | 0.294954i | ||||
\(997\) | −754.536 | − | 754.536i | −0.756806 | − | 0.756806i | 0.218934 | − | 0.975740i | \(-0.429742\pi\) |
−0.975740 | + | 0.218934i | \(0.929742\pi\) | |||||||
\(998\) | 0.286254 | − | 0.286254i | 0.000286827 | − | 0.000286827i | ||||
\(999\) | 462.630 | + | 842.503i | 0.463093 | + | 0.843346i |
(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 | 210.3.k.a.83.7 | ✓ | 32 | |
3.2 | odd | 2 | 210.3.k.b.83.2 | yes | 32 | ||
5.2 | odd | 4 | 210.3.k.b.167.15 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.a.83.10 | yes | 32 | |
15.2 | even | 4 | inner | 210.3.k.a.167.10 | yes | 32 | |
21.20 | even | 2 | 210.3.k.b.83.15 | yes | 32 | ||
35.27 | even | 4 | 210.3.k.b.167.2 | yes | 32 | ||
105.62 | odd | 4 | inner | 210.3.k.a.167.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.7 | ✓ | 32 | 1.1 | even | 1 | trivial | |
210.3.k.a.83.10 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.a.167.7 | yes | 32 | 105.62 | odd | 4 | inner | |
210.3.k.a.167.10 | yes | 32 | 15.2 | even | 4 | inner | |
210.3.k.b.83.2 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.83.15 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.b.167.2 | yes | 32 | 35.27 | even | 4 | ||
210.3.k.b.167.15 | yes | 32 | 5.2 | odd | 4 |