Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.g (of order \(12\), degree \(4\), 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: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 29.2 | ||
Character | \(\chi\) | \(=\) | 74.29 |
Dual form | 74.5.g.b.23.2 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.732051 | + | 2.73205i | −0.183013 | + | 0.683013i | ||||
\(3\) | −9.27942 | − | 5.35748i | −1.03105 | − | 0.595275i | −0.113763 | − | 0.993508i | \(-0.536290\pi\) |
−0.917284 | + | 0.398233i | \(0.869624\pi\) | |||||||
\(4\) | −6.92820 | − | 4.00000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 1.47068 | + | 5.48866i | 0.0588273 | + | 0.219546i | 0.989082 | − | 0.147369i | \(-0.0470805\pi\) |
−0.930254 | + | 0.366915i | \(0.880414\pi\) | |||||||
\(6\) | 21.4299 | − | 21.4299i | 0.595275 | − | 0.595275i | ||||
\(7\) | 20.7504 | − | 35.9408i | 0.423478 | − | 0.733485i | −0.572799 | − | 0.819696i | \(-0.694142\pi\) |
0.996277 | + | 0.0862105i | \(0.0274757\pi\) | |||||||
\(8\) | 16.0000 | − | 16.0000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 16.9051 | + | 29.2805i | 0.208705 | + | 0.361488i | ||||
\(10\) | −16.0719 | −0.160719 | ||||||||
\(11\) | 234.947i | 1.94171i | 0.239669 | + | 0.970855i | \(0.422961\pi\) | ||||
−0.239669 | + | 0.970855i | \(0.577039\pi\) | |||||||
\(12\) | 42.8598 | + | 74.2354i | 0.297638 | + | 0.515523i | ||||
\(13\) | 18.2333 | + | 68.0475i | 0.107889 | + | 0.402648i | 0.998657 | − | 0.0518108i | \(-0.0164993\pi\) |
−0.890768 | + | 0.454459i | \(0.849833\pi\) | |||||||
\(14\) | 83.0017 | + | 83.0017i | 0.423478 | + | 0.423478i | ||||
\(15\) | 15.7583 | − | 58.8107i | 0.0700369 | − | 0.261381i | ||||
\(16\) | 32.0000 | + | 55.4256i | 0.125000 | + | 0.216506i | ||||
\(17\) | 414.083 | + | 110.953i | 1.43281 | + | 0.383921i | 0.890011 | − | 0.455939i | \(-0.150696\pi\) |
0.542803 | + | 0.839860i | \(0.317363\pi\) | |||||||
\(18\) | −92.3713 | + | 24.7508i | −0.285097 | + | 0.0763914i | ||||
\(19\) | 62.9849 | + | 235.063i | 0.174474 | + | 0.651144i | 0.996641 | + | 0.0818979i | \(0.0260982\pi\) |
−0.822167 | + | 0.569246i | \(0.807235\pi\) | |||||||
\(20\) | 11.7655 | − | 43.9093i | 0.0294136 | − | 0.109773i | ||||
\(21\) | −385.104 | + | 222.340i | −0.873251 | + | 0.504172i | ||||
\(22\) | −641.887 | − | 171.993i | −1.32621 | − | 0.355357i | ||||
\(23\) | −60.2876 | + | 60.2876i | −0.113965 | + | 0.113965i | −0.761790 | − | 0.647824i | \(-0.775679\pi\) |
0.647824 | + | 0.761790i | \(0.275679\pi\) | |||||||
\(24\) | −234.190 | + | 62.7511i | −0.406581 | + | 0.108943i | ||||
\(25\) | 513.303 | − | 296.356i | 0.821285 | − | 0.474169i | ||||
\(26\) | −199.257 | −0.294759 | ||||||||
\(27\) | 505.636i | 0.693602i | ||||||||
\(28\) | −287.526 | + | 166.003i | −0.366743 | + | 0.211739i | ||||
\(29\) | 120.441 | + | 120.441i | 0.143211 | + | 0.143211i | 0.775078 | − | 0.631866i | \(-0.217711\pi\) |
−0.631866 | + | 0.775078i | \(0.717711\pi\) | |||||||
\(30\) | 149.138 | + | 86.1049i | 0.165709 | + | 0.0956721i | ||||
\(31\) | −633.328 | − | 633.328i | −0.659030 | − | 0.659030i | 0.296120 | − | 0.955151i | \(-0.404307\pi\) |
−0.955151 | + | 0.296120i | \(0.904307\pi\) | |||||||
\(32\) | −174.851 | + | 46.8513i | −0.170753 | + | 0.0457532i | ||||
\(33\) | 1258.72 | − | 2180.17i | 1.15585 | − | 2.00199i | ||||
\(34\) | −606.260 | + | 1050.07i | −0.524446 | + | 0.908368i | ||||
\(35\) | 227.784 | + | 61.0346i | 0.185946 | + | 0.0498241i | ||||
\(36\) | − | 270.482i | − | 0.208705i | ||||||
\(37\) | 1363.82 | + | 118.996i | 0.996215 | + | 0.0869217i | ||||
\(38\) | −688.312 | −0.476670 | ||||||||
\(39\) | 195.369 | − | 729.126i | 0.128448 | − | 0.479373i | ||||
\(40\) | 111.349 | + | 64.2877i | 0.0695934 | + | 0.0401798i | ||||
\(41\) | 951.238 | + | 549.198i | 0.565876 | + | 0.326709i | 0.755501 | − | 0.655148i | \(-0.227394\pi\) |
−0.189624 | + | 0.981857i | \(0.560727\pi\) | |||||||
\(42\) | −325.528 | − | 1214.89i | −0.184540 | − | 0.688712i | ||||
\(43\) | 692.344 | − | 692.344i | 0.374443 | − | 0.374443i | −0.494650 | − | 0.869092i | \(-0.664704\pi\) |
0.869092 | + | 0.494650i | \(0.164704\pi\) | |||||||
\(44\) | 939.787 | − | 1627.76i | 0.485427 | − | 0.840785i | ||||
\(45\) | −135.849 | + | 135.849i | −0.0670859 | + | 0.0670859i | ||||
\(46\) | −120.575 | − | 208.842i | −0.0569826 | − | 0.0986968i | ||||
\(47\) | −2409.85 | −1.09092 | −0.545461 | − | 0.838136i | \(-0.683646\pi\) | ||||
−0.545461 | + | 0.838136i | \(0.683646\pi\) | |||||||
\(48\) | − | 685.757i | − | 0.297638i | ||||||
\(49\) | 339.340 | + | 587.754i | 0.141333 | + | 0.244795i | ||||
\(50\) | 433.895 | + | 1619.32i | 0.173558 | + | 0.647727i | ||||
\(51\) | −3248.02 | − | 3248.02i | −1.24876 | − | 1.24876i | ||||
\(52\) | 145.866 | − | 544.380i | 0.0539446 | − | 0.201324i | ||||
\(53\) | 1730.78 | + | 2997.80i | 0.616156 | + | 1.06721i | 0.990180 | + | 0.139795i | \(0.0446444\pi\) |
−0.374024 | + | 0.927419i | \(0.622022\pi\) | |||||||
\(54\) | −1381.42 | − | 370.151i | −0.473739 | − | 0.126938i | ||||
\(55\) | −1289.54 | + | 345.532i | −0.426295 | + | 0.114225i | ||||
\(56\) | −243.046 | − | 907.059i | −0.0775019 | − | 0.289241i | ||||
\(57\) | 674.881 | − | 2518.69i | 0.207720 | − | 0.775220i | ||||
\(58\) | −417.219 | + | 240.882i | −0.124025 | + | 0.0716057i | ||||
\(59\) | 2051.96 | + | 549.822i | 0.589475 | + | 0.157949i | 0.541213 | − | 0.840885i | \(-0.317965\pi\) |
0.0482619 | + | 0.998835i | \(0.484632\pi\) | |||||||
\(60\) | −344.420 | + | 344.420i | −0.0956721 | + | 0.0956721i | ||||
\(61\) | −6411.54 | + | 1717.97i | −1.72307 | + | 0.461695i | −0.978568 | − | 0.205925i | \(-0.933980\pi\) |
−0.744502 | + | 0.667620i | \(0.767313\pi\) | |||||||
\(62\) | 2193.91 | − | 1266.66i | 0.570737 | − | 0.329515i | ||||
\(63\) | 1403.15 | 0.353528 | ||||||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | −346.674 | + | 200.153i | −0.0820531 | + | 0.0473734i | ||||
\(66\) | 5034.89 | + | 5034.89i | 1.15585 | + | 1.15585i | ||||
\(67\) | −3066.97 | − | 1770.71i | −0.683218 | − | 0.394456i | 0.117848 | − | 0.993032i | \(-0.462400\pi\) |
−0.801066 | + | 0.598576i | \(0.795734\pi\) | |||||||
\(68\) | −2425.04 | − | 2425.04i | −0.524446 | − | 0.524446i | ||||
\(69\) | 882.424 | − | 236.445i | 0.185344 | − | 0.0496628i | ||||
\(70\) | −333.499 | + | 577.637i | −0.0680610 | + | 0.117885i | ||||
\(71\) | −181.169 | + | 313.794i | −0.0359391 | + | 0.0622483i | −0.883435 | − | 0.468553i | \(-0.844776\pi\) |
0.847496 | + | 0.530801i | \(0.178109\pi\) | |||||||
\(72\) | 738.971 | + | 198.007i | 0.142548 | + | 0.0381957i | ||||
\(73\) | 6743.76i | 1.26548i | 0.774363 | + | 0.632741i | \(0.218070\pi\) | ||||
−0.774363 | + | 0.632741i | \(0.781930\pi\) | |||||||
\(74\) | −1323.49 | + | 3638.91i | −0.241689 | + | 0.664520i | ||||
\(75\) | −6350.88 | −1.12905 | ||||||||
\(76\) | 503.879 | − | 1880.50i | 0.0872368 | − | 0.325572i | ||||
\(77\) | 8444.17 | + | 4875.25i | 1.42422 | + | 0.822271i | ||||
\(78\) | 1848.99 | + | 1067.51i | 0.303910 | + | 0.175463i | ||||
\(79\) | 1467.49 | + | 5476.74i | 0.235137 | + | 0.877542i | 0.978087 | + | 0.208195i | \(0.0667590\pi\) |
−0.742951 | + | 0.669346i | \(0.766574\pi\) | |||||||
\(80\) | −257.151 | + | 257.151i | −0.0401798 | + | 0.0401798i | ||||
\(81\) | 4078.25 | − | 7063.73i | 0.621589 | − | 1.07662i | ||||
\(82\) | −2196.79 | + | 2196.79i | −0.326709 | + | 0.326709i | ||||
\(83\) | 1897.22 | + | 3286.08i | 0.275398 | + | 0.477003i | 0.970235 | − | 0.242163i | \(-0.0778570\pi\) |
−0.694837 | + | 0.719167i | \(0.744524\pi\) | |||||||
\(84\) | 3557.44 | 0.504172 | ||||||||
\(85\) | 2435.94i | 0.337154i | ||||||||
\(86\) | 1384.69 | + | 2398.35i | 0.187221 | + | 0.324277i | ||||
\(87\) | −472.362 | − | 1762.88i | −0.0624075 | − | 0.232908i | ||||
\(88\) | 3759.15 | + | 3759.15i | 0.485427 | + | 0.485427i | ||||
\(89\) | 2332.85 | − | 8706.32i | 0.294515 | − | 1.09914i | −0.647087 | − | 0.762416i | \(-0.724013\pi\) |
0.941602 | − | 0.336728i | \(-0.109320\pi\) | |||||||
\(90\) | −271.698 | − | 470.594i | −0.0335429 | − | 0.0580981i | ||||
\(91\) | 2824.03 | + | 756.697i | 0.341025 | + | 0.0913774i | ||||
\(92\) | 658.835 | − | 176.534i | 0.0778397 | − | 0.0208571i | ||||
\(93\) | 2483.88 | + | 9269.96i | 0.287187 | + | 1.07180i | ||||
\(94\) | 1764.13 | − | 6583.83i | 0.199653 | − | 0.745114i | ||||
\(95\) | −1197.55 | + | 691.406i | −0.132693 | + | 0.0766101i | ||||
\(96\) | 1873.52 | + | 502.009i | 0.203290 | + | 0.0544715i | ||||
\(97\) | −6290.73 | + | 6290.73i | −0.668587 | + | 0.668587i | −0.957389 | − | 0.288802i | \(-0.906743\pi\) |
0.288802 | + | 0.957389i | \(0.406743\pi\) | |||||||
\(98\) | −1854.19 | + | 496.828i | −0.193064 | + | 0.0517314i | ||||
\(99\) | −6879.37 | + | 3971.81i | −0.701905 | + | 0.405245i | ||||
\(100\) | −4741.69 | −0.474169 | ||||||||
\(101\) | − | 18005.4i | − | 1.76506i | −0.470253 | − | 0.882532i | \(-0.655837\pi\) | ||
0.470253 | − | 0.882532i | \(-0.344163\pi\) | |||||||
\(102\) | 11251.5 | − | 6496.05i | 1.08146 | − | 0.624380i | ||||
\(103\) | −3381.25 | − | 3381.25i | −0.318715 | − | 0.318715i | 0.529558 | − | 0.848273i | \(-0.322358\pi\) |
−0.848273 | + | 0.529558i | \(0.822358\pi\) | |||||||
\(104\) | 1380.49 | + | 797.028i | 0.127634 | + | 0.0736897i | ||||
\(105\) | −1786.71 | − | 1786.71i | −0.162060 | − | 0.162060i | ||||
\(106\) | −9457.18 | + | 2534.04i | −0.841685 | + | 0.225529i | ||||
\(107\) | −1171.10 | + | 2028.40i | −0.102288 | + | 0.177169i | −0.912627 | − | 0.408793i | \(-0.865950\pi\) |
0.810339 | + | 0.585962i | \(0.199283\pi\) | |||||||
\(108\) | 2022.54 | − | 3503.15i | 0.173401 | − | 0.300339i | ||||
\(109\) | 5047.67 | + | 1352.52i | 0.424852 | + | 0.113839i | 0.464909 | − | 0.885359i | \(-0.346087\pi\) |
−0.0400565 | + | 0.999197i | \(0.512754\pi\) | |||||||
\(110\) | − | 3776.04i | − | 0.312070i | ||||||
\(111\) | −12017.9 | − | 8410.84i | −0.975402 | − | 0.682643i | ||||
\(112\) | 2656.05 | 0.211739 | ||||||||
\(113\) | −1842.92 | + | 6877.86i | −0.144327 | + | 0.538638i | 0.855457 | + | 0.517874i | \(0.173276\pi\) |
−0.999784 | + | 0.0207635i | \(0.993390\pi\) | |||||||
\(114\) | 6387.14 | + | 3687.62i | 0.491470 | + | 0.283750i | ||||
\(115\) | −419.562 | − | 242.234i | −0.0317249 | − | 0.0183164i | ||||
\(116\) | −352.675 | − | 1316.20i | −0.0262095 | − | 0.0978152i | ||||
\(117\) | −1684.23 | + | 1684.23i | −0.123035 | + | 0.123035i | ||||
\(118\) | −3004.28 | + | 5203.57i | −0.215763 | + | 0.373712i | ||||
\(119\) | 12580.2 | − | 12580.2i | 0.888366 | − | 0.888366i | ||||
\(120\) | −688.839 | − | 1193.10i | −0.0478361 | − | 0.0828545i | ||||
\(121\) | −40559.0 | −2.77023 | ||||||||
\(122\) | − | 18774.3i | − | 1.26137i | ||||||
\(123\) | −5884.63 | − | 10192.5i | −0.388963 | − | 0.673705i | ||||
\(124\) | 1854.51 | + | 6921.14i | 0.120611 | + | 0.450126i | ||||
\(125\) | 4892.74 | + | 4892.74i | 0.313135 | + | 0.313135i | ||||
\(126\) | −1027.18 | + | 3833.49i | −0.0647002 | + | 0.241464i | ||||
\(127\) | −210.129 | − | 363.954i | −0.0130280 | − | 0.0225652i | 0.859438 | − | 0.511240i | \(-0.170814\pi\) |
−0.872466 | + | 0.488675i | \(0.837480\pi\) | |||||||
\(128\) | 1398.81 | + | 374.810i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | −10133.8 | + | 2715.34i | −0.608964 | + | 0.163171i | ||||
\(130\) | −293.044 | − | 1093.65i | −0.0173399 | − | 0.0647133i | ||||
\(131\) | 112.163 | − | 418.597i | 0.00653591 | − | 0.0243923i | −0.962581 | − | 0.270995i | \(-0.912647\pi\) |
0.969117 | + | 0.246602i | \(0.0793141\pi\) | |||||||
\(132\) | −17441.4 | + | 10069.8i | −1.00100 | + | 0.577926i | ||||
\(133\) | 9755.31 | + | 2613.93i | 0.551490 | + | 0.147771i | ||||
\(134\) | 7082.85 | − | 7082.85i | 0.394456 | − | 0.394456i | ||||
\(135\) | −2775.26 | + | 743.630i | −0.152278 | + | 0.0408027i | ||||
\(136\) | 8400.58 | − | 4850.08i | 0.454184 | − | 0.262223i | ||||
\(137\) | 24092.1 | 1.28361 | 0.641806 | − | 0.766867i | \(-0.278185\pi\) | ||||
0.641806 | + | 0.766867i | \(0.278185\pi\) | |||||||
\(138\) | 2583.92i | 0.135681i | ||||||||
\(139\) | 28873.3 | − | 16670.0i | 1.49440 | − | 0.862792i | 0.494420 | − | 0.869223i | \(-0.335381\pi\) |
0.999979 | + | 0.00643147i | \(0.00204722\pi\) | |||||||
\(140\) | −1334.00 | − | 1334.00i | −0.0680610 | − | 0.0680610i | ||||
\(141\) | 22362.0 | + | 12910.7i | 1.12479 | + | 0.649399i | ||||
\(142\) | −724.675 | − | 724.675i | −0.0359391 | − | 0.0359391i | ||||
\(143\) | −15987.6 | + | 4283.85i | −0.781826 | + | 0.209490i | ||||
\(144\) | −1081.93 | + | 1873.95i | −0.0521763 | + | 0.0903720i | ||||
\(145\) | −483.929 | + | 838.189i | −0.0230168 | + | 0.0398663i | ||||
\(146\) | −18424.3 | − | 4936.77i | −0.864341 | − | 0.231599i | ||||
\(147\) | − | 7272.02i | − | 0.336527i | ||||||
\(148\) | −8972.83 | − | 6279.70i | −0.409643 | − | 0.286692i | ||||
\(149\) | 25034.3 | 1.12762 | 0.563811 | − | 0.825904i | \(-0.309335\pi\) | ||||
0.563811 | + | 0.825904i | \(0.309335\pi\) | |||||||
\(150\) | 4649.17 | − | 17350.9i | 0.206630 | − | 0.771152i | ||||
\(151\) | −11271.0 | − | 6507.31i | −0.494320 | − | 0.285396i | 0.232045 | − | 0.972705i | \(-0.425458\pi\) |
−0.726365 | + | 0.687309i | \(0.758792\pi\) | |||||||
\(152\) | 4768.77 | + | 2753.25i | 0.206404 | + | 0.119168i | ||||
\(153\) | 3751.36 | + | 14000.3i | 0.160253 | + | 0.598072i | ||||
\(154\) | −19501.0 | + | 19501.0i | −0.822271 | + | 0.822271i | ||||
\(155\) | 2544.70 | − | 4407.55i | 0.105919 | − | 0.183457i | ||||
\(156\) | −4270.06 | + | 4270.06i | −0.175463 | + | 0.175463i | ||||
\(157\) | −557.314 | − | 965.296i | −0.0226100 | − | 0.0391617i | 0.854499 | − | 0.519453i | \(-0.173864\pi\) |
−0.877109 | + | 0.480291i | \(0.840531\pi\) | |||||||
\(158\) | −16037.0 | −0.642405 | ||||||||
\(159\) | − | 37090.5i | − | 1.46713i | ||||||
\(160\) | −514.301 | − | 890.796i | −0.0200899 | − | 0.0347967i | ||||
\(161\) | 915.791 | + | 3417.78i | 0.0353301 | + | 0.131854i | ||||
\(162\) | 16313.0 | + | 16313.0i | 0.621589 | + | 0.621589i | ||||
\(163\) | −9642.59 | + | 35986.6i | −0.362926 | + | 1.35446i | 0.507284 | + | 0.861779i | \(0.330650\pi\) |
−0.870210 | + | 0.492681i | \(0.836017\pi\) | |||||||
\(164\) | −4393.58 | − | 7609.91i | −0.163354 | − | 0.282938i | ||||
\(165\) | 13817.4 | + | 3702.36i | 0.507526 | + | 0.135991i | ||||
\(166\) | −10366.6 | + | 2777.72i | −0.376201 | + | 0.100803i | ||||
\(167\) | 2903.36 | + | 10835.5i | 0.104104 | + | 0.388521i | 0.998242 | − | 0.0592702i | \(-0.0188773\pi\) |
−0.894138 | + | 0.447792i | \(0.852211\pi\) | |||||||
\(168\) | −2604.23 | + | 9719.10i | −0.0922699 | + | 0.344356i | ||||
\(169\) | 20436.5 | − | 11799.0i | 0.715540 | − | 0.413117i | ||||
\(170\) | −6655.11 | − | 1783.23i | −0.230281 | − | 0.0617035i | ||||
\(171\) | −5818.00 | + | 5818.00i | −0.198967 | + | 0.198967i | ||||
\(172\) | −7566.08 | + | 2027.32i | −0.255749 | + | 0.0685277i | ||||
\(173\) | 32670.5 | − | 18862.3i | 1.09160 | − | 0.630236i | 0.157598 | − | 0.987503i | \(-0.449625\pi\) |
0.934002 | + | 0.357268i | \(0.116292\pi\) | |||||||
\(174\) | 5162.07 | 0.170500 | ||||||||
\(175\) | − | 24598.0i | − | 0.803201i | ||||||
\(176\) | −13022.1 | + | 7518.30i | −0.420392 | + | 0.242714i | ||||
\(177\) | −16095.4 | − | 16095.4i | −0.513753 | − | 0.513753i | ||||
\(178\) | 22078.4 | + | 12746.9i | 0.696830 | + | 0.402315i | ||||
\(179\) | −27882.7 | − | 27882.7i | −0.870218 | − | 0.870218i | 0.122278 | − | 0.992496i | \(-0.460980\pi\) |
−0.992496 | + | 0.122278i | \(0.960980\pi\) | |||||||
\(180\) | 1484.58 | − | 397.793i | 0.0458205 | − | 0.0122776i | ||||
\(181\) | −4673.20 | + | 8094.21i | −0.142645 | + | 0.247069i | −0.928492 | − | 0.371353i | \(-0.878894\pi\) |
0.785847 | + | 0.618421i | \(0.212227\pi\) | |||||||
\(182\) | −4134.67 | + | 7161.45i | −0.124824 | + | 0.216201i | ||||
\(183\) | 68699.4 | + | 18408.0i | 2.05140 | + | 0.549672i | ||||
\(184\) | 1929.20i | 0.0569826i | ||||||||
\(185\) | 1352.62 | + | 7660.54i | 0.0395213 | + | 0.223829i | ||||
\(186\) | −27144.3 | −0.784609 | ||||||||
\(187\) | −26068.1 | + | 97287.5i | −0.745464 | + | 2.78211i | ||||
\(188\) | 16695.9 | + | 9639.39i | 0.472383 | + | 0.272731i | ||||
\(189\) | 18173.0 | + | 10492.2i | 0.508747 | + | 0.293725i | ||||
\(190\) | −1012.29 | − | 3777.91i | −0.0280412 | − | 0.104651i | ||||
\(191\) | −49013.6 | + | 49013.6i | −1.34354 | + | 1.34354i | −0.451028 | + | 0.892510i | \(0.648943\pi\) |
−0.892510 | + | 0.451028i | \(0.851057\pi\) | |||||||
\(192\) | −2743.03 | + | 4751.06i | −0.0744094 | + | 0.128881i | ||||
\(193\) | 24829.8 | − | 24829.8i | 0.666590 | − | 0.666590i | −0.290335 | − | 0.956925i | \(-0.593767\pi\) |
0.956925 | + | 0.290335i | \(0.0937668\pi\) | |||||||
\(194\) | −12581.5 | − | 21791.7i | −0.334293 | − | 0.579013i | ||||
\(195\) | 4289.25 | 0.112801 | ||||||||
\(196\) | − | 5429.44i | − | 0.141333i | ||||||
\(197\) | 7073.27 | + | 12251.3i | 0.182259 | + | 0.315681i | 0.942649 | − | 0.333785i | \(-0.108326\pi\) |
−0.760391 | + | 0.649466i | \(0.774993\pi\) | |||||||
\(198\) | −5815.13 | − | 21702.3i | −0.148330 | − | 0.553575i | ||||
\(199\) | 4628.28 | + | 4628.28i | 0.116873 | + | 0.116873i | 0.763124 | − | 0.646252i | \(-0.223664\pi\) |
−0.646252 | + | 0.763124i | \(0.723664\pi\) | |||||||
\(200\) | 3471.16 | − | 12954.5i | 0.0867790 | − | 0.323864i | ||||
\(201\) | 18973.1 | + | 32862.4i | 0.469620 | + | 0.813405i | ||||
\(202\) | 49191.7 | + | 13180.9i | 1.20556 | + | 0.323029i | ||||
\(203\) | 6827.94 | − | 1829.54i | 0.165690 | − | 0.0443966i | ||||
\(204\) | 9510.87 | + | 35495.1i | 0.228539 | + | 0.852919i | ||||
\(205\) | −1615.39 | + | 6028.72i | −0.0384388 | + | 0.143456i | ||||
\(206\) | 11713.0 | − | 6762.50i | 0.276015 | − | 0.159358i | ||||
\(207\) | −2784.42 | − | 746.084i | −0.0649822 | − | 0.0174119i | ||||
\(208\) | −3188.11 | + | 3188.11i | −0.0736897 | + | 0.0736897i | ||||
\(209\) | −55227.3 | + | 14798.1i | −1.26433 | + | 0.338777i | ||||
\(210\) | 6189.36 | − | 3573.43i | 0.140348 | − | 0.0810301i | ||||
\(211\) | −16754.0 | −0.376317 | −0.188159 | − | 0.982139i | \(-0.560252\pi\) | ||||
−0.188159 | + | 0.982139i | \(0.560252\pi\) | |||||||
\(212\) | − | 27692.5i | − | 0.616156i | ||||||
\(213\) | 3362.28 | − | 1941.22i | 0.0741097 | − | 0.0427873i | ||||
\(214\) | −4684.40 | − | 4684.40i | −0.102288 | − | 0.102288i | ||||
\(215\) | 4818.26 | + | 2781.82i | 0.104235 | + | 0.0601801i | ||||
\(216\) | 8090.18 | + | 8090.18i | 0.173401 | + | 0.173401i | ||||
\(217\) | −35904.1 | + | 9620.48i | −0.762474 | + | 0.204304i | ||||
\(218\) | −7390.30 | + | 12800.4i | −0.155507 | + | 0.269346i | ||||
\(219\) | 36129.5 | − | 62578.2i | 0.753310 | − | 1.30477i | ||||
\(220\) | 10316.3 | + | 2764.26i | 0.213148 | + | 0.0571127i | ||||
\(221\) | 30200.4i | 0.618341i | ||||||||
\(222\) | 31776.6 | − | 26676.4i | 0.644765 | − | 0.541280i | ||||
\(223\) | −71472.4 | −1.43724 | −0.718619 | − | 0.695404i | \(-0.755225\pi\) | ||||
−0.718619 | + | 0.695404i | \(0.755225\pi\) | |||||||
\(224\) | −1944.37 | + | 7256.48i | −0.0387509 | + | 0.144620i | ||||
\(225\) | 17354.9 | + | 10019.9i | 0.342813 | + | 0.197923i | ||||
\(226\) | −17441.6 | − | 10069.9i | −0.341482 | − | 0.197155i | ||||
\(227\) | −22852.7 | − | 85287.3i | −0.443491 | − | 1.65513i | −0.719889 | − | 0.694089i | \(-0.755807\pi\) |
0.276398 | − | 0.961043i | \(-0.410859\pi\) | |||||||
\(228\) | −14750.5 | + | 14750.5i | −0.283750 | + | 0.283750i | ||||
\(229\) | −15885.5 | + | 27514.4i | −0.302921 | + | 0.524674i | −0.976796 | − | 0.214171i | \(-0.931295\pi\) |
0.673876 | + | 0.738845i | \(0.264628\pi\) | |||||||
\(230\) | 968.937 | − | 968.937i | 0.0183164 | − | 0.0183164i | ||||
\(231\) | −52238.0 | − | 90478.9i | −0.978955 | − | 1.69560i | ||||
\(232\) | 3854.11 | 0.0716057 | ||||||||
\(233\) | − | 40361.2i | − | 0.743451i | −0.928343 | − | 0.371726i | \(-0.878766\pi\) | ||
0.928343 | − | 0.371726i | \(-0.121234\pi\) | |||||||
\(234\) | −3368.46 | − | 5834.35i | −0.0615177 | − | 0.106552i | ||||
\(235\) | −3544.12 | − | 13226.8i | −0.0641760 | − | 0.239508i | ||||
\(236\) | −12017.1 | − | 12017.1i | −0.215763 | − | 0.215763i | ||||
\(237\) | 15724.1 | − | 58683.0i | 0.279942 | − | 1.04476i | ||||
\(238\) | 25160.3 | + | 43578.9i | 0.444183 | + | 0.769348i | ||||
\(239\) | −30627.2 | − | 8206.54i | −0.536182 | − | 0.143669i | −0.0194403 | − | 0.999811i | \(-0.506188\pi\) |
−0.516741 | + | 0.856142i | \(0.672855\pi\) | |||||||
\(240\) | 3763.89 | − | 1008.53i | 0.0653453 | − | 0.0175092i | ||||
\(241\) | −15204.5 | − | 56744.0i | −0.261781 | − | 0.976980i | −0.964191 | − | 0.265208i | \(-0.914559\pi\) |
0.702410 | − | 0.711772i | \(-0.252107\pi\) | |||||||
\(242\) | 29691.3 | − | 110809.i | 0.506988 | − | 1.89211i | ||||
\(243\) | −40218.2 | + | 23220.0i | −0.681099 | + | 0.393233i | ||||
\(244\) | 51292.4 | + | 13743.7i | 0.861535 | + | 0.230848i | ||||
\(245\) | −2726.92 | + | 2726.92i | −0.0454297 | + | 0.0454297i | ||||
\(246\) | 32154.2 | − | 8615.69i | 0.531334 | − | 0.142371i | ||||
\(247\) | −14847.0 | + | 8571.94i | −0.243358 | + | 0.140503i | ||||
\(248\) | −20266.5 | −0.329515 | ||||||||
\(249\) | − | 40657.2i | − | 0.655751i | ||||||
\(250\) | −16948.9 | + | 9785.48i | −0.271183 | + | 0.156568i | ||||
\(251\) | 71466.2 | + | 71466.2i | 1.13437 | + | 1.13437i | 0.989443 | + | 0.144924i | \(0.0462937\pi\) |
0.144924 | + | 0.989443i | \(0.453706\pi\) | |||||||
\(252\) | −9721.34 | − | 5612.62i | −0.153082 | − | 0.0883821i | ||||
\(253\) | −14164.4 | − | 14164.4i | −0.221287 | − | 0.221287i | ||||
\(254\) | 1148.17 | − | 307.650i | 0.0177966 | − | 0.00476859i | ||||
\(255\) | 13050.5 | − | 22604.1i | 0.200700 | − | 0.347622i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 70282.2 | + | 18832.1i | 1.06409 | + | 0.285123i | 0.748063 | − | 0.663627i | \(-0.230984\pi\) |
0.316028 | + | 0.948750i | \(0.397651\pi\) | |||||||
\(258\) | − | 29673.7i | − | 0.445793i | ||||||
\(259\) | 32576.6 | − | 46547.5i | 0.485631 | − | 0.693900i | ||||
\(260\) | 3202.44 | 0.0473734 | ||||||||
\(261\) | −1490.50 | + | 5562.64i | −0.0218803 | + | 0.0816582i | ||||
\(262\) | 1061.52 | + | 612.869i | 0.0154641 | + | 0.00892822i | ||||
\(263\) | 98764.4 | + | 57021.7i | 1.42787 | + | 0.824382i | 0.996953 | − | 0.0780093i | \(-0.0248564\pi\) |
0.430918 | + | 0.902391i | \(0.358190\pi\) | |||||||
\(264\) | −14743.2 | − | 55022.3i | −0.211535 | − | 0.789461i | ||||
\(265\) | −13908.5 | + | 13908.5i | −0.198056 | + | 0.198056i | ||||
\(266\) | −14282.8 | + | 24738.5i | −0.201859 | + | 0.349631i | ||||
\(267\) | −68291.5 | + | 68291.5i | −0.957952 | + | 0.957952i | ||||
\(268\) | 14165.7 | + | 24535.7i | 0.197228 | + | 0.341609i | ||||
\(269\) | −102466. | −1.41603 | −0.708017 | − | 0.706195i | \(-0.750410\pi\) | ||||
−0.708017 | + | 0.706195i | \(0.750410\pi\) | |||||||
\(270\) | − | 8126.54i | − | 0.111475i | ||||||
\(271\) | −43232.5 | − | 74880.9i | −0.588670 | − | 1.01961i | −0.994407 | − | 0.105616i | \(-0.966319\pi\) |
0.405737 | − | 0.913990i | \(-0.367015\pi\) | |||||||
\(272\) | 7101.01 | + | 26501.3i | 0.0959803 | + | 0.358204i | ||||
\(273\) | −22151.4 | − | 22151.4i | −0.297218 | − | 0.297218i | ||||
\(274\) | −17636.7 | + | 65820.9i | −0.234917 | + | 0.876724i | ||||
\(275\) | 69627.9 | + | 120599.i | 0.920699 | + | 1.59470i | ||||
\(276\) | −7059.39 | − | 1891.56i | −0.0926721 | − | 0.0248314i | ||||
\(277\) | 52386.2 | − | 14036.8i | 0.682743 | − | 0.182941i | 0.0992551 | − | 0.995062i | \(-0.468354\pi\) |
0.583488 | + | 0.812121i | \(0.301687\pi\) | |||||||
\(278\) | 24406.6 | + | 91086.6i | 0.315804 | + | 1.17860i | ||||
\(279\) | 7837.70 | − | 29250.7i | 0.100689 | − | 0.375775i | ||||
\(280\) | 4621.10 | − | 2667.99i | 0.0589426 | − | 0.0340305i | ||||
\(281\) | −87336.7 | − | 23401.8i | −1.10607 | − | 0.296372i | −0.340838 | − | 0.940122i | \(-0.610711\pi\) |
−0.765236 | + | 0.643750i | \(0.777378\pi\) | |||||||
\(282\) | −51642.8 | + | 51642.8i | −0.649399 | + | 0.649399i | ||||
\(283\) | −6991.08 | + | 1873.26i | −0.0872914 | + | 0.0233897i | −0.302200 | − | 0.953244i | \(-0.597721\pi\) |
0.214909 | + | 0.976634i | \(0.431055\pi\) | |||||||
\(284\) | 2510.35 | − | 1449.35i | 0.0311241 | − | 0.0179695i | ||||
\(285\) | 14816.8 | 0.182416 | ||||||||
\(286\) | − | 46814.8i | − | 0.572336i | ||||||
\(287\) | 39477.2 | − | 22792.2i | 0.479272 | − | 0.276708i | ||||
\(288\) | −4327.71 | − | 4327.71i | −0.0521763 | − | 0.0521763i | ||||
\(289\) | 86823.0 | + | 50127.3i | 1.03953 | + | 0.600176i | ||||
\(290\) | −1935.71 | − | 1935.71i | −0.0230168 | − | 0.0230168i | ||||
\(291\) | 92076.8 | − | 24671.9i | 1.08734 | − | 0.291351i | ||||
\(292\) | 26975.0 | − | 46722.1i | 0.316371 | − | 0.547970i | ||||
\(293\) | −1313.86 | + | 2275.68i | −0.0153044 | + | 0.0265079i | −0.873576 | − | 0.486687i | \(-0.838205\pi\) |
0.858272 | + | 0.513195i | \(0.171538\pi\) | |||||||
\(294\) | 19867.5 | + | 5323.49i | 0.229853 | + | 0.0615888i | ||||
\(295\) | 12071.1i | 0.138709i | ||||||||
\(296\) | 23725.0 | − | 19917.2i | 0.270784 | − | 0.227323i | ||||
\(297\) | −118798. | −1.34677 | ||||||||
\(298\) | −18326.4 | + | 68395.1i | −0.206369 | + | 0.770180i | ||||
\(299\) | −5201.66 | − | 3003.18i | −0.0581835 | − | 0.0335923i | ||||
\(300\) | 44000.2 | + | 25403.5i | 0.488891 | + | 0.282261i | ||||
\(301\) | −10517.0 | − | 39249.8i | −0.116080 | − | 0.433216i | ||||
\(302\) | 26029.3 | − | 26029.3i | 0.285396 | − | 0.285396i | ||||
\(303\) | −96463.6 | + | 167080.i | −1.05070 | + | 1.81986i | ||||
\(304\) | −11013.0 | + | 11013.0i | −0.119168 | + | 0.119168i | ||||
\(305\) | −18858.7 | − | 32664.2i | −0.202727 | − | 0.351134i | ||||
\(306\) | −40995.6 | −0.437819 | ||||||||
\(307\) | 24927.2i | 0.264482i | 0.991218 | + | 0.132241i | \(0.0422173\pi\) | ||||
−0.991218 | + | 0.132241i | \(0.957783\pi\) | |||||||
\(308\) | −39002.0 | − | 67553.4i | −0.411136 | − | 0.712108i | ||||
\(309\) | 13261.1 | + | 49491.0i | 0.138887 | + | 0.518333i | ||||
\(310\) | 10178.8 | + | 10178.8i | 0.105919 | + | 0.105919i | ||||
\(311\) | 23122.4 | − | 86294.1i | 0.239063 | − | 0.892196i | −0.737212 | − | 0.675662i | \(-0.763858\pi\) |
0.976275 | − | 0.216534i | \(-0.0694753\pi\) | |||||||
\(312\) | −8540.12 | − | 14791.9i | −0.0877313 | − | 0.151955i | ||||
\(313\) | −1731.49 | − | 463.952i | −0.0176739 | − | 0.00473570i | 0.249971 | − | 0.968253i | \(-0.419579\pi\) |
−0.267645 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(314\) | 3045.22 | − | 815.964i | 0.0308858 | − | 0.00827583i | ||||
\(315\) | 2063.59 | + | 7701.44i | 0.0207971 | + | 0.0776159i | ||||
\(316\) | 11739.9 | − | 43813.9i | 0.117568 | − | 0.438771i | ||||
\(317\) | −162164. | + | 93625.4i | −1.61375 | + | 0.931698i | −0.625257 | + | 0.780419i | \(0.715006\pi\) |
−0.988491 | + | 0.151279i | \(0.951661\pi\) | |||||||
\(318\) | 101333. | + | 27152.2i | 1.00207 | + | 0.268504i | ||||
\(319\) | −28297.2 | + | 28297.2i | −0.278075 | + | 0.278075i | ||||
\(320\) | 2810.19 | − | 752.989i | 0.0274433 | − | 0.00735341i | ||||
\(321\) | 21734.3 | − | 12548.3i | 0.210928 | − | 0.121779i | ||||
\(322\) | −10007.9 | −0.0965235 | ||||||||
\(323\) | 104324.i | 0.999952i | ||||||||
\(324\) | −56509.9 | + | 32626.0i | −0.538312 | + | 0.310795i | ||||
\(325\) | 29525.5 | + | 29525.5i | 0.279531 | + | 0.279531i | ||||
\(326\) | −91258.5 | − | 52688.1i | −0.858693 | − | 0.495767i | ||||
\(327\) | −39593.4 | − | 39593.4i | −0.370277 | − | 0.370277i | ||||
\(328\) | 24007.0 | − | 6432.65i | 0.223146 | − | 0.0597919i | ||||
\(329\) | −50005.4 | + | 86611.8i | −0.461982 | + | 0.800176i | ||||
\(330\) | −20230.1 | + | 35039.5i | −0.185767 | + | 0.321759i | ||||
\(331\) | 155957. | + | 41788.5i | 1.42347 | + | 0.381418i | 0.886713 | − | 0.462320i | \(-0.152983\pi\) |
0.536756 | + | 0.843737i | \(0.319649\pi\) | |||||||
\(332\) | − | 30355.5i | − | 0.275398i | ||||||
\(333\) | 19571.3 | + | 41945.0i | 0.176494 | + | 0.378261i | ||||
\(334\) | −31728.5 | −0.284417 | ||||||||
\(335\) | 5208.31 | − | 19437.7i | 0.0464096 | − | 0.173203i | ||||
\(336\) | −24646.7 | − | 14229.8i | −0.218313 | − | 0.126043i | ||||
\(337\) | −15810.1 | − | 9127.95i | −0.139211 | − | 0.0803736i | 0.428777 | − | 0.903410i | \(-0.358945\pi\) |
−0.567988 | + | 0.823037i | \(0.692278\pi\) | |||||||
\(338\) | 17275.0 | + | 64471.2i | 0.151211 | + | 0.564329i | ||||
\(339\) | 53949.2 | − | 53949.2i | 0.469446 | − | 0.469446i | ||||
\(340\) | 9743.76 | − | 16876.7i | 0.0842886 | − | 0.145992i | ||||
\(341\) | 148798. | − | 148798.i | 1.27965 | − | 1.27965i | ||||
\(342\) | −11636.0 | − | 20154.2i | −0.0994836 | − | 0.172311i | ||||
\(343\) | 127809. | 1.08636 | ||||||||
\(344\) | − | 22155.0i | − | 0.187221i | ||||||
\(345\) | 2595.53 | + | 4495.59i | 0.0218066 | + | 0.0377701i | ||||
\(346\) | 27616.4 | + | 103066.i | 0.230682 | + | 0.860918i | ||||
\(347\) | 102214. | + | 102214.i | 0.848894 | + | 0.848894i | 0.989995 | − | 0.141101i | \(-0.0450643\pi\) |
−0.141101 | + | 0.989995i | \(0.545064\pi\) | |||||||
\(348\) | −3778.90 | + | 14103.0i | −0.0312037 | + | 0.116454i | ||||
\(349\) | −83073.7 | − | 143888.i | −0.682044 | − | 1.18134i | −0.974356 | − | 0.225012i | \(-0.927758\pi\) |
0.292312 | − | 0.956323i | \(-0.405576\pi\) | |||||||
\(350\) | 67203.1 | + | 18007.0i | 0.548597 | + | 0.146996i | ||||
\(351\) | −34407.3 | + | 9219.40i | −0.279278 | + | 0.0748322i | ||||
\(352\) | −11007.6 | − | 41080.7i | −0.0888394 | − | 0.331553i | ||||
\(353\) | −569.952 | + | 2127.09i | −0.00457392 | + | 0.0170701i | −0.968175 | − | 0.250274i | \(-0.919479\pi\) |
0.963601 | + | 0.267344i | \(0.0861460\pi\) | |||||||
\(354\) | 55756.0 | − | 32190.8i | 0.444923 | − | 0.256877i | ||||
\(355\) | −1988.75 | − | 532.883i | −0.0157806 | − | 0.00422839i | ||||
\(356\) | −50987.8 | + | 50987.8i | −0.402315 | + | 0.402315i | ||||
\(357\) | −184134. | + | 49338.7i | −1.44477 | + | 0.387125i | ||||
\(358\) | 96588.3 | − | 55765.3i | 0.753631 | − | 0.435109i | ||||
\(359\) | 77086.5 | 0.598121 | 0.299061 | − | 0.954234i | \(-0.403327\pi\) | ||||
0.299061 | + | 0.954234i | \(0.403327\pi\) | |||||||
\(360\) | 4347.16i | 0.0335429i | ||||||||
\(361\) | 61573.8 | − | 35549.6i | 0.472478 | − | 0.272785i | ||||
\(362\) | −18692.8 | − | 18692.8i | −0.142645 | − | 0.142645i | ||||
\(363\) | 376364. | + | 217294.i | 2.85624 | + | 1.64905i | ||||
\(364\) | −16538.7 | − | 16538.7i | −0.124824 | − | 0.124824i | ||||
\(365\) | −37014.2 | + | 9917.92i | −0.277832 | + | 0.0744449i | ||||
\(366\) | −100583. | + | 174215.i | −0.750865 | + | 1.30054i | ||||
\(367\) | 108382. | − | 187724.i | 0.804685 | − | 1.39376i | −0.111818 | − | 0.993729i | \(-0.535667\pi\) |
0.916503 | − | 0.400027i | \(-0.130999\pi\) | |||||||
\(368\) | −5270.68 | − | 1412.27i | −0.0389198 | − | 0.0104285i | ||||
\(369\) | 37137.0i | 0.272743i | ||||||||
\(370\) | −21919.2 | − | 1912.49i | −0.160111 | − | 0.0139700i | ||||
\(371\) | 143658. | 1.04371 | ||||||||
\(372\) | 19871.0 | − | 74159.7i | 0.143593 | − | 0.535898i | ||||
\(373\) | −149252. | − | 86170.8i | −1.07276 | − | 0.619359i | −0.143826 | − | 0.989603i | \(-0.545941\pi\) |
−0.928934 | + | 0.370244i | \(0.879274\pi\) | |||||||
\(374\) | −246711. | − | 142439.i | −1.76379 | − | 1.01832i | ||||
\(375\) | −19189.1 | − | 71614.5i | −0.136456 | − | 0.509259i | ||||
\(376\) | −38557.6 | + | 38557.6i | −0.272731 | + | 0.272731i | ||||
\(377\) | −5999.67 | + | 10391.7i | −0.0422128 | + | 0.0731148i | ||||
\(378\) | −41968.6 | + | 41968.6i | −0.293725 | + | 0.293725i | ||||
\(379\) | −90455.5 | − | 156674.i | −0.629733 | − | 1.09073i | −0.987605 | − | 0.156959i | \(-0.949831\pi\) |
0.357872 | − | 0.933771i | \(-0.383502\pi\) | |||||||
\(380\) | 11062.5 | 0.0766101 | ||||||||
\(381\) | 4503.05i | 0.0310211i | ||||||||
\(382\) | −98027.2 | − | 169788.i | −0.671769 | − | 1.16354i | ||||
\(383\) | −23233.7 | − | 86709.3i | −0.158387 | − | 0.591110i | −0.998791 | − | 0.0491494i | \(-0.984349\pi\) |
0.840404 | − | 0.541960i | \(-0.182318\pi\) | |||||||
\(384\) | −10972.1 | − | 10972.1i | −0.0744094 | − | 0.0744094i | ||||
\(385\) | −14339.9 | + | 53517.1i | −0.0967440 | + | 0.361053i | ||||
\(386\) | 49659.6 | + | 86013.0i | 0.333295 | + | 0.577284i | ||||
\(387\) | 31976.4 | + | 8568.04i | 0.213505 | + | 0.0572084i | ||||
\(388\) | 68746.4 | − | 18420.5i | 0.456653 | − | 0.122360i | ||||
\(389\) | 67878.1 | + | 253325.i | 0.448570 | + | 1.67409i | 0.706334 | + | 0.707879i | \(0.250348\pi\) |
−0.257763 | + | 0.966208i | \(0.582986\pi\) | |||||||
\(390\) | −3139.95 | + | 11718.5i | −0.0206440 | + | 0.0770444i | ||||
\(391\) | −31653.2 | + | 18275.0i | −0.207045 | + | 0.119537i | ||||
\(392\) | 14833.5 | + | 3974.62i | 0.0965320 | + | 0.0258657i | ||||
\(393\) | −3283.43 | + | 3283.43i | −0.0212590 | + | 0.0212590i | ||||
\(394\) | −38649.1 | + | 10356.0i | −0.248970 | + | 0.0667113i | ||||
\(395\) | −27901.7 | + | 16109.1i | −0.178829 | + | 0.103247i | ||||
\(396\) | 63548.9 | 0.405245 | ||||||||
\(397\) | − | 264902.i | − | 1.68075i | −0.542002 | − | 0.840377i | \(-0.682333\pi\) | ||
0.542002 | − | 0.840377i | \(-0.317667\pi\) | |||||||
\(398\) | −16032.8 | + | 9256.56i | −0.101215 | + | 0.0584364i | ||||
\(399\) | −76519.6 | − | 76519.6i | −0.480648 | − | 0.480648i | ||||
\(400\) | 32851.4 | + | 18966.8i | 0.205321 | + | 0.118542i | ||||
\(401\) | −166248. | − | 166248.i | −1.03387 | − | 1.03387i | −0.999406 | − | 0.0344674i | \(-0.989027\pi\) |
−0.0344674 | − | 0.999406i | \(-0.510973\pi\) | |||||||
\(402\) | −103671. | + | 27778.6i | −0.641513 | + | 0.171893i | ||||
\(403\) | 31548.8 | − | 54644.1i | 0.194255 | − | 0.336460i | ||||
\(404\) | −72021.7 | + | 124745.i | −0.441266 | + | 0.764295i | ||||
\(405\) | 44768.2 | + | 11995.6i | 0.272935 | + | 0.0731328i | ||||
\(406\) | 19993.6i | 0.121294i | ||||||||
\(407\) | −27957.7 | + | 320425.i | −0.168777 | + | 1.93436i | ||||
\(408\) | −103937. | −0.624380 | ||||||||
\(409\) | 60573.9 | − | 226065.i | 0.362109 | − | 1.35141i | −0.509189 | − | 0.860655i | \(-0.670055\pi\) |
0.871298 | − | 0.490754i | \(-0.163279\pi\) | |||||||
\(410\) | −15288.2 | − | 8826.66i | −0.0909472 | − | 0.0525084i | ||||
\(411\) | −223561. | − | 129073.i | −1.32346 | − | 0.764103i | ||||
\(412\) | 9900.98 | + | 36951.0i | 0.0583289 | + | 0.217686i | ||||
\(413\) | 62340.1 | − | 62340.1i | 0.365483 | − | 0.365483i | ||||
\(414\) | 4076.68 | − | 7061.01i | 0.0237851 | − | 0.0411971i | ||||
\(415\) | −15246.0 | + | 15246.0i | −0.0885235 | + | 0.0885235i | ||||
\(416\) | −6376.22 | − | 11043.9i | −0.0368449 | − | 0.0638172i | ||||
\(417\) | −357237. | −2.05439 | ||||||||
\(418\) | − | 161717.i | − | 0.925555i | ||||||
\(419\) | −108768. | − | 188392.i | −0.619546 | − | 1.07308i | −0.989569 | − | 0.144062i | \(-0.953983\pi\) |
0.370023 | − | 0.929023i | \(-0.379350\pi\) | |||||||
\(420\) | 5231.86 | + | 19525.6i | 0.0296591 | + | 0.110689i | ||||
\(421\) | −190531. | − | 190531.i | −1.07498 | − | 1.07498i | −0.996951 | − | 0.0780342i | \(-0.975136\pi\) |
−0.0780342 | − | 0.996951i | \(-0.524864\pi\) | |||||||
\(422\) | 12264.8 | − | 45772.9i | 0.0688709 | − | 0.257030i | ||||
\(423\) | −40738.8 | − | 70561.6i | −0.227681 | − | 0.394356i | ||||
\(424\) | 75657.4 | + | 20272.3i | 0.420843 | + | 0.112764i | ||||
\(425\) | 245432. | − | 65763.3i | 1.35879 | − | 0.364087i | ||||
\(426\) | 2842.14 | + | 10607.0i | 0.0156612 | + | 0.0584485i | ||||
\(427\) | −71297.1 | + | 266085.i | −0.391036 | + | 1.45936i | ||||
\(428\) | 16227.2 | − | 9368.80i | 0.0885843 | − | 0.0511442i | ||||
\(429\) | 171306. | + | 45901.3i | 0.930803 | + | 0.249408i | ||||
\(430\) | −11127.3 | + | 11127.3i | −0.0601801 | + | 0.0601801i | ||||
\(431\) | 287329. | − | 76989.6i | 1.54677 | − | 0.414455i | 0.618323 | − | 0.785924i | \(-0.287812\pi\) |
0.928445 | + | 0.371469i | \(0.121146\pi\) | |||||||
\(432\) | −28025.2 | + | 16180.4i | −0.150169 | + | 0.0867003i | ||||
\(433\) | 265813. | 1.41775 | 0.708875 | − | 0.705334i | \(-0.249203\pi\) | ||||
0.708875 | + | 0.705334i | \(0.249203\pi\) | |||||||
\(434\) | − | 105135.i | − | 0.558170i | ||||||
\(435\) | 8981.16 | − | 5185.27i | 0.0474628 | − | 0.0274027i | ||||
\(436\) | −29561.2 | − | 29561.2i | −0.155507 | − | 0.155507i | ||||
\(437\) | −17968.6 | − | 10374.2i | −0.0940917 | − | 0.0543239i | ||||
\(438\) | 144518. | + | 144518.i | 0.753310 | + | 0.753310i | ||||
\(439\) | −31029.9 | + | 8314.44i | −0.161010 | + | 0.0431424i | −0.338423 | − | 0.940994i | \(-0.609894\pi\) |
0.177414 | + | 0.984136i | \(0.443227\pi\) | |||||||
\(440\) | −15104.2 | + | 26161.2i | −0.0780175 | + | 0.135130i | ||||
\(441\) | −11473.2 | + | 19872.1i | −0.0589938 | + | 0.102180i | ||||
\(442\) | −82509.0 | − | 22108.2i | −0.422335 | − | 0.113164i | ||||
\(443\) | 169359.i | 0.862979i | 0.902118 | + | 0.431490i | \(0.142012\pi\) | ||||
−0.902118 | + | 0.431490i | \(0.857988\pi\) | |||||||
\(444\) | 49619.3 | + | 106344.i | 0.251701 | + | 0.539443i | ||||
\(445\) | 51216.9 | 0.258639 | ||||||||
\(446\) | 52321.4 | − | 195266.i | 0.263033 | − | 0.981652i | ||||
\(447\) | −232304. | − | 134121.i | −1.16263 | − | 0.671245i | ||||
\(448\) | −18401.7 | − | 10624.2i | −0.0916857 | − | 0.0529348i | ||||
\(449\) | 86597.8 | + | 323187.i | 0.429550 | + | 1.60310i | 0.753781 | + | 0.657126i | \(0.228228\pi\) |
−0.324231 | + | 0.945978i | \(0.605105\pi\) | |||||||
\(450\) | −40079.5 | + | 40079.5i | −0.197923 | + | 0.197923i | ||||
\(451\) | −129032. | + | 223490.i | −0.634374 | + | 1.09877i | ||||
\(452\) | 40279.6 | − | 40279.6i | 0.197155 | − | 0.197155i | ||||
\(453\) | 69725.6 | + | 120768.i | 0.339778 | + | 0.588513i | ||||
\(454\) | 249739. | 1.21164 | ||||||||
\(455\) | 16613.0i | 0.0802464i | ||||||||
\(456\) | −29500.9 | − | 51097.1i | −0.141875 | − | 0.245735i | ||||
\(457\) | 32733.7 | + | 122164.i | 0.156734 | + | 0.584938i | 0.998951 | + | 0.0457993i | \(0.0145835\pi\) |
−0.842217 | + | 0.539139i | \(0.818750\pi\) | |||||||
\(458\) | −63541.8 | − | 63541.8i | −0.302921 | − | 0.302921i | ||||
\(459\) | −56102.0 | + | 209375.i | −0.266289 | + | 0.993803i | ||||
\(460\) | 1937.87 | + | 3356.50i | 0.00915820 | + | 0.0158625i | ||||
\(461\) | −163994. | − | 43942.0i | −0.771659 | − | 0.206765i | −0.148555 | − | 0.988904i | \(-0.547462\pi\) |
−0.623104 | + | 0.782139i | \(0.714129\pi\) | |||||||
\(462\) | 285434. | − | 76481.8i | 1.33728 | − | 0.358323i | ||||
\(463\) | −17588.9 | − | 65642.6i | −0.0820496 | − | 0.306213i | 0.912690 | − | 0.408654i | \(-0.134002\pi\) |
−0.994739 | + | 0.102440i | \(0.967335\pi\) | |||||||
\(464\) | −2821.40 | + | 10529.6i | −0.0131048 | + | 0.0489076i | ||||
\(465\) | −47226.7 | + | 27266.3i | −0.218414 | + | 0.126102i | ||||
\(466\) | 110269. | + | 29546.5i | 0.507787 | + | 0.136061i | ||||
\(467\) | −78715.9 | + | 78715.9i | −0.360935 | + | 0.360935i | −0.864157 | − | 0.503222i | \(-0.832148\pi\) |
0.503222 | + | 0.864157i | \(0.332148\pi\) | |||||||
\(468\) | 18405.6 | − | 4931.77i | 0.0840348 | − | 0.0225171i | ||||
\(469\) | −127282. | + | 73486.1i | −0.578656 | + | 0.334087i | ||||
\(470\) | 38730.9 | 0.175332 | ||||||||
\(471\) | 11943.2i | 0.0538367i | ||||||||
\(472\) | 41628.6 | − | 24034.3i | 0.186856 | − | 0.107881i | ||||
\(473\) | 162664. | + | 162664.i | 0.727059 | + | 0.727059i | ||||
\(474\) | 148814. | + | 85917.9i | 0.662350 | + | 0.382408i | ||||
\(475\) | 101993. | + | 101993.i | 0.452045 | + | 0.452045i | ||||
\(476\) | −137478. | + | 36837.2i | −0.606765 | + | 0.162582i | ||||
\(477\) | −58518.2 | + | 101357.i | −0.257190 | + | 0.445466i | ||||
\(478\) | 44841.4 | − | 77667.5i | 0.196256 | − | 0.339926i | ||||
\(479\) | −206223. | − | 55257.4i | −0.898808 | − | 0.240835i | −0.220304 | − | 0.975431i | \(-0.570705\pi\) |
−0.678504 | + | 0.734596i | \(0.737372\pi\) | |||||||
\(480\) | 11021.4i | 0.0478361i | ||||||||
\(481\) | 16769.5 | + | 94974.2i | 0.0724820 | + | 0.410502i | ||||
\(482\) | 166158. | 0.715199 | ||||||||
\(483\) | 9812.66 | − | 36621.3i | 0.0420622 | − | 0.156978i | ||||
\(484\) | 281001. | + | 162236.i | 1.19955 | + | 0.692559i | ||||
\(485\) | −43779.4 | − | 25276.0i | −0.186117 | − | 0.107455i | ||||
\(486\) | −33996.4 | − | 126876.i | −0.143933 | − | 0.537166i | ||||
\(487\) | 280352. | − | 280352.i | 1.18208 | − | 1.18208i | 0.202872 | − | 0.979205i | \(-0.434972\pi\) |
0.979205 | − | 0.202872i | \(-0.0650276\pi\) | |||||||
\(488\) | −75097.2 | + | 130072.i | −0.315344 | + | 0.546191i | ||||
\(489\) | 282275. | − | 282275.i | 1.18047 | − | 1.18047i | ||||
\(490\) | −5453.84 | − | 9446.33i | −0.0227149 | − | 0.0393433i | ||||
\(491\) | −209852. | −0.870463 | −0.435232 | − | 0.900318i | \(-0.643334\pi\) | ||||
−0.435232 | + | 0.900318i | \(0.643334\pi\) | |||||||
\(492\) | 94154.1i | 0.388963i | ||||||||
\(493\) | 36509.2 | + | 63235.8i | 0.150213 | + | 0.260177i | ||||
\(494\) | −12550.2 | − | 46837.9i | −0.0514276 | − | 0.191930i | ||||
\(495\) | −31917.3 | − | 31917.3i | −0.130261 | − | 0.130261i | ||||
\(496\) | 14836.1 | − | 55369.1i | 0.0603055 | − | 0.225063i | ||||
\(497\) | 7518.66 | + | 13022.7i | 0.0304388 | + | 0.0527215i | ||||
\(498\) | 111078. | + | 29763.1i | 0.447886 | + | 0.120011i | ||||
\(499\) | 320541. | − | 85888.8i | 1.28731 | − | 0.344933i | 0.450671 | − | 0.892690i | \(-0.351185\pi\) |
0.836638 | + | 0.547757i | \(0.184518\pi\) | |||||||
\(500\) | −14326.9 | − | 53468.8i | −0.0573077 | − | 0.213875i | ||||
\(501\) | 31109.3 | − | 116102.i | 0.123941 | − | 0.462554i | ||||
\(502\) | −247566. | + | 142932.i | −0.982390 | + | 0.567183i | ||||
\(503\) | −216377. | − | 57978.0i | −0.855215 | − | 0.229154i | −0.195531 | − | 0.980698i | \(-0.562643\pi\) |
−0.659684 | + | 0.751543i | \(0.729310\pi\) | |||||||
\(504\) | 22450.5 | − | 22450.5i | 0.0883821 | − | 0.0883821i | ||||
\(505\) | 98825.6 | − | 26480.2i | 0.387513 | − | 0.103834i | ||||
\(506\) | 49066.9 | − | 28328.8i | 0.191640 | − | 0.110644i | ||||
\(507\) | −252852. | −0.983674 | ||||||||
\(508\) | 3362.07i | 0.0130280i | ||||||||
\(509\) | −319612. | + | 184528.i | −1.23364 | + | 0.712240i | −0.967786 | − | 0.251774i | \(-0.918986\pi\) |
−0.265850 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(510\) | 52202.0 | + | 52202.0i | 0.200700 | + | 0.200700i | ||||
\(511\) | 242376. | + | 139936.i | 0.928213 | + | 0.535904i | ||||
\(512\) | −8192.00 | − | 8192.00i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −118856. | + | 31847.5i | −0.451635 | + | 0.121015i | ||||
\(514\) | −102900. | + | 178229.i | −0.389485 | + | 0.674607i | ||||
\(515\) | 13585.8 | − | 23531.3i | 0.0512236 | − | 0.0887219i | ||||
\(516\) | 81070.2 | + | 21722.7i | 0.304482 | + | 0.0815857i | ||||
\(517\) | − | 566186.i | − | 2.11825i | ||||||
\(518\) | 103322. | + | 123076.i | 0.385066 | + | 0.458685i | ||||
\(519\) | −404218. | −1.50065 | ||||||||
\(520\) | −2344.35 | + | 8749.23i | −0.00866993 | + | 0.0323566i | ||||
\(521\) | 143181. | + | 82665.5i | 0.527484 | + | 0.304543i | 0.739991 | − | 0.672616i | \(-0.234830\pi\) |
−0.212507 | + | 0.977160i | \(0.568163\pi\) | |||||||
\(522\) | −14106.3 | − | 8144.27i | −0.0517692 | − | 0.0298890i | ||||
\(523\) | 49592.3 | + | 185081.i | 0.181306 | + | 0.676642i | 0.995391 | + | 0.0958968i | \(0.0305719\pi\) |
−0.814086 | + | 0.580745i | \(0.802761\pi\) | |||||||
\(524\) | −2451.47 | + | 2451.47i | −0.00892822 | + | 0.00892822i | ||||
\(525\) | −131783. | + | 228256.i | −0.478126 | + | 0.828138i | ||||
\(526\) | −228087. | + | 228087.i | −0.824382 | + | 0.824382i | ||||
\(527\) | −191981. | − | 332520.i | −0.691252 | − | 1.19728i | ||||
\(528\) | 161116. | 0.577926 | ||||||||
\(529\) | 272572.i | 0.974024i | ||||||||
\(530\) | −27817.0 | − | 48180.5i | −0.0990281 | − | 0.171522i | ||||
\(531\) | 18589.6 | + | 69377.4i | 0.0659297 | + | 0.246053i | ||||
\(532\) | −57131.1 | − | 57131.1i | −0.201859 | − | 0.201859i | ||||
\(533\) | −20027.4 | + | 74743.1i | −0.0704968 | + | 0.263097i | ||||
\(534\) | −136583. | − | 236569.i | −0.478976 | − | 0.829611i | ||||
\(535\) | −12855.5 | − | 3444.63i | −0.0449141 | − | 0.0120347i | ||||
\(536\) | −77402.9 | + | 20740.0i | −0.269418 | + | 0.0721905i | ||||
\(537\) | 109354. | + | 408116.i | 0.379216 | + | 1.41525i | ||||
\(538\) | 75010.1 | − | 279941.i | 0.259152 | − | 0.967170i | ||||
\(539\) | −138091. | + | 79726.8i | −0.475322 | + | 0.274427i | ||||
\(540\) | 22202.1 | + | 5949.04i | 0.0761389 | + | 0.0204014i | ||||
\(541\) | −367330. | + | 367330.i | −1.25505 | + | 1.25505i | −0.301627 | + | 0.953426i | \(0.597530\pi\) |
−0.953426 | + | 0.301627i | \(0.902470\pi\) | |||||||
\(542\) | 236227. | − | 63296.8i | 0.804138 | − | 0.215468i | ||||
\(543\) | 86729.1 | − | 50073.1i | 0.294148 | − | 0.169826i | ||||
\(544\) | −77601.3 | −0.262223 | ||||||||
\(545\) | 29694.1i | 0.0999716i | ||||||||
\(546\) | 76734.7 | − | 44302.8i | 0.257399 | − | 0.148609i | ||||
\(547\) | 289443. | + | 289443.i | 0.967360 | + | 0.967360i | 0.999484 | − | 0.0321237i | \(-0.0102270\pi\) |
−0.0321237 | + | 0.999484i | \(0.510227\pi\) | |||||||
\(548\) | −166915. | − | 96368.5i | −0.555820 | − | 0.320903i | ||||
\(549\) | −158691. | − | 158691.i | −0.526511 | − | 0.526511i | ||||
\(550\) | −380454. | + | 101942.i | −1.25770 | + | 0.336999i | ||||
\(551\) | −20725.2 | + | 35897.1i | −0.0682647 | + | 0.118238i | ||||
\(552\) | 10335.7 | − | 17901.9i | 0.0339203 | − | 0.0587518i | ||||
\(553\) | 227289. | + | 60902.0i | 0.743239 | + | 0.199150i | ||||
\(554\) | 153398.i | 0.499803i | ||||||||
\(555\) | 28489.7 | − | 78332.0i | 0.0924915 | − | 0.254304i | ||||
\(556\) | −266720. | −0.862792 | ||||||||
\(557\) | −6371.77 | + | 23779.8i | −0.0205376 | + | 0.0766473i | −0.975434 | − | 0.220292i | \(-0.929299\pi\) |
0.954896 | + | 0.296939i | \(0.0959658\pi\) | |||||||
\(558\) | 74176.8 | + | 42826.0i | 0.238232 | + | 0.137543i | ||||
\(559\) | 59736.0 | + | 34488.6i | 0.191167 | + | 0.110370i | ||||
\(560\) | 3906.21 | + | 14578.2i | 0.0124560 | + | 0.0464865i | ||||
\(561\) | 763113. | − | 763113.i | 2.42473 | − | 2.42473i | ||||
\(562\) | 127870. | − | 221477.i | 0.404851 | − | 0.701223i | ||||
\(563\) | 336579. | − | 336579.i | 1.06187 | − | 1.06187i | 0.0639113 | − | 0.997956i | \(-0.479643\pi\) |
0.997956 | − | 0.0639113i | \(-0.0203575\pi\) | |||||||
\(564\) | −103286. | − | 178896.i | −0.324700 | − | 0.562396i | ||||
\(565\) | −40460.6 | −0.126746 | ||||||||
\(566\) | − | 20471.3i | − | 0.0639018i | ||||||
\(567\) | −169251. | − | 293151.i | −0.526459 | − | 0.911854i | ||||
\(568\) | 2122.00 | + | 7919.40i | 0.00657730 | + | 0.0245468i | ||||
\(569\) | −203824. | − | 203824.i | −0.629552 | − | 0.629552i | 0.318404 | − | 0.947955i | \(-0.396853\pi\) |
−0.947955 | + | 0.318404i | \(0.896853\pi\) | |||||||
\(570\) | −10846.6 | + | 40480.2i | −0.0333845 | + | 0.124593i | ||||
\(571\) | −78695.6 | − | 136305.i | −0.241367 | − | 0.418060i | 0.719737 | − | 0.694247i | \(-0.244262\pi\) |
−0.961104 | + | 0.276187i | \(0.910929\pi\) | |||||||
\(572\) | 127900. | + | 34270.8i | 0.390913 | + | 0.104745i | ||||
\(573\) | 717407. | − | 192229.i | 2.18503 | − | 0.585476i | ||||
\(574\) | 33370.1 | + | 124539.i | 0.101282 | + | 0.377990i | ||||
\(575\) | −13079.2 | + | 48812.4i | −0.0395592 | + | 0.147637i | ||||
\(576\) | 14991.6 | − | 8655.42i | 0.0451860 | − | 0.0260882i | ||||
\(577\) | −398717. | − | 106836.i | −1.19760 | − | 0.320897i | −0.395716 | − | 0.918373i | \(-0.629504\pi\) |
−0.801887 | + | 0.597476i | \(0.796170\pi\) | |||||||
\(578\) | −200509. | + | 200509.i | −0.600176 | + | 0.600176i | ||||
\(579\) | −363431. | + | 97381.1i | −1.08409 | + | 0.290481i | ||||
\(580\) | 6705.51 | − | 3871.43i | 0.0199331 | − | 0.0115084i | ||||
\(581\) | 157472. | 0.466500 | ||||||||
\(582\) | 269620.i | 0.795986i | ||||||||
\(583\) | −704325. | + | 406642.i | −2.07222 | + | 1.19640i | ||||
\(584\) | 107900. | + | 107900.i | 0.316371 | + | 0.316371i | ||||
\(585\) | −11721.2 | − | 6767.21i | −0.0342498 | − | 0.0197742i | ||||
\(586\) | −5255.45 | − | 5255.45i | −0.0153044 | − | 0.0153044i | ||||
\(587\) | 262411. | − | 70312.8i | 0.761563 | − | 0.204060i | 0.142922 | − | 0.989734i | \(-0.454350\pi\) |
0.618641 | + | 0.785674i | \(0.287684\pi\) | |||||||
\(588\) | −29088.1 | + | 50382.0i | −0.0841319 | + | 0.145721i | ||||
\(589\) | 108982. | − | 188762.i | 0.314140 | − | 0.544107i | ||||
\(590\) | −32979.0 | − | 8836.69i | −0.0947400 | − | 0.0253855i | ||||
\(591\) | − | 151580.i | − | 0.433976i | ||||||
\(592\) | 37046.8 | + | 79398.4i | 0.105708 | + | 0.226552i | ||||
\(593\) | 338120. | 0.961528 | 0.480764 | − | 0.876850i | \(-0.340359\pi\) | ||||
0.480764 | + | 0.876850i | \(0.340359\pi\) | |||||||
\(594\) | 86965.9 | − | 324561.i | 0.246477 | − | 0.919864i | ||||
\(595\) | 87549.6 | + | 50546.8i | 0.247298 | + | 0.142777i | ||||
\(596\) | −173443. | − | 100137.i | −0.488275 | − | 0.281905i | ||||
\(597\) | −18151.9 | − | 67743.7i | −0.0509299 | − | 0.190073i | ||||
\(598\) | 12012.7 | − | 12012.7i | 0.0335923 | − | 0.0335923i | ||||
\(599\) | −62264.0 | + | 107844.i | −0.173534 | + | 0.300569i | −0.939653 | − | 0.342129i | \(-0.888852\pi\) |
0.766119 | + | 0.642698i | \(0.222185\pi\) | |||||||
\(600\) | −101614. | + | 101614.i | −0.282261 | + | 0.282261i | ||||
\(601\) | −10591.5 | − | 18345.0i | −0.0293230 | − | 0.0507889i | 0.850992 | − | 0.525179i | \(-0.176002\pi\) |
−0.880314 | + | 0.474391i | \(0.842668\pi\) | |||||||
\(602\) | 114931. | 0.317136 | ||||||||
\(603\) | − | 119737.i | − | 0.329300i | ||||||
\(604\) | 52058.5 | + | 90168.0i | 0.142698 | + | 0.247160i | ||||
\(605\) | −59649.4 | − | 222615.i | −0.162965 | − | 0.608195i | ||||
\(606\) | −385854. | − | 385854.i | −1.05070 | − | 1.05070i | ||||
\(607\) | 62385.9 | − | 232827.i | 0.169320 | − | 0.631912i | −0.828129 | − | 0.560537i | \(-0.810595\pi\) |
0.997450 | − | 0.0713746i | \(-0.0227386\pi\) | |||||||
\(608\) | −22026.0 | − | 38150.1i | −0.0595838 | − | 0.103202i | ||||
\(609\) | −73161.0 | − | 19603.4i | −0.197263 | − | 0.0528564i | ||||
\(610\) | 103046. | − | 27611.0i | 0.276930 | − | 0.0742033i | ||||
\(611\) | −43939.4 | − | 163984.i | −0.117699 | − | 0.439258i | ||||
\(612\) | 30010.9 | − | 112002.i | 0.0801264 | − | 0.299036i | ||||
\(613\) | 68391.4 | − | 39485.8i | 0.182004 | − | 0.105080i | −0.406230 | − | 0.913771i | \(-0.633157\pi\) |
0.588234 | + | 0.808691i | \(0.299823\pi\) | |||||||
\(614\) | −68102.3 | − | 18248.0i | −0.180645 | − | 0.0484036i | ||||
\(615\) | 47288.6 | − | 47288.6i | 0.125028 | − | 0.125028i | ||||
\(616\) | 213111. | − | 57102.8i | 0.561622 | − | 0.150486i | ||||
\(617\) | −491855. | + | 283973.i | −1.29201 | + | 0.745944i | −0.979011 | − | 0.203809i | \(-0.934668\pi\) |
−0.313002 | + | 0.949753i | \(0.601335\pi\) | |||||||
\(618\) | −144920. | −0.379446 | ||||||||
\(619\) | 600999.i | 1.56853i | 0.620427 | + | 0.784264i | \(0.286959\pi\) | ||||
−0.620427 | + | 0.784264i | \(0.713041\pi\) | |||||||
\(620\) | −35260.4 | + | 20357.6i | −0.0917284 | + | 0.0529594i | ||||
\(621\) | −30483.6 | − | 30483.6i | −0.0790465 | − | 0.0790465i | ||||
\(622\) | 218833. | + | 126343.i | 0.565630 | + | 0.326566i | ||||
\(623\) | −264504. | − | 264504.i | −0.681486 | − | 0.681486i | ||||
\(624\) | 46664.1 | − | 12503.6i | 0.119843 | − | 0.0321119i | ||||
\(625\) | 165563. | − | 286764.i | 0.423843 | − | 0.734117i | ||||
\(626\) | 2535.08 | − | 4390.89i | 0.00646909 | − | 0.0112048i | ||||
\(627\) | 591758. | + | 158561.i | 1.50525 | + | 0.403331i | ||||
\(628\) | 8917.02i | 0.0226100i | ||||||||
\(629\) | 551531. | + | 200594.i | 1.39402 | + | 0.507011i | ||||
\(630\) | −22551.4 | −0.0568188 | ||||||||
\(631\) | 43382.0 | − | 161904.i | 0.108956 | − | 0.406629i | −0.889808 | − | 0.456335i | \(-0.849162\pi\) |
0.998764 | + | 0.0497060i | \(0.0158284\pi\) | |||||||
\(632\) | 111108. | + | 64148.0i | 0.278170 | + | 0.160601i | ||||
\(633\) | 155468. | + | 89759.3i | 0.388001 | + | 0.224012i | ||||
\(634\) | −137077. | − | 511579.i | −0.341025 | − | 1.27272i | ||||
\(635\) | 1688.59 | − | 1688.59i | 0.00418771 | − | 0.00418771i | ||||
\(636\) | −148362. | + | 256971.i | −0.366783 | + | 0.635286i | ||||
\(637\) | −33807.9 | + | 33807.9i | −0.0833181 | + | 0.0833181i | ||||
\(638\) | −56594.4 | − | 98024.3i | −0.139037 | − | 0.240820i | ||||
\(639\) | −12250.7 | −0.0300027 | ||||||||
\(640\) | 8228.82i | 0.0200899i | ||||||||
\(641\) | −87389.2 | − | 151363.i | −0.212687 | − | 0.368385i | 0.739867 | − | 0.672753i | \(-0.234888\pi\) |
−0.952555 | + | 0.304368i | \(0.901555\pi\) | |||||||
\(642\) | 18372.0 | + | 68565.1i | 0.0445744 | + | 0.166354i | ||||
\(643\) | −419716. | − | 419716.i | −1.01516 | − | 1.01516i | −0.999883 | − | 0.0152756i | \(-0.995137\pi\) |
−0.0152756 | − | 0.999883i | \(-0.504863\pi\) | |||||||
\(644\) | 7326.33 | − | 27342.2i | 0.0176650 | − | 0.0659268i | ||||
\(645\) | −29807.1 | − | 51627.4i | −0.0716474 | − | 0.124097i | ||||
\(646\) | −285019. | − | 76370.5i | −0.682980 | − | 0.183004i | ||||
\(647\) | 83195.8 | − | 22292.3i | 0.198744 | − | 0.0532532i | −0.158074 | − | 0.987427i | \(-0.550528\pi\) |
0.356818 | + | 0.934174i | \(0.383862\pi\) | |||||||
\(648\) | −47767.8 | − | 178272.i | −0.113759 | − | 0.424554i | ||||
\(649\) | −129179. | + | 482102.i | −0.306692 | + | 1.14459i | ||||
\(650\) | −102279. | + | 59051.0i | −0.242081 | + | 0.139766i | ||||
\(651\) | 384711. | + | 103083.i | 0.907764 | + | 0.243235i | ||||
\(652\) | 210752. | − | 210752.i | 0.495767 | − | 0.495767i | ||||
\(653\) | −75735.3 | + | 20293.2i | −0.177612 | + | 0.0475909i | −0.346529 | − | 0.938039i | \(-0.612640\pi\) |
0.168917 | + | 0.985630i | \(0.445973\pi\) | |||||||
\(654\) | 137155. | − | 79186.7i | 0.320669 | − | 0.185139i | ||||
\(655\) | 2462.49 | 0.00573974 | ||||||||
\(656\) | 70297.3i | 0.163354i | ||||||||
\(657\) | −197461. | + | 114004.i | −0.457457 | + | 0.264113i | ||||
\(658\) | −200021. | − | 200021.i | −0.461982 | − | 0.461982i | ||||
\(659\) | 175489. | + | 101319.i | 0.404091 | + | 0.233302i | 0.688248 | − | 0.725476i | \(-0.258380\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(660\) | −80920.3 | − | 80920.3i | −0.185767 | − | 0.185767i | ||||
\(661\) | −595926. | + | 159678.i | −1.36392 | + | 0.365462i | −0.865255 | − | 0.501332i | \(-0.832844\pi\) |
−0.498667 | + | 0.866794i | \(0.666177\pi\) | |||||||
\(662\) | −228337. | + | 395491.i | −0.521026 | + | 0.902444i | ||||
\(663\) | 161798. | − | 280242.i | 0.368083 | − | 0.637538i | ||||
\(664\) | 82932.7 | + | 22221.8i | 0.188100 | + | 0.0504013i | ||||
\(665\) | 57387.9i | 0.129771i | ||||||||
\(666\) | −128923. | + | 22763.8i | −0.290658 | + | 0.0513212i | ||||
\(667\) | −14522.2 | −0.0326422 | ||||||||
\(668\) | 23226.8 | − | 86683.8i | 0.0520520 | − | 0.194261i | ||||
\(669\) | 663223. | + | 382912.i | 1.48186 | + | 0.855552i | ||||
\(670\) | 49292.0 | + | 28458.7i | 0.109806 | + | 0.0633966i | ||||
\(671\) | −403631. | − | 1.50637e6i | −0.896478 | − | 3.34570i | ||||
\(672\) | 56919.0 | − | 56919.0i | 0.126043 | − | 0.126043i | ||||
\(673\) | −180783. | + | 313125.i | −0.399141 | + | 0.691333i | −0.993620 | − | 0.112778i | \(-0.964025\pi\) |
0.594479 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(674\) | 36511.8 | − | 36511.8i | 0.0803736 | − | 0.0803736i | ||||
\(675\) | 149848. | + | 259545.i | 0.328885 | + | 0.569645i | ||||
\(676\) | −188785. | −0.413117 | ||||||||
\(677\) | − | 352425.i | − | 0.768935i | −0.923138 | − | 0.384468i | \(-0.874385\pi\) | ||
0.923138 | − | 0.384468i | \(-0.125615\pi\) | |||||||
\(678\) | 107898. | + | 186886.i | 0.234723 | + | 0.406552i | ||||
\(679\) | 95558.5 | + | 356629.i | 0.207267 | + | 0.773530i | ||||
\(680\) | 38975.0 | + | 38975.0i | 0.0842886 | + | 0.0842886i | ||||
\(681\) | −244865. | + | 913850.i | −0.527999 | + | 1.97052i | ||||
\(682\) | 297597. | + | 515453.i | 0.639823 | + | 1.10821i | ||||
\(683\) | 764061. | + | 204730.i | 1.63790 | + | 0.438873i | 0.956189 | − | 0.292750i | \(-0.0945703\pi\) |
0.681709 | + | 0.731623i | \(0.261237\pi\) | |||||||
\(684\) | 63580.3 | − | 17036.3i | 0.135897 | − | 0.0364135i | ||||
\(685\) | 35431.9 | + | 132233.i | 0.0755114 | + | 0.281813i | ||||
\(686\) | −93562.9 | + | 349182.i | −0.198818 | + | 0.741999i | ||||
\(687\) | 294816. | − | 170212.i | 0.624651 | − | 0.360642i | ||||
\(688\) | 60528.6 | + | 16218.6i | 0.127875 | + | 0.0342639i | ||||
\(689\) | −172435. | + | 172435.i | −0.363235 | + | 0.363235i | ||||
\(690\) | −14182.2 | + | 3800.12i | −0.0297884 | + | 0.00798177i | ||||
\(691\) | −159216. | + | 91923.4i | −0.333450 | + | 0.192517i | −0.657372 | − | 0.753567i | \(-0.728332\pi\) |
0.323922 | + | 0.946084i | \(0.394998\pi\) | |||||||
\(692\) | −301797. | −0.630236 | ||||||||
\(693\) | 329667.i | 0.686449i | ||||||||
\(694\) | −354081. | + | 204429.i | −0.735164 | + | 0.424447i | ||||
\(695\) | 133959. | + | 133959.i | 0.277334 | + | 0.277334i | ||||
\(696\) | −35763.9 | − | 20648.3i | −0.0738289 | − | 0.0426251i | ||||
\(697\) | 332957. | + | 332957.i | 0.685365 | + | 0.685365i | ||||
\(698\) | 453923. | − | 121628.i | 0.931690 | − | 0.249645i | ||||
\(699\) | −216234. | + | 374529.i | −0.442558 | + | 0.766533i | ||||
\(700\) | −98392.2 | + | 170420.i | −0.200800 | + | 0.347796i | ||||
\(701\) | −25008.9 | − | 6701.12i | −0.0508931 | − | 0.0136368i | 0.233283 | − | 0.972409i | \(-0.425053\pi\) |
−0.284176 | + | 0.958772i | \(0.591720\pi\) | |||||||
\(702\) | − | 100752.i | − | 0.204445i | ||||||
\(703\) | 57928.5 | + | 328078.i | 0.117215 | + | 0.663845i | ||||
\(704\) | 120293. | 0.242714 | ||||||||
\(705\) | −37975.1 | + | 141725.i | −0.0764048 | + | 0.285147i | ||||
\(706\) | −5394.08 | − | 3114.27i | −0.0108220 | − | 0.00624809i | ||||
\(707\) | −647129. | − | 373620.i | −1.29465 | − | 0.747466i | ||||
\(708\) | 47130.5 | + | 175894.i | 0.0940234 | + | 0.350900i | ||||
\(709\) | 313781. | − | 313781.i | 0.624215 | − | 0.624215i | −0.322392 | − | 0.946606i | \(-0.604487\pi\) |
0.946606 | + | 0.322392i | \(0.104487\pi\) | |||||||
\(710\) | 2911.73 | − | 5043.26i | 0.00577609 | − | 0.0100045i | ||||
\(711\) | −135554. | + | 135554.i | −0.268147 | + | 0.268147i | ||||
\(712\) | −101976. | − | 176627.i | −0.201157 | − | 0.348415i | ||||
\(713\) | 76363.7 | 0.150213 | ||||||||
\(714\) | − | 539183.i | − | 1.05764i | ||||||
\(715\) | −47025.2 | − | 81450.1i | −0.0919853 | − | 0.159323i | ||||
\(716\) | 81646.1 | + | 304707.i | 0.159261 | + | 0.594370i | ||||
\(717\) | 240237. | + | 240237.i | 0.467306 | + | 0.467306i | ||||
\(718\) | −56431.2 | + | 210604.i | −0.109464 | + | 0.408524i | ||||
\(719\) | 136676. | + | 236729.i | 0.264383 | + | 0.457924i | 0.967402 | − | 0.253247i | \(-0.0814984\pi\) |
−0.703019 | + | 0.711171i | \(0.748165\pi\) | |||||||
\(720\) | −11876.7 | − | 3182.34i | −0.0229102 | − | 0.00613878i | ||||
\(721\) | −191687. | + | 51362.4i | −0.368742 | + | 0.0988040i | ||||
\(722\) | 52048.3 | + | 194247.i | 0.0998463 | + | 0.372632i | ||||
\(723\) | −162916. | + | 608009.i | −0.311663 | + | 1.16314i | ||||
\(724\) | 64753.7 | − | 37385.6i | 0.123534 | − | 0.0713226i | ||||
\(725\) | 97516.0 | + | 26129.3i | 0.185524 | + | 0.0497110i | ||||
\(726\) | −869176. | + | 869176.i | −1.64905 | + | 1.64905i | ||||
\(727\) | −142052. | + | 38062.8i | −0.268769 | + | 0.0720165i | −0.390687 | − | 0.920524i | \(-0.627762\pi\) |
0.121917 | + | 0.992540i | \(0.461096\pi\) | |||||||
\(728\) | 57291.6 | − | 33077.3i | 0.108101 | − | 0.0624120i | ||||
\(729\) | −163074. | −0.306852 | ||||||||
\(730\) | − | 108385.i | − | 0.203387i | ||||||
\(731\) | 363506. | − | 209870.i | 0.680263 | − | 0.392750i | ||||
\(732\) | −402332. | − | 402332.i | −0.750865 | − | 0.750865i | ||||
\(733\) | 267208. | + | 154273.i | 0.497327 | + | 0.287132i | 0.727609 | − | 0.685992i | \(-0.240632\pi\) |
−0.230282 | + | 0.973124i | \(0.573965\pi\) | |||||||
\(734\) | 433529. | + | 433529.i | 0.804685 | + | 0.804685i | ||||
\(735\) | 39913.7 | − | 10694.8i | 0.0738834 | − | 0.0197970i | ||||
\(736\) | 7716.81 | − | 13365.9i | 0.0142457 | − | 0.0246742i | ||||
\(737\) | 416023. | − | 720574.i | 0.765919 | − | 1.32661i | ||||
\(738\) | −101460. | − | 27186.2i | −0.186287 | − | 0.0499155i | ||||
\(739\) | − | 161160.i | − | 0.295099i | −0.989055 | − | 0.147549i | \(-0.952861\pi\) | ||
0.989055 | − | 0.147549i | \(-0.0471386\pi\) | |||||||
\(740\) | 21271.0 | − | 58484.3i | 0.0388440 | − | 0.106801i | ||||
\(741\) | 183696. | 0.334551 | ||||||||
\(742\) | −105165. | + | 392481.i | −0.191013 | + | 0.712870i | ||||
\(743\) | −371981. | − | 214763.i | −0.673819 | − | 0.389029i | 0.123703 | − | 0.992319i | \(-0.460523\pi\) |
−0.797522 | + | 0.603290i | \(0.793856\pi\) | |||||||
\(744\) | 188061. | + | 108577.i | 0.339746 | + | 0.196152i | ||||
\(745\) | 36817.5 | + | 137405.i | 0.0663349 | + | 0.247565i | ||||
\(746\) | 344683. | − | 344683.i | 0.619359 | − | 0.619359i | ||||
\(747\) | −64145.4 | + | 111103.i | −0.114954 | + | 0.199106i | ||||
\(748\) | 569755. | − | 569755.i | 1.01832 | − | 1.01832i | ||||
\(749\) | 48601.6 | + | 84180.5i | 0.0866338 | + | 0.150054i | ||||
\(750\) | 209702. | 0.372803 | ||||||||
\(751\) | − | 149933.i | − | 0.265838i | −0.991127 | − | 0.132919i | \(-0.957565\pi\) | ||
0.991127 | − | 0.132919i | \(-0.0424349\pi\) | |||||||
\(752\) | −77115.1 | − | 133567.i | −0.136365 | − | 0.236192i | ||||
\(753\) | −280287. | − | 1.04604e6i | −0.494325 | − | 1.84485i | ||||
\(754\) | −23998.7 | − | 23998.7i | −0.0422128 | − | 0.0422128i | ||||
\(755\) | 19140.4 | − | 71432.9i | 0.0335781 | − | 0.125315i | ||||
\(756\) | −83937.3 | − | 145384.i | −0.146863 | − | 0.254374i | ||||
\(757\) | 1.05926e6 | + | 283829.i | 1.84847 | + | 0.495296i | 0.999453 | − | 0.0330697i | \(-0.0105283\pi\) |
0.849017 | + | 0.528366i | \(0.177195\pi\) | |||||||
\(758\) | 494258. | − | 132436.i | 0.860232 | − | 0.230498i | ||||
\(759\) | 55551.9 | + | 207323.i | 0.0964308 | + | 0.359885i | ||||
\(760\) | −8098.31 | + | 30223.3i | −0.0140206 | + | 0.0523256i | ||||
\(761\) | 12805.3 | − | 7393.14i | 0.0221116 | − | 0.0127661i | −0.488903 | − | 0.872338i | \(-0.662603\pi\) |
0.511015 | + | 0.859572i | \(0.329270\pi\) | |||||||
\(762\) | −12302.6 | − | 3296.46i | −0.0211878 | − | 0.00567725i | ||||
\(763\) | 153352. | − | 153352.i | 0.263415 | − | 0.263415i | ||||
\(764\) | 535631. | − | 143522.i | 0.917654 | − | 0.245885i | ||||
\(765\) | −71325.6 | + | 41179.9i | −0.121877 | + | 0.0703659i | ||||
\(766\) | 253902. | 0.432722 | ||||||||
\(767\) | 149656.i | 0.254392i | ||||||||
\(768\) | 38008.5 | − | 21944.2i | 0.0644404 | − | 0.0372047i | ||||
\(769\) | −498901. | − | 498901.i | −0.843650 | − | 0.843650i | 0.145682 | − | 0.989331i | \(-0.453462\pi\) |
−0.989331 | + | 0.145682i | \(0.953462\pi\) | |||||||
\(770\) | −135714. | − | 78354.5i | −0.228899 | − | 0.132155i | ||||
\(771\) | −551286. | − | 551286.i | −0.927402 | − | 0.927402i | ||||
\(772\) | −271345. | + | 72706.7i | −0.455289 | + | 0.121994i | ||||
\(773\) | 47564.4 | − | 82383.9i | 0.0796018 | − | 0.137874i | −0.823476 | − | 0.567351i | \(-0.807968\pi\) |
0.903078 | + | 0.429476i | \(0.141302\pi\) | |||||||
\(774\) | −46816.7 | + | 81088.8i | −0.0781481 | + | 0.135357i | ||||
\(775\) | −512780. | − | 137399.i | −0.853744 | − | 0.228760i | ||||
\(776\) | 201303.i | 0.334293i | ||||||||
\(777\) | −551669. | + | 257405.i | −0.913770 | + | 0.426359i | ||||
\(778\) | −741786. | −1.22552 | ||||||||
\(779\) | −69182.4 | + | 258192.i | −0.114004 | + | 0.425469i | ||||
\(780\) | −29716.8 | − | 17157.0i | −0.0488442 | − | 0.0282002i | ||||
\(781\) | −73724.8 | − | 42565.0i | −0.120868 | − | 0.0697832i | ||||
\(782\) | −26756.4 | − | 99856.3i | −0.0437537 | − | 0.163291i | ||||
\(783\) | −60899.2 | + | 60899.2i | −0.0993318 | + | 0.0993318i | ||||
\(784\) | −21717.8 | + | 37616.2i | −0.0353332 | + | 0.0611989i | ||||
\(785\) | 4478.55 | − | 4478.55i | 0.00726772 | − | 0.00726772i | ||||
\(786\) | −6566.86 | − | 11374.1i | −0.0106295 | − | 0.0184108i | ||||
\(787\) | −240228. | −0.387859 | −0.193930 | − | 0.981015i | \(-0.562123\pi\) | ||||
−0.193930 | + | 0.981015i | \(0.562123\pi\) | |||||||
\(788\) | − | 113172.i | − | 0.182259i | ||||||
\(789\) | −610984. | − | 1.05826e6i | −0.981468 | − | 1.69995i | ||||
\(790\) | −23585.3 | − | 88021.7i | −0.0377909 | − | 0.141038i | ||||
\(791\) | 208954. | + | 208954.i | 0.333963 | + | 0.333963i | ||||
\(792\) | −46521.0 | + | 173619.i | −0.0741650 | + | 0.276787i | ||||
\(793\) | −233807. | − | 404966.i | −0.371801 | − | 0.643979i | ||||
\(794\) | 723726. | + | 193922.i | 1.14798 | + | 0.307599i | ||||
\(795\) | 203577. | − | 54548.4i | 0.322103 | − | 0.0863073i | ||||
\(796\) | −13552.5 | − | 50578.8i | −0.0213892 | − | 0.0798256i | ||||
\(797\) | −10149.0 | + | 37876.5i | −0.0159774 | + | 0.0596284i | −0.973454 | − | 0.228882i | \(-0.926493\pi\) |
0.957477 | + | 0.288510i | \(0.0931598\pi\) | |||||||
\(798\) | 265072. | − | 153039.i | 0.416253 | − | 0.240324i | ||||
\(799\) | −997878. | − | 267381.i | −1.56309 | − | 0.418829i | ||||
\(800\) | −75867.1 | + | 75867.1i | −0.118542 | + | 0.118542i | ||||
\(801\) | 294363. | − | 78874.3i | 0.458794 | − | 0.122934i | ||||
\(802\) | 575899. | − | 332496.i | 0.895361 | − | 0.516937i | ||||
\(803\) | −1.58442e6 | −2.45720 | ||||||||
\(804\) | − | 303570.i | − | 0.469620i | ||||||
\(805\) | −17412.2 | + | 10052.9i | −0.0268696 | + | 0.0155132i | ||||
\(806\) | 126195. | + | 126195.i | 0.194255 | + | 0.194255i | ||||
\(807\) | 950823. | + | 548958.i | 1.46000 | + | 0.842931i | ||||
\(808\) | −288087. | − | 288087.i | −0.441266 | − | 0.441266i | ||||
\(809\) | −24658.9 | + | 6607.33i | −0.0376770 | + | 0.0100955i | −0.277608 | − | 0.960694i | \(-0.589542\pi\) |
0.239931 | + | 0.970790i | \(0.422875\pi\) | |||||||
\(810\) | −65545.3 | + | 113528.i | −0.0999013 | + | 0.173034i | ||||
\(811\) | 344458. | − | 596618.i | 0.523714 | − | 0.907099i | −0.475905 | − | 0.879497i | \(-0.657879\pi\) |
0.999619 | − | 0.0276027i | \(-0.00878732\pi\) | |||||||
\(812\) | −54623.5 | − | 14636.3i | −0.0828452 | − | 0.0221983i | ||||
\(813\) | 926468.i | 1.40168i | ||||||||
\(814\) | −854950. | − | 310949.i | −1.29030 | − | 0.469289i | ||||
\(815\) | −211700. | −0.318717 | ||||||||
\(816\) | 76087.0 | − | 283961.i | 0.114269 | − | 0.426459i | ||||
\(817\) | 206352. | + | 119137.i | 0.309146 | + | 0.178486i | ||||
\(818\) | 573278. | + | 330982.i | 0.856759 | + | 0.494650i | ||||
\(819\) | 25584.1 | + | 95481.2i | 0.0381419 | + | 0.142348i | ||||
\(820\) | 35306.6 | − | 35306.6i | 0.0525084 | − | 0.0525084i | ||||
\(821\) | −8141.17 | + | 14100.9i | −0.0120782 | + | 0.0209200i | −0.872001 | − | 0.489504i | \(-0.837178\pi\) |
0.859923 | + | 0.510424i | \(0.170511\pi\) | |||||||
\(822\) | 516292. | − | 516292.i | 0.764103 | − | 0.764103i | ||||
\(823\) | 156139. | + | 270441.i | 0.230522 | + | 0.399275i | 0.957962 | − | 0.286896i | \(-0.0926234\pi\) |
−0.727440 | + | 0.686171i | \(0.759290\pi\) | |||||||
\(824\) | −108200. | −0.159358 | ||||||||
\(825\) | − | 1.49212e6i | − | 2.19228i | ||||||
\(826\) | 124680. | + | 215953.i | 0.182742 | + | 0.316518i | ||||
\(827\) | 106830. | + | 398696.i | 0.156201 | + | 0.582950i | 0.999000 | + | 0.0447207i | \(0.0142398\pi\) |
−0.842799 | + | 0.538229i | \(0.819094\pi\) | |||||||
\(828\) | 16306.7 | + | 16306.7i | 0.0237851 | + | 0.0237851i | ||||
\(829\) | −32687.9 | + | 121993.i | −0.0475639 | + | 0.177511i | −0.985621 | − | 0.168969i | \(-0.945956\pi\) |
0.938058 | + | 0.346480i | \(0.112623\pi\) | |||||||
\(830\) | −30491.9 | − | 52813.5i | −0.0442617 | − | 0.0766636i | ||||
\(831\) | −561316. | − | 150404.i | −0.812841 | − | 0.217800i | ||||
\(832\) | 34840.3 | − | 9335.44i | 0.0503310 | − | 0.0134862i | ||||
\(833\) | 75301.7 | + | 281030.i | 0.108521 | + | 0.405007i | ||||
\(834\) | 261515. | − | 975988.i | 0.375980 | − | 1.40318i | ||||
\(835\) | −55202.3 | + | 31871.1i | −0.0791743 | + | 0.0457113i | ||||
\(836\) | 441818. | + | 118385.i | 0.632166 | + | 0.169388i | ||||
\(837\) | 320234. | − | 320234.i | 0.457105 | − | 0.457105i | ||||
\(838\) | 594320. | − | 159248.i | 0.846315 | − | 0.226770i | ||||
\(839\) | 586042. | − | 338352.i | 0.832540 | − | 0.480667i | −0.0221815 | − | 0.999754i | \(-0.507061\pi\) |
0.854722 | + | 0.519087i | \(0.173728\pi\) | |||||||
\(840\) | −57174.8 | −0.0810301 | ||||||||
\(841\) | − | 678269.i | − | 0.958981i | ||||||
\(842\) | 660020. | − | 381063.i | 0.930964 | − | 0.537492i | ||||
\(843\) | 685060. | + | 685060.i | 0.963992 | + | 0.963992i | ||||
\(844\) | 116075. | + | 67016.1i | 0.162950 | + | 0.0940794i | ||||
\(845\) | 94816.6 | + | 94816.6i | 0.132792 | + | 0.132792i | ||||
\(846\) | 222601. | − | 59645.7i | 0.311018 | − | 0.0833371i | ||||
\(847\) | −841616. | + | 1.45772e6i | −1.17313 | + | 2.03193i | ||||
\(848\) | −110770. | + | 191860.i | −0.154039 | + | 0.266804i | ||||
\(849\) | 74909.2 | + | 20071.8i | 0.103925 | + | 0.0278466i | ||||
\(850\) | 718675.i | 0.994706i | ||||||||
\(851\) | −89395.3 | + | 75047.4i | −0.123440 | + | 0.103628i | ||||
\(852\) | −31059.4 | −0.0427873 | ||||||||
\(853\) | −104634. | + | 390498.i | −0.143805 | + | 0.536686i | 0.856001 | + | 0.516974i | \(0.172942\pi\) |
−0.999806 | + | 0.0197123i | \(0.993725\pi\) | |||||||
\(854\) | −674763. | − | 389575.i | −0.925200 | − | 0.534165i | ||||
\(855\) | −40489.5 | − | 23376.6i | −0.0553873 | − | 0.0319778i | ||||
\(856\) | 13716.9 | + | 51192.1i | 0.0187201 | + | 0.0698643i | ||||
\(857\) | 64844.7 | − | 64844.7i | 0.0882903 | − | 0.0882903i | −0.661582 | − | 0.749873i | \(-0.730115\pi\) |
0.749873 | + | 0.661582i | \(0.230115\pi\) | |||||||
\(858\) | −250809. | + | 434414.i | −0.340697 | + | 0.590105i | ||||
\(859\) | −224873. | + | 224873.i | −0.304756 | + | 0.304756i | −0.842871 | − | 0.538115i | \(-0.819136\pi\) |
0.538115 | + | 0.842871i | \(0.319136\pi\) | |||||||
\(860\) | −22254.6 | − | 38546.1i | −0.0300900 | − | 0.0521175i | ||||
\(861\) | −488434. | −0.658870 | ||||||||
\(862\) | 841358.i | 1.13231i | ||||||||
\(863\) | −622990. | − | 1.07905e6i | −0.836488 | − | 1.44884i | −0.892813 | − | 0.450427i | \(-0.851272\pi\) |
0.0563254 | − | 0.998412i | \(-0.482062\pi\) | |||||||
\(864\) | −23689.7 | − | 88411.1i | −0.0317345 | − | 0.118435i | ||||
\(865\) | 151577. | + | 151577.i | 0.202582 | + | 0.202582i | ||||
\(866\) | −194588. | + | 726214.i | −0.259466 | + | 0.968342i | ||||
\(867\) | −537112. | − | 930305.i | −0.714540 | − | 1.23762i | ||||
\(868\) | 287233. | + | 76963.9i | 0.381237 | + | 0.102152i | ||||
\(869\) | −1.28674e6 | + | 344781.i | −1.70393 | + | 0.456567i | ||||
\(870\) | 7591.77 | + | 28332.9i | 0.0100301 | + | 0.0374328i | ||||
\(871\) | 64571.8 | − | 240985.i | 0.0851151 | − | 0.317654i | ||||
\(872\) | 102403. | − | 59122.4i | 0.134673 | − | 0.0777534i | ||||
\(873\) | −290542. | − | 77850.4i | −0.381224 | − | 0.102149i | ||||
\(874\) | 41496.7 | − | 41496.7i | 0.0543239 | − | 0.0543239i | ||||
\(875\) | 277375. | − | 74322.5i | 0.362286 | − | 0.0970743i | ||||
\(876\) | −500625. | + | 289036.i | −0.652386 | + | 0.376655i | ||||
\(877\) | 62196.2 | 0.0808658 | 0.0404329 | − | 0.999182i | \(-0.487126\pi\) | ||||
0.0404329 | + | 0.999182i | \(0.487126\pi\) | |||||||
\(878\) | − | 90861.9i | − | 0.117867i | ||||||
\(879\) | 24383.8 | − | 14078.0i | 0.0315590 | − | 0.0182206i | ||||
\(880\) | −60416.7 | − | 60416.7i | −0.0780175 | − | 0.0780175i | ||||
\(881\) | 725506. | + | 418871.i | 0.934737 | + | 0.539671i | 0.888307 | − | 0.459251i | \(-0.151882\pi\) |
0.0464303 | + | 0.998922i | \(0.485215\pi\) | |||||||
\(882\) | −45892.7 | − | 45892.7i | −0.0589938 | − | 0.0589938i | ||||
\(883\) | −474755. | + | 127210.i | −0.608904 | + | 0.163155i | −0.550078 | − | 0.835113i | \(-0.685402\pi\) |
−0.0588252 | + | 0.998268i | \(0.518735\pi\) | |||||||
\(884\) | 120802. | − | 209234.i | 0.154585 | − | 0.267749i | ||||
\(885\) | 64670.9 | − | 112013.i | 0.0825700 | − | 0.143015i | ||||
\(886\) | −462697. | − | 123979.i | −0.589426 | − | 0.157936i | ||||
\(887\) | − | 282573.i | − | 0.359156i | −0.983744 | − | 0.179578i | \(-0.942527\pi\) | ||
0.983744 | − | 0.179578i | \(-0.0574733\pi\) | |||||||
\(888\) | −326860. | + | 57713.5i | −0.414511 | + | 0.0731899i | ||||
\(889\) | −17441.1 | −0.0220683 | ||||||||
\(890\) | −37493.4 | + | 139927.i | −0.0473342 | + | 0.176654i | ||||
\(891\) | 1.65960e6 | + | 958172.i | 2.09049 | + | 1.20695i | ||||
\(892\) | 495175. | + | 285890.i | 0.622342 | + | 0.359309i | ||||
\(893\) | −151784. | − | 566466.i | −0.190337 | − | 0.710348i | ||||
\(894\) | 536484. | − | 536484.i | 0.671245 | − | 0.671245i | ||||
\(895\) | 112032. | − | 194045.i | 0.139861 | − | 0.242246i | ||||
\(896\) | 42496.9 | − | 42496.9i | 0.0529348 | − | 0.0529348i | ||||
\(897\) | 32179.0 | + | 55735.6i | 0.0399933 | + | 0.0692704i | ||||
\(898\) | −946358. | −1.17355 | ||||||||
\(899\) | − | 152557.i | − | 0.188761i | ||||||
\(900\) | −80158.9 | − | 138839.i | −0.0989616 | − | 0.171407i | ||||
\(901\) | 384072. | + | 1.43338e6i | 0.473111 | + | 1.76568i | ||||
\(902\) | −516129. | − | 516129.i | −0.634374 | − | 0.634374i | ||||
\(903\) | −112689. | + | 420560.i | −0.138199 | + | 0.515766i | ||||
\(904\) | 80559.1 | + | 139532.i | 0.0985775 | + | 0.170741i | ||||
\(905\) | −51299.2 | − | 13745.6i | −0.0626344 | − | 0.0167828i | ||||
\(906\) | −380988. | + | 102085.i | −0.464146 | + | 0.124368i | ||||
\(907\) | −147392. | − | 550076.i | −0.179168 | − | 0.668664i | −0.995804 | − | 0.0915113i | \(-0.970830\pi\) |
0.816636 | − | 0.577153i | \(-0.195836\pi\) | |||||||
\(908\) | −182821. | + | 682298.i | −0.221746 | + | 0.827566i | ||||
\(909\) | 527208. | − | 304384.i | 0.638050 | − | 0.368378i | ||||
\(910\) | −45387.6 | − | 12161.6i | −0.0548093 | − | 0.0146861i | ||||
\(911\) | 1.16096e6 | − | 1.16096e6i | 1.39887 | − | 1.39887i | 0.595574 | − | 0.803300i | \(-0.296925\pi\) |
0.803300 | − | 0.595574i | \(-0.203075\pi\) | |||||||
\(912\) | 161196. | − | 43192.4i | 0.193805 | − | 0.0519299i | ||||
\(913\) | −772053. | + | 445745.i | −0.926202 | + | 0.534743i | ||||
\(914\) | −357720. | −0.428204 | ||||||||
\(915\) | 404140.i | 0.482714i | ||||||||
\(916\) | 220115. | − | 127084.i | 0.262337 | − | 0.151460i | ||||
\(917\) | −12717.3 | − | 12717.3i | −0.0151236 | − | 0.0151236i | ||||
\(918\) | −530955. | − | 306547.i | −0.630046 | − | 0.363757i | ||||
\(919\) | 20617.6 | + | 20617.6i | 0.0244122 | + | 0.0244122i | 0.719208 | − | 0.694795i | \(-0.244505\pi\) |
−0.694795 | + | 0.719208i | \(0.744505\pi\) | |||||||
\(920\) | −10588.7 | + | 2837.24i | −0.0125103 | + | 0.00335213i | ||||
\(921\) | 133547. | − | 231310.i | 0.157440 | − | 0.272694i | ||||
\(922\) | 240103. | − | 415871.i | 0.282447 | − | 0.489212i | ||||
\(923\) | −24656.2 | − | 6606.60i | −0.0289416 | − | 0.00775487i | ||||
\(924\) | 835809.i | 0.978955i | ||||||||
\(925\) | 735318. | − | 343095.i | 0.859393 | − | 0.400987i | ||||
\(926\) | 192215. | 0.224164 | ||||||||
\(927\) | 41844.3 | − | 156165.i | 0.0486942 | − | 0.181729i | ||||
\(928\) | −26702.0 | − | 15416.4i | −0.0310062 | − | 0.0179014i | ||||
\(929\) | 303499. | + | 175226.i | 0.351663 | + | 0.203033i | 0.665417 | − | 0.746471i | \(-0.268254\pi\) |
−0.313755 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(930\) | −39920.7 | − | 148986.i | −0.0461564 | − | 0.172258i | ||||
\(931\) | −116786. | + | 116786.i | −0.134738 | + | 0.134738i | ||||
\(932\) | −161445. | + | 279631.i | −0.185863 | + | 0.321924i | ||||
\(933\) | −676881. | + | 676881.i | −0.777588 | + | 0.777588i | ||||
\(934\) | −157432. | − | 272680.i | −0.180467 | − | 0.312579i | ||||
\(935\) | −572316. | −0.654655 | ||||||||
\(936\) | 53895.4i | 0.0615177i | ||||||||
\(937\) | −280332. | − | 485549.i | −0.319296 | − | 0.553036i | 0.661046 | − | 0.750346i | \(-0.270113\pi\) |
−0.980341 | + | 0.197309i | \(0.936780\pi\) | |||||||
\(938\) | −107591. | − | 401536.i | −0.122284 | − | 0.456371i | ||||
\(939\) | 13581.6 | + | 13581.6i | 0.0154036 | + | 0.0154036i | ||||
\(940\) | −28353.0 | + | 105815.i | −0.0320880 | + | 0.119754i | ||||
\(941\) | 765015. | + | 1.32504e6i | 0.863954 | + | 1.49641i | 0.868082 | + | 0.496421i | \(0.165353\pi\) |
−0.00412832 | + | 0.999991i | \(0.501314\pi\) | |||||||
\(942\) | −32629.4 | − | 8743.02i | −0.0367711 | − | 0.00985280i | ||||
\(943\) | −90457.7 | + | 24238.1i | −0.101724 | + | 0.0272568i | ||||
\(944\) | 35188.6 | + | 131326.i | 0.0394874 | + | 0.147369i | ||||
\(945\) | −30861.3 | + | 115176.i | −0.0345581 | + | 0.128973i | ||||
\(946\) | −563485. | + | 325328.i | −0.629651 | + | 0.363529i | ||||
\(947\) | −41146.1 | − | 11025.1i | −0.0458806 | − | 0.0122937i | 0.235806 | − | 0.971800i | \(-0.424227\pi\) |
−0.281686 | + | 0.959507i | \(0.590894\pi\) | |||||||
\(948\) | −343671. | + | 343671.i | −0.382408 | + | 0.382408i | ||||
\(949\) | −458896. | + | 122961.i | −0.509544 | + | 0.136532i | ||||
\(950\) | −353313. | + | 203985.i | −0.391483 | + | 0.226023i | ||||
\(951\) | 2.00638e6 | 2.21847 | ||||||||
\(952\) | − | 402565.i | − | 0.444183i | ||||||
\(953\) | −231448. | + | 133627.i | −0.254840 | + | 0.147132i | −0.621979 | − | 0.783034i | \(-0.713671\pi\) |
0.367138 | + | 0.930166i | \(0.380338\pi\) | |||||||
\(954\) | −234073. | − | 234073.i | −0.257190 | − | 0.257190i | ||||
\(955\) | −341102. | − | 196936.i | −0.374006 | − | 0.215932i | ||||
\(956\) | 179366. | + | 179366.i | 0.196256 | + | 0.196256i | ||||
\(957\) | 414183. | − | 110980.i | 0.452240 | − | 0.121177i | ||||
\(958\) | 301932. | − | 522962.i | 0.328987 | − | 0.569822i | ||||
\(959\) | 499922. | − | 865890.i | 0.543582 | − | 0.941511i | ||||
\(960\) | −30111.1 | − | 8068.25i | −0.0326726 | − | 0.00875461i | ||||
\(961\) | − | 121312.i | − | 0.131358i | ||||||
\(962\) | −271750. | − | 23710.8i | −0.293643 | − | 0.0256210i | ||||
\(963\) | −79190.3 | −0.0853925 | ||||||||
\(964\) | −121636. | + | 453952.i | −0.130890 | + | 0.488490i | ||||
\(965\) | 172799. | + | 99765.6i | 0.185561 | + | 0.107134i | ||||
\(966\) | 92868.0 | + | 53617.3i | 0.0995203 | + | 0.0574581i | ||||
\(967\) | 386333. | + | 1.44181e6i | 0.413151 | + | 1.54190i | 0.788511 | + | 0.615021i | \(0.210852\pi\) |
−0.375360 | + | 0.926879i | \(0.622481\pi\) | |||||||
\(968\) | −648944. | + | 648944.i | −0.692559 | + | 0.692559i | ||||
\(969\) | 558914. | − | 968067.i | 0.595247 | − | 1.03100i | ||||
\(970\) | 101104. | − | 101104.i | 0.107455 | − | 0.107455i | ||||
\(971\) | 662325. | + | 1.14718e6i | 0.702478 | + | 1.21673i | 0.967594 | + | 0.252510i | \(0.0812562\pi\) |
−0.265117 | + | 0.964216i | \(0.585410\pi\) | |||||||
\(972\) | 371520. | 0.393233 | ||||||||
\(973\) | − | 1.38364e6i | − | 1.46149i | ||||||
\(974\) | 560704. | + | 971168.i | 0.591039 | + | 1.02371i | ||||
\(975\) | −115797. | − | 432162.i | −0.121812 | − | 0.454608i | ||||
\(976\) | −300389. | − | 300389.i | −0.315344 | − | 0.315344i | ||||
\(977\) | −169557. | + | 632795.i | −0.177634 | + | 0.662939i | 0.818454 | + | 0.574572i | \(0.194832\pi\) |
−0.996088 | + | 0.0883672i | \(0.971835\pi\) | |||||||
\(978\) | 564551. | + | 977830.i | 0.590235 | + | 1.02232i | ||||
\(979\) | 2.04552e6 | + | 548096.i | 2.13422 | + | 0.571862i | ||||
\(980\) | 29800.3 | − | 7984.98i | 0.0310291 | − | 0.00831422i | ||||
\(981\) | 45729.0 | + | 170663.i | 0.0475175 | + | 0.177338i | ||||
\(982\) | 153622. | − | 573327.i | 0.159306 | − | 0.594538i | ||||
\(983\) | 589591. | − | 340400.i | 0.610160 | − | 0.352276i | −0.162868 | − | 0.986648i | \(-0.552075\pi\) |
0.773028 | + | 0.634372i | \(0.218741\pi\) | |||||||
\(984\) | −257234. | − | 68925.6i | −0.265667 | − | 0.0711853i | ||||
\(985\) | −56840.5 | + | 56840.5i | −0.0585849 | + | 0.0585849i | ||||
\(986\) | −199490. | + | 53453.2i | −0.205195 | + | 0.0549819i | ||||
\(987\) | 928042. | − | 535805.i | 0.952650 | − | 0.550013i | ||||
\(988\) | 137151. | 0.140503 | ||||||||
\(989\) | 83479.6i | 0.0853469i | ||||||||
\(990\) | 110565. | − | 63834.5i | 0.112810 | − | 0.0651306i | ||||
\(991\) | 1.06539e6 | + | 1.06539e6i | 1.08483 | + | 1.08483i | 0.996052 | + | 0.0887770i | \(0.0282958\pi\) |
0.0887770 | + | 0.996052i | \(0.471704\pi\) | |||||||
\(992\) | 140410. | + | 81066.0i | 0.142684 | + | 0.0823788i | ||||
\(993\) | −1.22331e6 | − | 1.22331e6i | −1.24062 | − | 1.24062i | ||||
\(994\) | −41082.7 | + | 11008.1i | −0.0415802 | + | 0.0111414i | ||||
\(995\) | −18596.3 | + | 32209.8i | −0.0187837 | + | 0.0325343i | ||||
\(996\) | −162629. | + | 281681.i | −0.163938 | + | 0.283948i | ||||
\(997\) | 459313. | + | 123073.i | 0.462082 | + | 0.123814i | 0.482347 | − | 0.875980i | \(-0.339784\pi\) |
−0.0202654 | + | 0.999795i | \(0.506451\pi\) | |||||||
\(998\) | 938610.i | 0.942375i | ||||||||
\(999\) | −60168.6 | + | 689596.i | −0.0602891 | + | 0.690977i |
(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 | 74.5.g.b.29.2 | yes | 28 | |
37.23 | odd | 12 | inner | 74.5.g.b.23.2 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.g.b.23.2 | ✓ | 28 | 37.23 | odd | 12 | inner | |
74.5.g.b.29.2 | yes | 28 | 1.1 | even | 1 | trivial |