Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(20,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.20");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 20.18 | ||
Character | \(\chi\) | \(=\) | 63.20 |
Dual form | 63.4.o.a.41.18 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59186 | + | 1.49641i | 0.916362 | + | 0.529062i | 0.882473 | − | 0.470364i | \(-0.155877\pi\) |
0.0338893 | + | 0.999426i | \(0.489211\pi\) | |||||||
\(3\) | 1.03772 | + | 5.09148i | 0.199709 | + | 0.979855i | ||||
\(4\) | 0.478502 | + | 0.828790i | 0.0598128 | + | 0.103599i | ||||
\(5\) | 7.80147 | + | 13.5125i | 0.697785 | + | 1.20860i | 0.969233 | + | 0.246146i | \(0.0791642\pi\) |
−0.271448 | + | 0.962453i | \(0.587502\pi\) | |||||||
\(6\) | −4.92933 | + | 14.7493i | −0.335398 | + | 1.00356i | ||||
\(7\) | −13.5435 | − | 12.6323i | −0.731278 | − | 0.682080i | ||||
\(8\) | − | 21.0785i | − | 0.931545i | ||||||
\(9\) | −24.8463 | + | 10.5670i | −0.920233 | + | 0.391372i | ||||
\(10\) | 46.6969i | 1.47669i | ||||||||
\(11\) | 46.4700 | + | 26.8295i | 1.27375 | + | 0.735400i | 0.975692 | − | 0.219148i | \(-0.0703277\pi\) |
0.298058 | + | 0.954548i | \(0.403661\pi\) | |||||||
\(12\) | −3.72322 | + | 3.29633i | −0.0895667 | + | 0.0792975i | ||||
\(13\) | 29.1434 | − | 16.8260i | 0.621764 | − | 0.358976i | −0.155791 | − | 0.987790i | \(-0.549793\pi\) |
0.777555 | + | 0.628814i | \(0.216459\pi\) | |||||||
\(14\) | −16.1997 | − | 53.0078i | −0.309253 | − | 1.01192i | ||||
\(15\) | −60.7031 | + | 53.7432i | −1.04490 | + | 0.925096i | ||||
\(16\) | 35.3701 | − | 61.2628i | 0.552658 | − | 0.957231i | ||||
\(17\) | −43.5488 | −0.621302 | −0.310651 | − | 0.950524i | \(-0.600547\pi\) | ||||
−0.310651 | + | 0.950524i | \(0.600547\pi\) | |||||||
\(18\) | −80.2108 | − | 9.79199i | −1.05033 | − | 0.128222i | ||||
\(19\) | − | 32.2524i | − | 0.389432i | −0.980860 | − | 0.194716i | \(-0.937621\pi\) | ||
0.980860 | − | 0.194716i | \(-0.0623785\pi\) | |||||||
\(20\) | −7.46605 | + | 12.9316i | −0.0834729 | + | 0.144579i | ||||
\(21\) | 50.2627 | − | 82.0650i | 0.522297 | − | 0.852764i | ||||
\(22\) | 80.2960 | + | 139.077i | 0.778144 | + | 1.34778i | ||||
\(23\) | 129.309 | − | 74.6565i | 1.17229 | − | 0.676824i | 0.218074 | − | 0.975932i | \(-0.430023\pi\) |
0.954219 | + | 0.299108i | \(0.0966892\pi\) | |||||||
\(24\) | 107.320 | − | 21.8735i | 0.912779 | − | 0.186038i | ||||
\(25\) | −59.2260 | + | 102.582i | −0.473808 | + | 0.820659i | ||||
\(26\) | 100.714 | 0.759681 | ||||||||
\(27\) | −79.5852 | − | 115.539i | −0.567266 | − | 0.823534i | ||||
\(28\) | 3.98894 | − | 17.2693i | 0.0269228 | − | 0.116557i | ||||
\(29\) | −127.390 | − | 73.5487i | −0.815715 | − | 0.470953i | 0.0332217 | − | 0.999448i | \(-0.489423\pi\) |
−0.848937 | + | 0.528495i | \(0.822757\pi\) | |||||||
\(30\) | −237.756 | + | 48.4582i | −1.44694 | + | 0.294907i | ||||
\(31\) | 61.1678 | − | 35.3153i | 0.354389 | − | 0.204607i | −0.312228 | − | 0.950007i | \(-0.601075\pi\) |
0.666617 | + | 0.745401i | \(0.267742\pi\) | |||||||
\(32\) | 37.3130 | − | 21.5427i | 0.206127 | − | 0.119008i | ||||
\(33\) | −88.3790 | + | 264.443i | −0.466206 | + | 1.39496i | ||||
\(34\) | −112.873 | − | 65.1670i | −0.569338 | − | 0.328707i | ||||
\(35\) | 65.0355 | − | 281.557i | 0.314086 | − | 1.35977i | ||||
\(36\) | −20.6469 | − | 15.5360i | −0.0955873 | − | 0.0719260i | ||||
\(37\) | 40.3540 | 0.179302 | 0.0896509 | − | 0.995973i | \(-0.471425\pi\) | ||||
0.0896509 | + | 0.995973i | \(0.471425\pi\) | |||||||
\(38\) | 48.2629 | − | 83.5938i | 0.206034 | − | 0.356861i | ||||
\(39\) | 115.912 | + | 130.922i | 0.475916 | + | 0.537548i | ||||
\(40\) | 284.824 | − | 164.443i | 1.12586 | − | 0.650018i | ||||
\(41\) | −179.454 | − | 310.824i | −0.683562 | − | 1.18396i | −0.973886 | − | 0.227036i | \(-0.927096\pi\) |
0.290324 | − | 0.956928i | \(-0.406237\pi\) | |||||||
\(42\) | 253.077 | − | 137.487i | 0.929778 | − | 0.505113i | ||||
\(43\) | −253.886 | + | 439.743i | −0.900400 | + | 1.55954i | −0.0734235 | + | 0.997301i | \(0.523392\pi\) |
−0.826976 | + | 0.562237i | \(0.809941\pi\) | |||||||
\(44\) | 51.3519i | 0.175945i | ||||||||
\(45\) | −336.625 | − | 253.298i | −1.11514 | − | 0.839099i | ||||
\(46\) | 446.867 | 1.43233 | ||||||||
\(47\) | −228.160 | + | 395.185i | −0.708098 | + | 1.22646i | 0.257464 | + | 0.966288i | \(0.417113\pi\) |
−0.965562 | + | 0.260174i | \(0.916220\pi\) | |||||||
\(48\) | 348.622 | + | 116.513i | 1.04832 | + | 0.350357i | ||||
\(49\) | 23.8504 | + | 342.170i | 0.0695348 | + | 0.997580i | ||||
\(50\) | −307.011 | + | 177.253i | −0.868359 | + | 0.501347i | ||||
\(51\) | −45.1914 | − | 221.728i | −0.124080 | − | 0.608786i | ||||
\(52\) | 27.8904 | + | 16.1025i | 0.0743789 | + | 0.0429427i | ||||
\(53\) | − | 213.420i | − | 0.553123i | −0.960996 | − | 0.276561i | \(-0.910805\pi\) | ||
0.960996 | − | 0.276561i | \(-0.0891949\pi\) | |||||||
\(54\) | −33.3805 | − | 418.553i | −0.0841205 | − | 1.05477i | ||||
\(55\) | 837.238i | 2.05260i | ||||||||
\(56\) | −266.269 | + | 285.475i | −0.635388 | + | 0.681218i | ||||
\(57\) | 164.212 | − | 33.4689i | 0.381587 | − | 0.0777731i | ||||
\(58\) | −220.118 | − | 381.256i | −0.498327 | − | 0.863127i | ||||
\(59\) | 159.593 | + | 276.424i | 0.352157 | + | 0.609954i | 0.986627 | − | 0.162993i | \(-0.0521149\pi\) |
−0.634470 | + | 0.772947i | \(0.718782\pi\) | |||||||
\(60\) | −73.5884 | − | 24.5939i | −0.158337 | − | 0.0529176i | ||||
\(61\) | −303.662 | − | 175.319i | −0.637375 | − | 0.367989i | 0.146227 | − | 0.989251i | \(-0.453287\pi\) |
−0.783603 | + | 0.621262i | \(0.786620\pi\) | |||||||
\(62\) | 211.385 | 0.432998 | ||||||||
\(63\) | 469.990 | + | 170.751i | 0.939892 | + | 0.341471i | ||||
\(64\) | −436.974 | −0.853466 | ||||||||
\(65\) | 454.723 | + | 262.535i | 0.867715 | + | 0.500976i | ||||
\(66\) | −624.782 | + | 553.148i | −1.16523 | + | 1.03163i | ||||
\(67\) | −289.258 | − | 501.009i | −0.527440 | − | 0.913553i | −0.999489 | − | 0.0319801i | \(-0.989819\pi\) |
0.472049 | − | 0.881572i | \(-0.343515\pi\) | |||||||
\(68\) | −20.8382 | − | 36.0928i | −0.0371618 | − | 0.0643662i | ||||
\(69\) | 514.298 | + | 580.900i | 0.897307 | + | 1.01351i | ||||
\(70\) | 589.889 | − | 632.437i | 1.00722 | − | 1.07987i | ||||
\(71\) | 787.243i | 1.31589i | 0.753064 | + | 0.657947i | \(0.228575\pi\) | ||||
−0.753064 | + | 0.657947i | \(0.771425\pi\) | |||||||
\(72\) | 222.737 | + | 523.721i | 0.364580 | + | 0.857238i | ||||
\(73\) | − | 146.373i | − | 0.234681i | −0.993092 | − | 0.117340i | \(-0.962563\pi\) | ||
0.993092 | − | 0.117340i | \(-0.0374368\pi\) | |||||||
\(74\) | 104.592 | + | 60.3863i | 0.164305 | + | 0.0948617i | ||||
\(75\) | −583.756 | − | 195.096i | −0.898751 | − | 0.300370i | ||||
\(76\) | 26.7305 | − | 15.4329i | 0.0403447 | − | 0.0232930i | ||||
\(77\) | −290.447 | − | 950.387i | −0.429864 | − | 1.40658i | ||||
\(78\) | 104.513 | + | 512.785i | 0.151715 | + | 0.744378i | ||||
\(79\) | −193.095 | + | 334.451i | −0.274999 | + | 0.476312i | −0.970135 | − | 0.242566i | \(-0.922011\pi\) |
0.695136 | + | 0.718878i | \(0.255344\pi\) | |||||||
\(80\) | 1103.76 | 1.54254 | ||||||||
\(81\) | 505.676 | − | 525.103i | 0.693656 | − | 0.720306i | ||||
\(82\) | − | 1074.15i | − | 1.44659i | ||||||
\(83\) | 98.9043 | − | 171.307i | 0.130797 | − | 0.226547i | −0.793187 | − | 0.608978i | \(-0.791580\pi\) |
0.923984 | + | 0.382431i | \(0.124913\pi\) | |||||||
\(84\) | 92.0655 | + | 2.38900i | 0.119585 | + | 0.00310311i | ||||
\(85\) | −339.745 | − | 588.455i | −0.433535 | − | 0.750905i | ||||
\(86\) | −1316.07 | + | 759.835i | −1.65018 | + | 0.952734i | ||||
\(87\) | 242.276 | − | 724.926i | 0.298560 | − | 0.893336i | ||||
\(88\) | 565.524 | − | 979.517i | 0.685058 | − | 1.18656i | ||||
\(89\) | 596.020 | 0.709865 | 0.354932 | − | 0.934892i | \(-0.384504\pi\) | ||||
0.354932 | + | 0.934892i | \(0.384504\pi\) | |||||||
\(90\) | −493.448 | − | 1160.24i | −0.577933 | − | 1.35889i | ||||
\(91\) | −607.253 | − | 140.267i | −0.699532 | − | 0.161582i | ||||
\(92\) | 123.749 | + | 71.4466i | 0.140236 | + | 0.0809654i | ||||
\(93\) | 243.282 | + | 274.787i | 0.271260 | + | 0.306388i | ||||
\(94\) | −1182.72 | + | 682.844i | −1.29775 | + | 0.749255i | ||||
\(95\) | 435.812 | − | 251.616i | 0.470667 | − | 0.271740i | ||||
\(96\) | 148.404 | + | 167.623i | 0.157776 | + | 0.178208i | ||||
\(97\) | −631.485 | − | 364.588i | −0.661006 | − | 0.381632i | 0.131654 | − | 0.991296i | \(-0.457971\pi\) |
−0.792660 | + | 0.609664i | \(0.791304\pi\) | |||||||
\(98\) | −450.210 | + | 922.547i | −0.464062 | + | 0.950932i | ||||
\(99\) | −1438.12 | − | 175.563i | −1.45996 | − | 0.178229i | ||||
\(100\) | −113.359 | −0.113359 | ||||||||
\(101\) | 286.723 | − | 496.619i | 0.282476 | − | 0.489262i | −0.689518 | − | 0.724268i | \(-0.742178\pi\) |
0.971994 | + | 0.235006i | \(0.0755111\pi\) | |||||||
\(102\) | 214.666 | − | 642.313i | 0.208384 | − | 0.623514i | ||||
\(103\) | 1420.04 | − | 819.860i | 1.35845 | − | 0.784303i | 0.369038 | − | 0.929414i | \(-0.379687\pi\) |
0.989415 | + | 0.145111i | \(0.0463539\pi\) | |||||||
\(104\) | −354.665 | − | 614.298i | −0.334402 | − | 0.579201i | ||||
\(105\) | 1501.03 | + | 38.9501i | 1.39510 | + | 0.0362013i | ||||
\(106\) | 319.365 | − | 553.156i | 0.292636 | − | 0.506861i | ||||
\(107\) | − | 377.596i | − | 0.341155i | −0.985344 | − | 0.170577i | \(-0.945437\pi\) | ||
0.985344 | − | 0.170577i | \(-0.0545633\pi\) | |||||||
\(108\) | 57.6756 | − | 121.245i | 0.0513874 | − | 0.108026i | ||||
\(109\) | −1166.06 | −1.02467 | −0.512334 | − | 0.858787i | \(-0.671219\pi\) | ||||
−0.512334 | + | 0.858787i | \(0.671219\pi\) | |||||||
\(110\) | −1252.85 | + | 2170.01i | −1.08595 | + | 1.88093i | ||||
\(111\) | 41.8761 | + | 205.462i | 0.0358081 | + | 0.175690i | ||||
\(112\) | −1252.92 | + | 382.905i | −1.05705 | + | 0.323045i | ||||
\(113\) | −279.069 | + | 161.121i | −0.232324 | + | 0.134132i | −0.611644 | − | 0.791133i | \(-0.709491\pi\) |
0.379320 | + | 0.925266i | \(0.376158\pi\) | |||||||
\(114\) | 475.699 | + | 158.983i | 0.390819 | + | 0.130615i | ||||
\(115\) | 2017.60 | + | 1164.86i | 1.63602 | + | 0.944555i | ||||
\(116\) | − | 140.773i | − | 0.112676i | ||||||
\(117\) | −546.305 | + | 726.022i | −0.431675 | + | 0.573682i | ||||
\(118\) | 955.269i | 0.745252i | ||||||||
\(119\) | 589.802 | + | 550.121i | 0.454345 | + | 0.423778i | ||||
\(120\) | 1132.82 | + | 1279.53i | 0.861769 | + | 0.973370i | ||||
\(121\) | 774.144 | + | 1340.86i | 0.581626 | + | 1.00741i | ||||
\(122\) | −524.700 | − | 908.806i | −0.389378 | − | 0.674422i | ||||
\(123\) | 1396.33 | − | 1236.24i | 1.02360 | − | 0.906241i | ||||
\(124\) | 58.5379 | + | 33.7969i | 0.0423940 | + | 0.0244762i | ||||
\(125\) | 102.169 | 0.0731064 | ||||||||
\(126\) | 962.636 | + | 1145.86i | 0.680623 | + | 0.810172i | ||||
\(127\) | 1356.31 | 0.947663 | 0.473832 | − | 0.880615i | \(-0.342871\pi\) | ||||
0.473832 | + | 0.880615i | \(0.342871\pi\) | |||||||
\(128\) | −1431.08 | − | 826.236i | −0.988211 | − | 0.570544i | ||||
\(129\) | −2502.40 | − | 836.324i | −1.70794 | − | 0.570808i | ||||
\(130\) | 785.720 | + | 1360.91i | 0.530094 | + | 0.918150i | ||||
\(131\) | 978.999 | + | 1695.68i | 0.652943 | + | 1.13093i | 0.982405 | + | 0.186762i | \(0.0597992\pi\) |
−0.329462 | + | 0.944169i | \(0.606867\pi\) | |||||||
\(132\) | −261.457 | + | 53.2888i | −0.172401 | + | 0.0351378i | ||||
\(133\) | −407.422 | + | 436.809i | −0.265624 | + | 0.284783i | ||||
\(134\) | − | 1731.40i | − | 1.11619i | ||||||
\(135\) | 940.340 | − | 1976.77i | 0.599493 | − | 1.26025i | ||||
\(136\) | 917.942i | 0.578771i | ||||||||
\(137\) | −859.395 | − | 496.172i | −0.535935 | − | 0.309422i | 0.207495 | − | 0.978236i | \(-0.433469\pi\) |
−0.743430 | + | 0.668814i | \(0.766802\pi\) | |||||||
\(138\) | 463.722 | + | 2275.22i | 0.286048 | + | 1.40347i | ||||
\(139\) | −722.161 | + | 416.940i | −0.440668 | + | 0.254420i | −0.703881 | − | 0.710318i | \(-0.748551\pi\) |
0.263213 | + | 0.964738i | \(0.415218\pi\) | |||||||
\(140\) | 264.471 | − | 80.8249i | 0.159657 | − | 0.0487925i | ||||
\(141\) | −2248.84 | − | 751.583i | −1.34317 | − | 0.448898i | ||||
\(142\) | −1178.04 | + | 2040.43i | −0.696190 | + | 1.20584i | ||||
\(143\) | 1805.73 | 1.05596 | ||||||||
\(144\) | −231.449 | + | 1895.91i | −0.133941 | + | 1.09717i | ||||
\(145\) | − | 2295.15i | − | 1.31450i | ||||||
\(146\) | 219.035 | − | 379.379i | 0.124161 | − | 0.215052i | ||||
\(147\) | −1717.40 | + | 476.510i | −0.963597 | + | 0.267360i | ||||
\(148\) | 19.3095 | + | 33.4450i | 0.0107245 | + | 0.0185754i | ||||
\(149\) | 1324.03 | − | 764.428i | 0.727978 | − | 0.420298i | −0.0897042 | − | 0.995968i | \(-0.528592\pi\) |
0.817682 | + | 0.575670i | \(0.195259\pi\) | |||||||
\(150\) | −1221.07 | − | 1379.20i | −0.664667 | − | 0.750742i | ||||
\(151\) | −373.571 | + | 647.044i | −0.201330 | + | 0.348713i | −0.948957 | − | 0.315405i | \(-0.897860\pi\) |
0.747627 | + | 0.664118i | \(0.231193\pi\) | |||||||
\(152\) | −679.831 | −0.362774 | ||||||||
\(153\) | 1082.03 | − | 460.182i | 0.571743 | − | 0.243160i | ||||
\(154\) | 669.373 | − | 2897.90i | 0.350257 | − | 1.51636i | ||||
\(155\) | 954.398 | + | 551.022i | 0.494575 | + | 0.285543i | ||||
\(156\) | −53.0433 | + | 158.713i | −0.0272235 | + | 0.0814566i | ||||
\(157\) | −1193.21 | + | 688.900i | −0.606551 | + | 0.350192i | −0.771614 | − | 0.636091i | \(-0.780550\pi\) |
0.165064 | + | 0.986283i | \(0.447217\pi\) | |||||||
\(158\) | −1000.95 | + | 577.901i | −0.503997 | + | 0.290983i | ||||
\(159\) | 1086.62 | − | 221.470i | 0.541980 | − | 0.110464i | ||||
\(160\) | 582.193 | + | 336.129i | 0.287665 | + | 0.166083i | ||||
\(161\) | −2694.37 | − | 622.360i | −1.31892 | − | 0.304651i | ||||
\(162\) | 2096.41 | − | 604.296i | 1.01673 | − | 0.293074i | ||||
\(163\) | 1900.28 | 0.913139 | 0.456569 | − | 0.889688i | \(-0.349078\pi\) | ||||
0.456569 | + | 0.889688i | \(0.349078\pi\) | |||||||
\(164\) | 171.739 | − | 297.460i | 0.0817715 | − | 0.141632i | ||||
\(165\) | −4262.78 | + | 868.817i | −2.01125 | + | 0.409923i | ||||
\(166\) | 512.693 | − | 296.003i | 0.239715 | − | 0.138399i | ||||
\(167\) | −836.404 | − | 1448.69i | −0.387562 | − | 0.671277i | 0.604559 | − | 0.796560i | \(-0.293349\pi\) |
−0.992121 | + | 0.125283i | \(0.960016\pi\) | |||||||
\(168\) | −1729.80 | − | 1059.46i | −0.794388 | − | 0.486543i | ||||
\(169\) | −532.274 | + | 921.925i | −0.242273 | + | 0.419629i | ||||
\(170\) | − | 2033.59i | − | 0.917468i | ||||||
\(171\) | 340.812 | + | 801.353i | 0.152413 | + | 0.358368i | ||||
\(172\) | −485.939 | −0.215422 | ||||||||
\(173\) | 496.398 | − | 859.787i | 0.218153 | − | 0.377852i | −0.736090 | − | 0.676883i | \(-0.763330\pi\) |
0.954243 | + | 0.299031i | \(0.0966635\pi\) | |||||||
\(174\) | 1712.74 | − | 1516.36i | 0.746219 | − | 0.660662i | ||||
\(175\) | 2097.97 | − | 641.160i | 0.906240 | − | 0.276955i | ||||
\(176\) | 3287.30 | − | 1897.92i | 1.40790 | − | 0.812849i | ||||
\(177\) | −1241.79 | + | 1099.42i | −0.527338 | + | 0.466876i | ||||
\(178\) | 1544.80 | + | 891.891i | 0.650493 | + | 0.375562i | ||||
\(179\) | 145.772i | 0.0608687i | 0.999537 | + | 0.0304343i | \(0.00968905\pi\) | ||||
−0.999537 | + | 0.0304343i | \(0.990311\pi\) | |||||||
\(180\) | 48.8551 | − | 400.195i | 0.0202303 | − | 0.165716i | ||||
\(181\) | 2253.56i | 0.925448i | 0.886502 | + | 0.462724i | \(0.153128\pi\) | ||||
−0.886502 | + | 0.462724i | \(0.846872\pi\) | |||||||
\(182\) | −1364.02 | − | 1272.25i | −0.555538 | − | 0.518163i | ||||
\(183\) | 577.518 | − | 1728.02i | 0.233286 | − | 0.698026i | ||||
\(184\) | −1573.64 | − | 2725.63i | −0.630492 | − | 1.09204i | ||||
\(185\) | 314.821 | + | 545.286i | 0.125114 | + | 0.216704i | ||||
\(186\) | 219.358 | + | 1076.26i | 0.0864736 | + | 0.424276i | ||||
\(187\) | −2023.72 | − | 1168.39i | −0.791384 | − | 0.456906i | ||||
\(188\) | −436.701 | −0.169413 | ||||||||
\(189\) | −381.659 | + | 2570.14i | −0.146887 | + | 0.989153i | ||||
\(190\) | 1506.09 | 0.575069 | ||||||||
\(191\) | 3201.45 | + | 1848.36i | 1.21282 | + | 0.700222i | 0.963373 | − | 0.268166i | \(-0.0864175\pi\) |
0.249448 | + | 0.968388i | \(0.419751\pi\) | |||||||
\(192\) | −453.456 | − | 2224.85i | −0.170445 | − | 0.836273i | ||||
\(193\) | 2194.75 | + | 3801.42i | 0.818559 | + | 1.41779i | 0.906744 | + | 0.421681i | \(0.138560\pi\) |
−0.0881856 | + | 0.996104i | \(0.528107\pi\) | |||||||
\(194\) | −1091.15 | − | 1889.92i | −0.403814 | − | 0.699426i | ||||
\(195\) | −864.815 | + | 2587.65i | −0.317593 | + | 0.950285i | ||||
\(196\) | −272.174 | + | 183.496i | −0.0991890 | + | 0.0668717i | ||||
\(197\) | 2110.35i | 0.763229i | 0.924322 | + | 0.381615i | \(0.124632\pi\) | ||||
−0.924322 | + | 0.381615i | \(0.875368\pi\) | |||||||
\(198\) | −3464.69 | − | 2607.05i | −1.24356 | − | 0.935732i | ||||
\(199\) | 3443.20i | 1.22654i | 0.789873 | + | 0.613271i | \(0.210146\pi\) | ||||
−0.789873 | + | 0.613271i | \(0.789854\pi\) | |||||||
\(200\) | 2162.28 | + | 1248.39i | 0.764481 | + | 0.441373i | ||||
\(201\) | 2250.71 | − | 1992.66i | 0.789815 | − | 0.699259i | ||||
\(202\) | 1486.29 | − | 858.113i | 0.517700 | − | 0.298894i | ||||
\(203\) | 796.213 | + | 2605.33i | 0.275287 | + | 0.900780i | ||||
\(204\) | 162.142 | − | 143.551i | 0.0556480 | − | 0.0492677i | ||||
\(205\) | 2800.02 | − | 4849.77i | 0.953959 | − | 1.65231i | ||||
\(206\) | 4907.40 | 1.65978 | ||||||||
\(207\) | −2423.95 | + | 3221.35i | −0.813893 | + | 1.08164i | ||||
\(208\) | − | 2380.54i | − | 0.793562i | ||||||
\(209\) | 865.316 | − | 1498.77i | 0.286388 | − | 0.496039i | ||||
\(210\) | 3832.18 | + | 2347.11i | 1.25926 | + | 0.771268i | ||||
\(211\) | −1865.08 | − | 3230.41i | −0.608518 | − | 1.05398i | −0.991485 | − | 0.130223i | \(-0.958431\pi\) |
0.382966 | − | 0.923762i | \(-0.374903\pi\) | |||||||
\(212\) | 176.881 | − | 102.122i | 0.0573028 | − | 0.0330838i | ||||
\(213\) | −4008.23 | + | 816.936i | −1.28939 | + | 0.262796i | ||||
\(214\) | 565.039 | − | 978.676i | 0.180492 | − | 0.312621i | ||||
\(215\) | −7922.73 | −2.51314 | ||||||||
\(216\) | −2435.38 | + | 1677.53i | −0.767159 | + | 0.528434i | ||||
\(217\) | −1274.54 | − | 294.399i | −0.398715 | − | 0.0920973i | ||||
\(218\) | −3022.28 | − | 1744.91i | −0.938966 | − | 0.542112i | ||||
\(219\) | 745.256 | − | 151.894i | 0.229953 | − | 0.0468678i | ||||
\(220\) | −693.895 | + | 400.620i | −0.212647 | + | 0.122772i | ||||
\(221\) | −1269.16 | + | 732.751i | −0.386303 | + | 0.223032i | ||||
\(222\) | −198.918 | + | 595.192i | −0.0601375 | + | 0.179940i | ||||
\(223\) | −2359.66 | − | 1362.35i | −0.708585 | − | 0.409101i | 0.101952 | − | 0.994789i | \(-0.467491\pi\) |
−0.810537 | + | 0.585688i | \(0.800824\pi\) | |||||||
\(224\) | −777.481 | − | 179.587i | −0.231909 | − | 0.0535675i | ||||
\(225\) | 387.554 | − | 3174.63i | 0.114831 | − | 0.940632i | ||||
\(226\) | −964.411 | −0.283857 | ||||||||
\(227\) | 2832.72 | − | 4906.41i | 0.828256 | − | 1.43458i | −0.0711495 | − | 0.997466i | \(-0.522667\pi\) |
0.899405 | − | 0.437116i | \(-0.144000\pi\) | |||||||
\(228\) | 106.315 | + | 120.083i | 0.0308810 | + | 0.0348801i | ||||
\(229\) | −366.827 | + | 211.787i | −0.105854 | + | 0.0611149i | −0.551992 | − | 0.833849i | \(-0.686132\pi\) |
0.446138 | + | 0.894964i | \(0.352799\pi\) | |||||||
\(230\) | 3486.22 | + | 6038.32i | 0.999456 | + | 1.73111i | ||||
\(231\) | 4537.47 | − | 2465.04i | 1.29240 | − | 0.702111i | ||||
\(232\) | −1550.29 | + | 2685.18i | −0.438714 | + | 0.759875i | ||||
\(233\) | 234.803i | 0.0660192i | 0.999455 | + | 0.0330096i | \(0.0105092\pi\) | ||||
−0.999455 | + | 0.0330096i | \(0.989491\pi\) | |||||||
\(234\) | −2502.38 | + | 1064.25i | −0.699083 | + | 0.297318i | ||||
\(235\) | −7119.95 | −1.97640 | ||||||||
\(236\) | −152.731 | + | 264.539i | −0.0421270 | + | 0.0729661i | ||||
\(237\) | −1903.23 | − | 636.075i | −0.521637 | − | 0.174335i | ||||
\(238\) | 705.476 | + | 2308.43i | 0.192140 | + | 0.628710i | ||||
\(239\) | 1575.90 | − | 909.844i | 0.426511 | − | 0.246246i | −0.271348 | − | 0.962481i | \(-0.587469\pi\) |
0.697859 | + | 0.716235i | \(0.254136\pi\) | |||||||
\(240\) | 1145.39 | + | 5619.74i | 0.308060 | + | 1.51147i | ||||
\(241\) | −2358.44 | − | 1361.65i | −0.630377 | − | 0.363948i | 0.150521 | − | 0.988607i | \(-0.451905\pi\) |
−0.780898 | + | 0.624659i | \(0.785238\pi\) | |||||||
\(242\) | 4633.75i | 1.23086i | ||||||||
\(243\) | 3198.30 | + | 2029.73i | 0.844325 | + | 0.535831i | ||||
\(244\) | − | 335.562i | − | 0.0880417i | ||||||
\(245\) | −4437.52 | + | 2991.71i | −1.15715 | + | 0.780136i | ||||
\(246\) | 5469.02 | − | 1114.67i | 1.41745 | − | 0.288896i | ||||
\(247\) | −542.678 | − | 939.946i | −0.139797 | − | 0.242135i | ||||
\(248\) | −744.391 | − | 1289.32i | −0.190600 | − | 0.330129i | ||||
\(249\) | 974.842 | + | 325.800i | 0.248105 | + | 0.0829187i | ||||
\(250\) | 264.809 | + | 152.887i | 0.0669919 | + | 0.0386778i | ||||
\(251\) | 4214.66 | 1.05987 | 0.529934 | − | 0.848039i | \(-0.322217\pi\) | ||||
0.529934 | + | 0.848039i | \(0.322217\pi\) | |||||||
\(252\) | 83.3745 | + | 471.228i | 0.0208417 | + | 0.117796i | ||||
\(253\) | 8011.98 | 1.99094 | ||||||||
\(254\) | 3515.38 | + | 2029.60i | 0.868403 | + | 0.501372i | ||||
\(255\) | 2643.55 | − | 2340.45i | 0.649198 | − | 0.574764i | ||||
\(256\) | −724.881 | − | 1255.53i | −0.176973 | − | 0.306526i | ||||
\(257\) | 1388.99 | + | 2405.80i | 0.337132 | + | 0.583929i | 0.983892 | − | 0.178764i | \(-0.0572099\pi\) |
−0.646760 | + | 0.762693i | \(0.723877\pi\) | |||||||
\(258\) | −5234.40 | − | 5912.26i | −1.26310 | − | 1.42667i | ||||
\(259\) | −546.533 | − | 509.764i | −0.131119 | − | 0.122298i | ||||
\(260\) | 502.494i | 0.119859i | ||||||||
\(261\) | 3942.36 | + | 481.276i | 0.934965 | + | 0.114139i | ||||
\(262\) | 5859.95i | 1.38179i | ||||||||
\(263\) | −2737.40 | − | 1580.44i | −0.641808 | − | 0.370548i | 0.143503 | − | 0.989650i | \(-0.454163\pi\) |
−0.785311 | + | 0.619102i | \(0.787497\pi\) | |||||||
\(264\) | 5574.04 | + | 1862.89i | 1.29946 | + | 0.434292i | ||||
\(265\) | 2883.85 | − | 1664.99i | 0.668504 | − | 0.385961i | ||||
\(266\) | −1709.63 | + | 522.478i | −0.394075 | + | 0.120433i | ||||
\(267\) | 618.500 | + | 3034.62i | 0.141766 | + | 0.695565i | ||||
\(268\) | 276.821 | − | 479.468i | 0.0630953 | − | 0.109284i | ||||
\(269\) | −4337.32 | −0.983088 | −0.491544 | − | 0.870853i | \(-0.663567\pi\) | ||||
−0.491544 | + | 0.870853i | \(0.663567\pi\) | |||||||
\(270\) | 5395.30 | − | 3716.38i | 1.21610 | − | 0.837674i | ||||
\(271\) | 8399.64i | 1.88281i | 0.337276 | + | 0.941406i | \(0.390495\pi\) | ||||
−0.337276 | + | 0.941406i | \(0.609505\pi\) | |||||||
\(272\) | −1540.33 | + | 2667.92i | −0.343368 | + | 0.594730i | ||||
\(273\) | 84.0062 | − | 3237.37i | 0.0186238 | − | 0.717710i | ||||
\(274\) | −1484.96 | − | 2572.02i | −0.327407 | − | 0.567085i | ||||
\(275\) | −5504.47 | + | 3178.01i | −1.20702 | + | 0.696876i | ||||
\(276\) | −235.352 | + | 704.207i | −0.0513280 | + | 0.153581i | ||||
\(277\) | 1826.45 | − | 3163.50i | 0.396176 | − | 0.686197i | −0.597075 | − | 0.802186i | \(-0.703670\pi\) |
0.993250 | + | 0.115989i | \(0.0370038\pi\) | |||||||
\(278\) | −2495.66 | −0.538415 | ||||||||
\(279\) | −1146.62 | + | 1523.82i | −0.246043 | + | 0.326984i | ||||
\(280\) | −5934.79 | − | 1370.85i | −1.26668 | − | 0.292585i | ||||
\(281\) | −7198.88 | − | 4156.27i | −1.52829 | − | 0.882358i | −0.999434 | − | 0.0336451i | \(-0.989288\pi\) |
−0.528854 | − | 0.848713i | \(-0.677378\pi\) | |||||||
\(282\) | −4704.02 | − | 5313.20i | −0.993334 | − | 1.12197i | ||||
\(283\) | −1294.63 | + | 747.458i | −0.271937 | + | 0.157003i | −0.629767 | − | 0.776784i | \(-0.716850\pi\) |
0.357831 | + | 0.933786i | \(0.383516\pi\) | |||||||
\(284\) | −652.459 | + | 376.697i | −0.136325 | + | 0.0787073i | ||||
\(285\) | 1733.35 | + | 1957.82i | 0.360262 | + | 0.406917i | ||||
\(286\) | 4680.20 | + | 2702.12i | 0.967644 | + | 0.558669i | ||||
\(287\) | −1495.99 | + | 6476.55i | −0.307684 | + | 1.33205i | ||||
\(288\) | −699.448 | + | 929.543i | −0.143109 | + | 0.190187i | ||||
\(289\) | −3016.50 | −0.613983 | ||||||||
\(290\) | 3434.49 | − | 5948.72i | 0.695450 | − | 1.20455i | ||||
\(291\) | 1200.99 | − | 3593.53i | 0.241935 | − | 0.723905i | ||||
\(292\) | 121.313 | − | 70.0399i | 0.0243126 | − | 0.0140369i | ||||
\(293\) | 139.838 | + | 242.207i | 0.0278820 | + | 0.0482931i | 0.879630 | − | 0.475659i | \(-0.157790\pi\) |
−0.851748 | + | 0.523952i | \(0.824457\pi\) | |||||||
\(294\) | −5164.32 | − | 1334.89i | −1.02445 | − | 0.264804i | ||||
\(295\) | −2490.12 | + | 4313.02i | −0.491460 | + | 0.851233i | ||||
\(296\) | − | 850.601i | − | 0.167028i | ||||||
\(297\) | −598.486 | − | 7504.32i | −0.116928 | − | 1.46614i | ||||
\(298\) | 4575.60 | 0.889455 | ||||||||
\(299\) | 2512.33 | − | 4351.49i | 0.485926 | − | 0.841649i | ||||
\(300\) | −117.635 | − | 577.165i | −0.0226388 | − | 0.111075i | ||||
\(301\) | 8993.45 | − | 2748.48i | 1.72217 | − | 0.526311i | ||||
\(302\) | −1936.49 | + | 1118.03i | −0.368982 | + | 0.213032i | ||||
\(303\) | 2826.06 | + | 944.494i | 0.535819 | + | 0.179075i | ||||
\(304\) | −1975.87 | − | 1140.77i | −0.372777 | − | 0.215223i | ||||
\(305\) | − | 5470.99i | − | 1.02711i | ||||||
\(306\) | 3493.09 | + | 426.430i | 0.652570 | + | 0.0796646i | ||||
\(307\) | − | 10727.5i | − | 1.99430i | −0.0754451 | − | 0.997150i | \(-0.524038\pi\) | ||
0.0754451 | − | 0.997150i | \(-0.475962\pi\) | |||||||
\(308\) | 648.692 | − | 695.482i | 0.120009 | − | 0.128665i | ||||
\(309\) | 5647.90 | + | 6379.32i | 1.03980 | + | 1.17446i | ||||
\(310\) | 1649.11 | + | 2856.35i | 0.302140 | + | 0.523321i | ||||
\(311\) | 4776.34 | + | 8272.87i | 0.870873 | + | 1.50840i | 0.861095 | + | 0.508445i | \(0.169779\pi\) |
0.00977881 | + | 0.999952i | \(0.496887\pi\) | |||||||
\(312\) | 2759.64 | − | 2443.24i | 0.500750 | − | 0.443337i | ||||
\(313\) | −3195.36 | − | 1844.84i | −0.577037 | − | 0.333153i | 0.182918 | − | 0.983128i | \(-0.441446\pi\) |
−0.759955 | + | 0.649976i | \(0.774779\pi\) | |||||||
\(314\) | −4123.51 | −0.741093 | ||||||||
\(315\) | 1359.33 | + | 7682.88i | 0.243142 | + | 1.37423i | ||||
\(316\) | −369.586 | −0.0657938 | ||||||||
\(317\) | −652.484 | − | 376.712i | −0.115606 | − | 0.0667453i | 0.441082 | − | 0.897467i | \(-0.354595\pi\) |
−0.556688 | + | 0.830722i | \(0.687928\pi\) | |||||||
\(318\) | 3147.79 | + | 1052.02i | 0.555092 | + | 0.185516i | ||||
\(319\) | −3946.55 | − | 6835.62i | −0.692678 | − | 1.19975i | ||||
\(320\) | −3409.04 | − | 5904.64i | −0.595536 | − | 1.03150i | ||||
\(321\) | 1922.52 | − | 391.838i | 0.334282 | − | 0.0681316i | ||||
\(322\) | −6052.13 | − | 5644.96i | −1.04743 | − | 0.976961i | ||||
\(323\) | 1404.55i | 0.241955i | ||||||||
\(324\) | 677.167 | + | 167.836i | 0.116112 | + | 0.0287785i | ||||
\(325\) | 3986.14i | 0.680342i | ||||||||
\(326\) | 4925.27 | + | 2843.61i | 0.836766 | + | 0.483107i | ||||
\(327\) | −1210.05 | − | 5936.99i | −0.204635 | − | 1.00403i | ||||
\(328\) | −6551.69 | + | 3782.62i | −1.10292 | + | 0.636769i | ||||
\(329\) | 8082.18 | − | 2469.99i | 1.35436 | − | 0.413905i | ||||
\(330\) | −12348.7 | − | 4127.02i | −2.05991 | − | 0.688440i | ||||
\(331\) | −3119.34 | + | 5402.86i | −0.517989 | + | 0.897184i | 0.481792 | + | 0.876285i | \(0.339986\pi\) |
−0.999782 | + | 0.0208983i | \(0.993347\pi\) | |||||||
\(332\) | 189.304 | 0.0312933 | ||||||||
\(333\) | −1002.65 | + | 426.423i | −0.164999 | + | 0.0701736i | ||||
\(334\) | − | 5006.42i | − | 0.820177i | ||||||
\(335\) | 4513.27 | − | 7817.22i | 0.736079 | − | 1.27493i | ||||
\(336\) | −3249.73 | − | 5981.88i | −0.527641 | − | 0.971245i | ||||
\(337\) | −3929.76 | − | 6806.55i | −0.635216 | − | 1.10023i | −0.986469 | − | 0.163946i | \(-0.947578\pi\) |
0.351254 | − | 0.936280i | \(-0.385756\pi\) | |||||||
\(338\) | −2759.16 | + | 1593.00i | −0.444020 | + | 0.256355i | ||||
\(339\) | −1109.94 | − | 1253.68i | −0.177827 | − | 0.200856i | ||||
\(340\) | 325.137 | − | 563.155i | 0.0518619 | − | 0.0898275i | ||||
\(341\) | 3789.96 | 0.601871 | ||||||||
\(342\) | −315.815 | + | 2586.99i | −0.0499337 | + | 0.409031i | ||||
\(343\) | 3999.37 | − | 4935.45i | 0.629579 | − | 0.776936i | ||||
\(344\) | 9269.10 | + | 5351.52i | 1.45278 | + | 0.838763i | ||||
\(345\) | −3837.16 | + | 11481.4i | −0.598800 | + | 1.79170i | ||||
\(346\) | 2573.19 | − | 1485.63i | 0.399814 | − | 0.230833i | ||||
\(347\) | 1142.47 | − | 659.607i | 0.176747 | − | 0.102045i | −0.409016 | − | 0.912527i | \(-0.634128\pi\) |
0.585763 | + | 0.810482i | \(0.300795\pi\) | |||||||
\(348\) | 716.742 | − | 146.082i | 0.110406 | − | 0.0225024i | ||||
\(349\) | 4291.07 | + | 2477.45i | 0.658153 | + | 0.379985i | 0.791573 | − | 0.611075i | \(-0.209262\pi\) |
−0.133420 | + | 0.991060i | \(0.542596\pi\) | |||||||
\(350\) | 6397.10 | + | 1477.64i | 0.976970 | + | 0.225666i | ||||
\(351\) | −4263.44 | − | 2028.09i | −0.648335 | − | 0.308409i | ||||
\(352\) | 2311.92 | 0.350073 | ||||||||
\(353\) | −2690.76 | + | 4660.53i | −0.405707 | + | 0.702706i | −0.994404 | − | 0.105648i | \(-0.966308\pi\) |
0.588696 | + | 0.808354i | \(0.299641\pi\) | |||||||
\(354\) | −4863.73 | + | 991.300i | −0.730239 | + | 0.148833i | ||||
\(355\) | −10637.7 | + | 6141.65i | −1.59039 | + | 0.918211i | ||||
\(356\) | 285.197 | + | 493.975i | 0.0424590 | + | 0.0735411i | ||||
\(357\) | −2188.88 | + | 3573.83i | −0.324504 | + | 0.529824i | ||||
\(358\) | −218.135 | + | 377.820i | −0.0322033 | + | 0.0557777i | ||||
\(359\) | − | 3814.03i | − | 0.560715i | −0.959896 | − | 0.280357i | \(-0.909547\pi\) | ||
0.959896 | − | 0.280357i | \(-0.0904530\pi\) | |||||||
\(360\) | −5339.13 | + | 7095.54i | −0.781659 | + | 1.03880i | ||||
\(361\) | 5818.78 | 0.848343 | ||||||||
\(362\) | −3372.26 | + | 5840.93i | −0.489619 | + | 0.848046i | ||||
\(363\) | −6023.60 | + | 5332.97i | −0.870955 | + | 0.771097i | ||||
\(364\) | −174.321 | − | 570.403i | −0.0251013 | − | 0.0821353i | ||||
\(365\) | 1977.88 | − | 1141.93i | 0.283635 | − | 0.163757i | ||||
\(366\) | 4082.68 | − | 3614.58i | 0.583074 | − | 0.516222i | ||||
\(367\) | 10883.1 | + | 6283.37i | 1.54794 | + | 0.893704i | 0.998299 | + | 0.0583038i | \(0.0185692\pi\) |
0.549642 | + | 0.835400i | \(0.314764\pi\) | |||||||
\(368\) | − | 10562.4i | − | 1.49621i | ||||||
\(369\) | 7743.26 | + | 5826.52i | 1.09241 | + | 0.821996i | ||||
\(370\) | 1884.41i | 0.264772i | ||||||||
\(371\) | −2695.99 | + | 2890.45i | −0.377274 | + | 0.404486i | ||||
\(372\) | −111.330 | + | 333.116i | −0.0155167 | + | 0.0464281i | ||||
\(373\) | 2338.60 | + | 4050.58i | 0.324633 | + | 0.562281i | 0.981438 | − | 0.191779i | \(-0.0614258\pi\) |
−0.656805 | + | 0.754061i | \(0.728092\pi\) | |||||||
\(374\) | −3496.80 | − | 6056.63i | −0.483463 | − | 0.837382i | ||||
\(375\) | 106.023 | + | 520.193i | 0.0146000 | + | 0.0716337i | ||||
\(376\) | 8329.90 | + | 4809.27i | 1.14250 | + | 0.659625i | ||||
\(377\) | −4950.11 | −0.676243 | ||||||||
\(378\) | −4835.19 | + | 6090.32i | −0.657925 | + | 0.828710i | ||||
\(379\) | −4851.71 | −0.657561 | −0.328780 | − | 0.944406i | \(-0.606638\pi\) | ||||
−0.328780 | + | 0.944406i | \(0.606638\pi\) | |||||||
\(380\) | 417.074 | + | 240.798i | 0.0563038 | + | 0.0325070i | ||||
\(381\) | 1407.47 | + | 6905.63i | 0.189257 | + | 0.928573i | ||||
\(382\) | 5531.81 | + | 9581.38i | 0.740922 | + | 1.28331i | ||||
\(383\) | −2456.18 | − | 4254.22i | −0.327689 | − | 0.567573i | 0.654364 | − | 0.756180i | \(-0.272936\pi\) |
−0.982053 | + | 0.188606i | \(0.939603\pi\) | |||||||
\(384\) | 2721.70 | − | 8143.72i | 0.361696 | − | 1.08225i | ||||
\(385\) | 10576.2 | − | 11339.1i | 1.40004 | − | 1.50102i | ||||
\(386\) | 13137.0i | 1.73227i | ||||||||
\(387\) | 1661.34 | − | 13608.8i | 0.218218 | − | 1.78753i | ||||
\(388\) | − | 697.825i | − | 0.0913059i | ||||||
\(389\) | −4621.95 | − | 2668.48i | −0.602421 | − | 0.347808i | 0.167572 | − | 0.985860i | \(-0.446407\pi\) |
−0.769994 | + | 0.638052i | \(0.779741\pi\) | |||||||
\(390\) | −6113.67 | + | 5412.72i | −0.793790 | + | 0.702778i | ||||
\(391\) | −5631.24 | + | 3251.20i | −0.728349 | + | 0.420512i | ||||
\(392\) | 7212.41 | − | 502.731i | 0.929290 | − | 0.0647748i | ||||
\(393\) | −7617.57 | + | 6744.18i | −0.977750 | + | 0.865646i | ||||
\(394\) | −3157.95 | + | 5469.74i | −0.403795 | + | 0.699394i | ||||
\(395\) | −6025.71 | −0.767561 | ||||||||
\(396\) | −542.637 | − | 1275.90i | −0.0688600 | − | 0.161911i | ||||
\(397\) | − | 1308.17i | − | 0.165378i | −0.996575 | − | 0.0826889i | \(-0.973649\pi\) | ||
0.996575 | − | 0.0826889i | \(-0.0263508\pi\) | |||||||
\(398\) | −5152.44 | + | 8924.29i | −0.648916 | + | 1.12396i | ||||
\(399\) | −2646.79 | − | 1621.09i | −0.332094 | − | 0.203399i | ||||
\(400\) | 4189.66 | + | 7256.70i | 0.523707 | + | 0.907087i | ||||
\(401\) | −1742.21 | + | 1005.86i | −0.216962 | + | 0.125263i | −0.604543 | − | 0.796573i | \(-0.706644\pi\) |
0.387581 | + | 0.921836i | \(0.373311\pi\) | |||||||
\(402\) | 8815.37 | − | 1796.70i | 1.09371 | − | 0.222914i | ||||
\(403\) | 1188.43 | − | 2058.42i | 0.146898 | − | 0.254434i | ||||
\(404\) | 548.791 | 0.0675826 | ||||||||
\(405\) | 11040.5 | + | 2736.39i | 1.35458 | + | 0.335734i | ||||
\(406\) | −1834.98 | + | 7944.12i | −0.224306 | + | 0.971084i | ||||
\(407\) | 1875.25 | + | 1082.68i | 0.228386 | + | 0.131858i | ||||
\(408\) | −4673.68 | + | 952.565i | −0.567112 | + | 0.115586i | ||||
\(409\) | −61.5250 | + | 35.5215i | −0.00743818 | + | 0.00429444i | −0.503714 | − | 0.863870i | \(-0.668034\pi\) |
0.496276 | + | 0.868165i | \(0.334700\pi\) | |||||||
\(410\) | 14514.5 | − | 8379.96i | 1.74834 | − | 1.00941i | ||||
\(411\) | 1634.44 | − | 4890.48i | 0.196158 | − | 0.586933i | ||||
\(412\) | 1358.98 | + | 784.610i | 0.162506 | + | 0.0938227i | ||||
\(413\) | 1330.42 | − | 5759.76i | 0.158512 | − | 0.686245i | ||||
\(414\) | −11103.0 | + | 4722.06i | −1.31807 | + | 0.560572i | ||||
\(415\) | 3086.40 | 0.365073 | ||||||||
\(416\) | 724.953 | − | 1255.66i | 0.0854417 | − | 0.147989i | ||||
\(417\) | −2872.24 | − | 3244.20i | −0.337300 | − | 0.380981i | ||||
\(418\) | 4485.56 | − | 2589.74i | 0.524871 | − | 0.303034i | ||||
\(419\) | 1825.15 | + | 3161.25i | 0.212803 | + | 0.368585i | 0.952591 | − | 0.304255i | \(-0.0984076\pi\) |
−0.739788 | + | 0.672840i | \(0.765074\pi\) | |||||||
\(420\) | 685.965 | + | 1262.68i | 0.0796944 | + | 0.146696i | ||||
\(421\) | −2970.12 | + | 5144.40i | −0.343836 | + | 0.595541i | −0.985142 | − | 0.171744i | \(-0.945060\pi\) |
0.641306 | + | 0.767285i | \(0.278393\pi\) | |||||||
\(422\) | − | 11163.7i | − | 1.28778i | ||||||
\(423\) | 1493.00 | − | 12229.9i | 0.171613 | − | 1.40576i | ||||
\(424\) | −4498.57 | −0.515259 | ||||||||
\(425\) | 2579.22 | − | 4467.34i | 0.294378 | − | 0.509877i | ||||
\(426\) | −11611.3 | − | 3880.58i | −1.32058 | − | 0.441349i | ||||
\(427\) | 1897.95 | + | 6210.37i | 0.215101 | + | 0.703843i | ||||
\(428\) | 312.948 | − | 180.680i | 0.0353432 | − | 0.0204054i | ||||
\(429\) | 1873.84 | + | 9193.83i | 0.210885 | + | 1.03469i | ||||
\(430\) | −20534.6 | − | 11855.7i | −2.30295 | − | 1.32961i | ||||
\(431\) | 7508.08i | 0.839098i | 0.907733 | + | 0.419549i | \(0.137812\pi\) | ||||
−0.907733 | + | 0.419549i | \(0.862188\pi\) | |||||||
\(432\) | −9893.16 | + | 789.001i | −1.10182 | + | 0.0878723i | ||||
\(433\) | − | 6880.95i | − | 0.763689i | −0.924227 | − | 0.381845i | \(-0.875289\pi\) | ||
0.924227 | − | 0.381845i | \(-0.124711\pi\) | |||||||
\(434\) | −2862.88 | − | 2670.27i | −0.316642 | − | 0.295339i | ||||
\(435\) | 11685.7 | − | 2381.72i | 1.28802 | − | 0.262517i | ||||
\(436\) | −557.964 | − | 966.423i | −0.0612882 | − | 0.106154i | ||||
\(437\) | −2407.85 | − | 4170.52i | −0.263577 | − | 0.456529i | ||||
\(438\) | 2158.90 | + | 721.522i | 0.235516 | + | 0.0787115i | ||||
\(439\) | −4495.14 | − | 2595.27i | −0.488705 | − | 0.282154i | 0.235332 | − | 0.971915i | \(-0.424382\pi\) |
−0.724037 | + | 0.689761i | \(0.757715\pi\) | |||||||
\(440\) | 17647.7 | 1.91209 | ||||||||
\(441\) | −4208.31 | − | 8249.62i | −0.454413 | − | 0.890791i | ||||
\(442\) | −4385.99 | −0.471992 | ||||||||
\(443\) | −878.510 | − | 507.208i | −0.0942196 | − | 0.0543977i | 0.452150 | − | 0.891942i | \(-0.350657\pi\) |
−0.546369 | + | 0.837544i | \(0.683991\pi\) | |||||||
\(444\) | −150.247 | + | 133.020i | −0.0160595 | + | 0.0142182i | ||||
\(445\) | 4649.83 | + | 8053.74i | 0.495333 | + | 0.857942i | ||||
\(446\) | −4077.27 | − | 7062.04i | −0.432880 | − | 0.749770i | ||||
\(447\) | 5266.04 | + | 5948.00i | 0.557215 | + | 0.629376i | ||||
\(448\) | 5918.14 | + | 5519.99i | 0.624121 | + | 0.582132i | ||||
\(449\) | − | 6361.05i | − | 0.668589i | −0.942469 | − | 0.334295i | \(-0.891502\pi\) | ||
0.942469 | − | 0.334295i | \(-0.108498\pi\) | |||||||
\(450\) | 5755.05 | − | 7648.27i | 0.602879 | − | 0.801207i | ||||
\(451\) | − | 19258.7i | − | 2.01077i | ||||||
\(452\) | −267.070 | − | 154.193i | −0.0277919 | − | 0.0160456i | ||||
\(453\) | −3682.07 | − | 1230.58i | −0.381896 | − | 0.127633i | ||||
\(454\) | 14684.0 | − | 8477.83i | 1.51796 | − | 0.876397i | ||||
\(455\) | −2842.11 | − | 9299.82i | −0.292836 | − | 0.958203i | ||||
\(456\) | −705.473 | − | 3461.34i | −0.0724491 | − | 0.355466i | ||||
\(457\) | −2808.03 | + | 4863.65i | −0.287427 | + | 0.497838i | −0.973195 | − | 0.229982i | \(-0.926133\pi\) |
0.685768 | + | 0.727820i | \(0.259467\pi\) | |||||||
\(458\) | −1267.69 | −0.129334 | ||||||||
\(459\) | 3465.84 | + | 5031.57i | 0.352444 | + | 0.511664i | ||||
\(460\) | 2229.55i | 0.225986i | ||||||||
\(461\) | −2311.52 | + | 4003.68i | −0.233532 | + | 0.404490i | −0.958845 | − | 0.283929i | \(-0.908362\pi\) |
0.725313 | + | 0.688420i | \(0.241695\pi\) | |||||||
\(462\) | 15449.2 | + | 400.890i | 1.55576 | + | 0.0403703i | ||||
\(463\) | 2180.04 | + | 3775.94i | 0.218823 | + | 0.379012i | 0.954448 | − | 0.298376i | \(-0.0964450\pi\) |
−0.735626 | + | 0.677388i | \(0.763112\pi\) | |||||||
\(464\) | −9011.59 | + | 5202.85i | −0.901622 | + | 0.520552i | ||||
\(465\) | −1815.12 | + | 5431.10i | −0.181020 | + | 0.541637i | ||||
\(466\) | −351.363 | + | 608.578i | −0.0349283 | + | 0.0604975i | ||||
\(467\) | 10923.9 | 1.08243 | 0.541216 | − | 0.840884i | \(-0.317964\pi\) | ||||
0.541216 | + | 0.840884i | \(0.317964\pi\) | |||||||
\(468\) | −863.129 | − | 105.369i | −0.0852524 | − | 0.0104075i | ||||
\(469\) | −2411.34 | + | 10439.4i | −0.237410 | + | 1.02782i | ||||
\(470\) | −18453.9 | − | 10654.4i | −1.81110 | − | 1.04564i | ||||
\(471\) | −4745.73 | − | 5360.31i | −0.464271 | − | 0.524395i | ||||
\(472\) | 5826.58 | − | 3363.98i | 0.568200 | − | 0.328050i | ||||
\(473\) | −23596.1 | + | 13623.2i | −2.29377 | + | 1.32431i | ||||
\(474\) | −3981.07 | − | 4496.63i | −0.385774 | − | 0.435732i | ||||
\(475\) | 3308.53 | + | 1910.18i | 0.319591 | + | 0.184516i | ||||
\(476\) | −173.714 | + | 752.056i | −0.0167272 | + | 0.0724169i | ||||
\(477\) | 2255.22 | + | 5302.70i | 0.216477 | + | 0.509002i | ||||
\(478\) | 5446.01 | 0.521118 | ||||||||
\(479\) | −4797.57 | + | 8309.64i | −0.457634 | + | 0.792645i | −0.998835 | − | 0.0482479i | \(-0.984636\pi\) |
0.541202 | + | 0.840893i | \(0.317970\pi\) | |||||||
\(480\) | −1107.24 | + | 3313.03i | −0.105288 | + | 0.315038i | ||||
\(481\) | 1176.06 | − | 678.996i | 0.111483 | − | 0.0643649i | ||||
\(482\) | −4075.18 | − | 7058.41i | −0.385102 | − | 0.667016i | ||||
\(483\) | 372.734 | − | 14364.2i | 0.0351138 | − | 1.35319i | ||||
\(484\) | −740.859 | + | 1283.21i | −0.0695773 | + | 0.120511i | ||||
\(485\) | − | 11377.3i | − | 1.06519i | ||||||
\(486\) | 5252.24 | + | 10046.7i | 0.490219 | + | 0.937716i | ||||
\(487\) | −8240.46 | −0.766758 | −0.383379 | − | 0.923591i | \(-0.625240\pi\) | ||||
−0.383379 | + | 0.923591i | \(0.625240\pi\) | |||||||
\(488\) | −3695.46 | + | 6400.72i | −0.342798 | + | 0.593744i | ||||
\(489\) | 1971.96 | + | 9675.25i | 0.182362 | + | 0.894744i | ||||
\(490\) | −15978.3 | + | 1113.74i | −1.47311 | + | 0.102681i | ||||
\(491\) | 1742.44 | − | 1006.00i | 0.160153 | − | 0.0924645i | −0.417781 | − | 0.908548i | \(-0.637192\pi\) |
0.577935 | + | 0.816083i | \(0.303859\pi\) | |||||||
\(492\) | 1692.73 | + | 565.724i | 0.155110 | + | 0.0518390i | ||||
\(493\) | 5547.68 | + | 3202.96i | 0.506806 | + | 0.292604i | ||||
\(494\) | − | 3248.28i | − | 0.295844i | ||||||
\(495\) | −8847.13 | − | 20802.3i | −0.803331 | − | 1.88887i | ||||
\(496\) | − | 4996.42i | − | 0.452310i | ||||||
\(497\) | 9944.68 | − | 10662.0i | 0.897545 | − | 0.962285i | ||||
\(498\) | 2039.12 | + | 2303.20i | 0.183485 | + | 0.207246i | ||||
\(499\) | −7186.51 | − | 12447.4i | −0.644714 | − | 1.11668i | −0.984367 | − | 0.176127i | \(-0.943643\pi\) |
0.339653 | − | 0.940551i | \(-0.389690\pi\) | |||||||
\(500\) | 48.8883 | + | 84.6769i | 0.00437270 | + | 0.00757374i | ||||
\(501\) | 6508.04 | − | 5761.87i | 0.580355 | − | 0.513815i | ||||
\(502\) | 10923.8 | + | 6306.87i | 0.971222 | + | 0.560735i | ||||
\(503\) | −12261.8 | −1.08693 | −0.543467 | − | 0.839430i | \(-0.682889\pi\) | ||||
−0.543467 | + | 0.839430i | \(0.682889\pi\) | |||||||
\(504\) | 3599.17 | − | 9906.67i | 0.318095 | − | 0.875552i | ||||
\(505\) | 8947.46 | 0.788429 | ||||||||
\(506\) | 20766.0 | + | 11989.2i | 1.82443 | + | 1.05333i | ||||
\(507\) | −5246.31 | − | 1753.36i | −0.459560 | − | 0.153589i | ||||
\(508\) | 648.998 | + | 1124.10i | 0.0566824 | + | 0.0981768i | ||||
\(509\) | 10985.2 | + | 19026.9i | 0.956602 | + | 1.65688i | 0.730658 | + | 0.682744i | \(0.239213\pi\) |
0.225945 | + | 0.974140i | \(0.427453\pi\) | |||||||
\(510\) | 10354.0 | − | 2110.30i | 0.898986 | − | 0.183227i | ||||
\(511\) | −1849.03 | + | 1982.40i | −0.160071 | + | 0.171617i | ||||
\(512\) | 8880.88i | 0.766569i | ||||||||
\(513\) | −3726.40 | + | 2566.82i | −0.320711 | + | 0.220912i | ||||
\(514\) | 8314.01i | 0.713454i | ||||||||
\(515\) | 22156.8 | + | 12792.2i | 1.89582 | + | 1.09455i | ||||
\(516\) | −504.268 | − | 2474.15i | −0.0430216 | − | 0.211082i | ||||
\(517\) | −21205.3 | + | 12242.9i | −1.80388 | + | 1.04147i | ||||
\(518\) | −653.722 | − | 2139.08i | −0.0554496 | − | 0.181440i | ||||
\(519\) | 4892.71 | + | 1635.18i | 0.413807 | + | 0.138298i | ||||
\(520\) | 5533.82 | − | 9584.87i | 0.466681 | − | 0.808316i | ||||
\(521\) | 9869.79 | 0.829949 | 0.414974 | − | 0.909833i | \(-0.363791\pi\) | ||||
0.414974 | + | 0.909833i | \(0.363791\pi\) | |||||||
\(522\) | 9497.87 | + | 7146.80i | 0.796380 | + | 0.599247i | ||||
\(523\) | 4243.21i | 0.354766i | 0.984142 | + | 0.177383i | \(0.0567632\pi\) | ||||
−0.984142 | + | 0.177383i | \(0.943237\pi\) | |||||||
\(524\) | −936.906 | + | 1622.77i | −0.0781087 | + | 0.135288i | ||||
\(525\) | 5441.56 | + | 10016.4i | 0.452360 | + | 0.832673i | ||||
\(526\) | −4729.98 | − | 8192.57i | −0.392086 | − | 0.679112i | ||||
\(527\) | −2663.79 | + | 1537.94i | −0.220183 | + | 0.127123i | ||||
\(528\) | 13074.5 | + | 14767.7i | 1.07764 | + | 1.21720i | ||||
\(529\) | 5063.67 | − | 8770.54i | 0.416181 | − | 0.720846i | ||||
\(530\) | 9966.06 | 0.816788 | ||||||||
\(531\) | −6886.28 | − | 5181.67i | −0.562785 | − | 0.423475i | ||||
\(532\) | −556.976 | − | 128.653i | −0.0453909 | − | 0.0104846i | ||||
\(533\) | −10459.8 | − | 6038.99i | −0.850029 | − | 0.490765i | ||||
\(534\) | −2937.98 | + | 8790.85i | −0.238087 | + | 0.712392i | ||||
\(535\) | 5102.28 | − | 2945.80i | 0.412319 | − | 0.238053i | ||||
\(536\) | −10560.5 | + | 6097.11i | −0.851015 | + | 0.491334i | ||||
\(537\) | −742.194 | + | 151.270i | −0.0596425 | + | 0.0121560i | ||||
\(538\) | −11241.7 | − | 6490.41i | −0.900865 | − | 0.520115i | ||||
\(539\) | −8071.91 | + | 16540.5i | −0.645050 | + | 1.32180i | ||||
\(540\) | 2088.28 | − | 166.545i | 0.166417 | − | 0.0132721i | ||||
\(541\) | 3649.63 | 0.290037 | 0.145018 | − | 0.989429i | \(-0.453676\pi\) | ||||
0.145018 | + | 0.989429i | \(0.453676\pi\) | |||||||
\(542\) | −12569.3 | + | 21770.7i | −0.996124 | + | 1.72534i | ||||
\(543\) | −11474.0 | + | 2338.56i | −0.906805 | + | 0.184820i | ||||
\(544\) | −1624.94 | + | 938.158i | −0.128067 | + | 0.0739397i | ||||
\(545\) | −9097.02 | − | 15756.5i | −0.714997 | − | 1.23841i | ||||
\(546\) | 5062.18 | − | 8265.12i | 0.396779 | − | 0.647829i | ||||
\(547\) | 758.912 | − | 1314.47i | 0.0593212 | − | 0.102747i | −0.834840 | − | 0.550493i | \(-0.814440\pi\) |
0.894161 | + | 0.447746i | \(0.147773\pi\) | |||||||
\(548\) | − | 949.678i | − | 0.0740296i | ||||||
\(549\) | 9397.47 | + | 1147.23i | 0.730554 | + | 0.0891847i | ||||
\(550\) | −19022.4 | −1.47476 | ||||||||
\(551\) | −2372.12 | + | 4108.64i | −0.183404 | + | 0.317666i | ||||
\(552\) | 12244.5 | − | 10840.6i | 0.944130 | − | 0.835882i | ||||
\(553\) | 6840.06 | − | 2090.39i | 0.525984 | − | 0.160745i | ||||
\(554\) | 9467.81 | − | 5466.24i | 0.726081 | − | 0.419203i | ||||
\(555\) | −2449.62 | + | 2168.76i | −0.187352 | + | 0.165871i | ||||
\(556\) | −691.111 | − | 399.013i | −0.0527152 | − | 0.0304351i | ||||
\(557\) | 3101.35i | 0.235922i | 0.993018 | + | 0.117961i | \(0.0376357\pi\) | ||||
−0.993018 | + | 0.117961i | \(0.962364\pi\) | |||||||
\(558\) | −5252.13 | + | 2233.71i | −0.398459 | + | 0.169463i | ||||
\(559\) | 17087.5i | 1.29289i | ||||||||
\(560\) | −14948.7 | − | 13943.0i | −1.12803 | − | 1.05214i | ||||
\(561\) | 3848.80 | − | 11516.2i | 0.289655 | − | 0.866690i | ||||
\(562\) | −12439.0 | − | 21545.0i | −0.933643 | − | 1.61712i | ||||
\(563\) | 488.465 | + | 846.047i | 0.0365655 | + | 0.0633333i | 0.883729 | − | 0.467999i | \(-0.155025\pi\) |
−0.847164 | + | 0.531332i | \(0.821692\pi\) | |||||||
\(564\) | −453.173 | − | 2223.45i | −0.0338333 | − | 0.166001i | ||||
\(565\) | −4354.30 | − | 2513.96i | −0.324224 | − | 0.187191i | ||||
\(566\) | −4474.02 | −0.332256 | ||||||||
\(567\) | −13481.8 | + | 723.870i | −0.998562 | + | 0.0536149i | ||||
\(568\) | 16593.9 | 1.22581 | ||||||||
\(569\) | 14997.0 | + | 8658.53i | 1.10493 | + | 0.637934i | 0.937513 | − | 0.347952i | \(-0.113123\pi\) |
0.167421 | + | 0.985885i | \(0.446456\pi\) | |||||||
\(570\) | 1562.89 | + | 7668.21i | 0.114846 | + | 0.563484i | ||||
\(571\) | −9602.72 | − | 16632.4i | −0.703785 | − | 1.21899i | −0.967128 | − | 0.254289i | \(-0.918158\pi\) |
0.263343 | − | 0.964702i | \(-0.415175\pi\) | |||||||
\(572\) | 864.045 | + | 1496.57i | 0.0631601 | + | 0.109396i | ||||
\(573\) | −6088.67 | + | 18218.2i | −0.443906 | + | 1.32823i | ||||
\(574\) | −13569.0 | + | 14547.7i | −0.986688 | + | 1.05786i | ||||
\(575\) | 17686.4i | 1.28274i | ||||||||
\(576\) | 10857.2 | − | 4617.52i | 0.785387 | − | 0.334022i | ||||
\(577\) | − | 19299.1i | − | 1.39243i | −0.717832 | − | 0.696216i | \(-0.754866\pi\) | ||
0.717832 | − | 0.696216i | \(-0.245134\pi\) | |||||||
\(578\) | −7818.36 | − | 4513.93i | −0.562631 | − | 0.324835i | ||||
\(579\) | −17077.3 | + | 15119.3i | −1.22575 | + | 1.08521i | ||||
\(580\) | 1902.20 | − | 1098.24i | 0.136180 | − | 0.0786237i | ||||
\(581\) | −3503.51 | + | 1070.70i | −0.250172 | + | 0.0764549i | ||||
\(582\) | 8490.20 | − | 7516.76i | 0.604691 | − | 0.535361i | ||||
\(583\) | 5725.95 | − | 9917.64i | 0.406766 | − | 0.704540i | ||||
\(584\) | −3085.32 | −0.218616 | ||||||||
\(585\) | −14072.4 | − | 1717.93i | −0.994568 | − | 0.121415i | ||||
\(586\) | 837.023i | 0.0590053i | ||||||||
\(587\) | 4690.62 | − | 8124.39i | 0.329817 | − | 0.571260i | −0.652658 | − | 0.757652i | \(-0.726346\pi\) |
0.982475 | + | 0.186392i | \(0.0596796\pi\) | |||||||
\(588\) | −1216.71 | − | 1195.35i | −0.0853335 | − | 0.0838359i | ||||
\(589\) | −1139.00 | − | 1972.81i | −0.0796804 | − | 0.138011i | ||||
\(590\) | −12908.1 | + | 7452.51i | −0.900710 | + | 0.520025i | ||||
\(591\) | −10744.8 | + | 2189.95i | −0.747854 | + | 0.152424i | ||||
\(592\) | 1427.33 | − | 2472.20i | 0.0990925 | − | 0.171633i | ||||
\(593\) | 21351.5 | 1.47859 | 0.739294 | − | 0.673383i | \(-0.235159\pi\) | ||||
0.739294 | + | 0.673383i | \(0.235159\pi\) | |||||||
\(594\) | 9678.37 | − | 20345.8i | 0.668532 | − | 1.40538i | ||||
\(595\) | −2832.22 | + | 12261.5i | −0.195142 | + | 0.844826i | ||||
\(596\) | 1267.10 | + | 731.562i | 0.0870847 | + | 0.0502784i | ||||
\(597\) | −17531.0 | + | 3573.07i | −1.20183 | + | 0.244951i | ||||
\(598\) | 13023.2 | − | 7518.98i | 0.890569 | − | 0.514170i | ||||
\(599\) | 15576.0 | − | 8992.82i | 1.06247 | − | 0.613417i | 0.136355 | − | 0.990660i | \(-0.456461\pi\) |
0.926114 | + | 0.377243i | \(0.123128\pi\) | |||||||
\(600\) | −4112.32 | + | 12304.7i | −0.279808 | + | 0.837227i | ||||
\(601\) | −14051.1 | − | 8112.39i | −0.953669 | − | 0.550601i | −0.0594502 | − | 0.998231i | \(-0.518935\pi\) |
−0.894219 | + | 0.447630i | \(0.852268\pi\) | |||||||
\(602\) | 27422.6 | + | 6334.22i | 1.85658 | + | 0.428843i | ||||
\(603\) | 12481.2 | + | 9391.62i | 0.842906 | + | 0.634256i | ||||
\(604\) | −715.019 | −0.0481684 | ||||||||
\(605\) | −12078.9 | + | 20921.3i | −0.811699 | + | 1.40590i | ||||
\(606\) | 5911.42 | + | 6676.96i | 0.396262 | + | 0.447579i | ||||
\(607\) | 9689.02 | − | 5593.96i | 0.647883 | − | 0.374055i | −0.139762 | − | 0.990185i | \(-0.544634\pi\) |
0.787645 | + | 0.616130i | \(0.211300\pi\) | |||||||
\(608\) | −694.803 | − | 1203.43i | −0.0463454 | − | 0.0802726i | ||||
\(609\) | −12438.7 | + | 6757.50i | −0.827657 | + | 0.449635i | ||||
\(610\) | 8186.86 | − | 14180.1i | 0.543404 | − | 0.941203i | ||||
\(611\) | 15356.1i | 1.01676i | ||||||||
\(612\) | 899.146 | + | 676.575i | 0.0593886 | + | 0.0446878i | ||||
\(613\) | 26379.5 | 1.73810 | 0.869052 | − | 0.494720i | \(-0.164729\pi\) | ||||
0.869052 | + | 0.494720i | \(0.164729\pi\) | |||||||
\(614\) | 16052.7 | − | 27804.2i | 1.05511 | − | 1.82750i | ||||
\(615\) | 27598.1 | + | 9223.53i | 1.80953 | + | 0.604762i | ||||
\(616\) | −20032.7 | + | 6122.18i | −1.31029 | + | 0.400438i | ||||
\(617\) | 18989.8 | − | 10963.8i | 1.23906 | − | 0.715371i | 0.270157 | − | 0.962816i | \(-0.412924\pi\) |
0.968902 | + | 0.247445i | \(0.0795909\pi\) | |||||||
\(618\) | 5092.49 | + | 24985.9i | 0.331473 | + | 1.62634i | ||||
\(619\) | −15019.6 | − | 8671.59i | −0.975267 | − | 0.563071i | −0.0744291 | − | 0.997226i | \(-0.523713\pi\) |
−0.900838 | + | 0.434156i | \(0.857047\pi\) | |||||||
\(620\) | 1054.66i | 0.0683165i | ||||||||
\(621\) | −18916.8 | − | 8998.61i | −1.22239 | − | 0.581485i | ||||
\(622\) | 28589.5i | 1.84298i | ||||||||
\(623\) | −8072.17 | − | 7529.09i | −0.519108 | − | 0.484184i | ||||
\(624\) | 12120.5 | − | 2470.33i | 0.777576 | − | 0.158481i | ||||
\(625\) | 8200.32 | + | 14203.4i | 0.524820 | + | 0.909015i | ||||
\(626\) | −5521.30 | − | 9563.17i | −0.352517 | − | 0.610577i | ||||
\(627\) | 8528.91 | + | 2850.44i | 0.543241 | + | 0.181556i | ||||
\(628\) | −1141.91 | − | 659.280i | −0.0725590 | − | 0.0418919i | ||||
\(629\) | −1757.37 | −0.111401 | ||||||||
\(630\) | −7973.56 | + | 21947.1i | −0.504245 | + | 1.38793i | ||||
\(631\) | −30543.8 | −1.92699 | −0.963495 | − | 0.267727i | \(-0.913727\pi\) | ||||
−0.963495 | + | 0.267727i | \(0.913727\pi\) | |||||||
\(632\) | 7049.71 | + | 4070.15i | 0.443706 | + | 0.256174i | ||||
\(633\) | 14512.1 | − | 12848.3i | 0.911226 | − | 0.806750i | ||||
\(634\) | −1127.43 | − | 1952.77i | −0.0706248 | − | 0.122326i | ||||
\(635\) | 10581.2 | + | 18327.2i | 0.661265 | + | 1.14534i | ||||
\(636\) | 703.504 | + | 794.609i | 0.0438612 | + | 0.0495414i | ||||
\(637\) | 6452.42 | + | 9570.69i | 0.401341 | + | 0.595298i | ||||
\(638\) | − | 23622.7i | − | 1.46588i | ||||||
\(639\) | −8318.82 | − | 19560.1i | −0.515004 | − | 1.21093i | ||||
\(640\) | − | 25783.4i | − | 1.59247i | ||||||
\(641\) | −513.438 | − | 296.433i | −0.0316374 | − | 0.0182659i | 0.484098 | − | 0.875014i | \(-0.339148\pi\) |
−0.515735 | + | 0.856748i | \(0.672481\pi\) | |||||||
\(642\) | 5569.26 | + | 1861.29i | 0.342369 | + | 0.114423i | ||||
\(643\) | 27553.5 | − | 15908.0i | 1.68990 | − | 0.975661i | 0.735307 | − | 0.677735i | \(-0.237038\pi\) |
0.954589 | − | 0.297927i | \(-0.0962951\pi\) | |||||||
\(644\) | −773.457 | − | 2530.87i | −0.0473268 | − | 0.154861i | ||||
\(645\) | −8221.55 | − | 40338.4i | −0.501897 | − | 2.46251i | ||||
\(646\) | −2101.79 | + | 3640.41i | −0.128009 | + | 0.221718i | ||||
\(647\) | −14337.8 | −0.871218 | −0.435609 | − | 0.900136i | \(-0.643467\pi\) | ||||
−0.435609 | + | 0.900136i | \(0.643467\pi\) | |||||||
\(648\) | −11068.4 | − | 10658.9i | −0.670997 | − | 0.646172i | ||||
\(649\) | 17127.2i | 1.03591i | ||||||||
\(650\) | −5964.90 | + | 10331.5i | −0.359943 | + | 0.623439i | ||||
\(651\) | 176.317 | − | 6794.78i | 0.0106151 | − | 0.409076i | ||||
\(652\) | 909.290 | + | 1574.94i | 0.0546174 | + | 0.0946001i | ||||
\(653\) | 1310.50 | − | 756.617i | 0.0785356 | − | 0.0453426i | −0.460218 | − | 0.887806i | \(-0.652229\pi\) |
0.538754 | + | 0.842463i | \(0.318895\pi\) | |||||||
\(654\) | 5747.92 | − | 17198.6i | 0.343672 | − | 1.02832i | ||||
\(655\) | −15275.3 | + | 26457.5i | −0.911228 | + | 1.57829i | ||||
\(656\) | −25389.3 | −1.51110 | ||||||||
\(657\) | 1546.73 | + | 3636.83i | 0.0918474 | + | 0.215961i | ||||
\(658\) | 24644.0 | + | 5692.40i | 1.46007 | + | 0.337254i | ||||
\(659\) | 2743.47 | + | 1583.94i | 0.162171 | + | 0.0936293i | 0.578889 | − | 0.815406i | \(-0.303486\pi\) |
−0.416718 | + | 0.909036i | \(0.636820\pi\) | |||||||
\(660\) | −2759.82 | − | 3117.22i | −0.162766 | − | 0.183845i | ||||
\(661\) | −4954.29 | + | 2860.36i | −0.291527 | + | 0.168313i | −0.638630 | − | 0.769514i | \(-0.720499\pi\) |
0.347103 | + | 0.937827i | \(0.387165\pi\) | |||||||
\(662\) | −16169.8 | + | 9335.64i | −0.949331 | + | 0.548097i | ||||
\(663\) | −5047.82 | − | 5701.52i | −0.295688 | − | 0.333980i | ||||
\(664\) | −3610.89 | − | 2084.75i | −0.211039 | − | 0.121843i | ||||
\(665\) | −9080.90 | − | 2097.55i | −0.529537 | − | 0.122315i | ||||
\(666\) | −3236.83 | − | 395.146i | −0.188325 | − | 0.0229904i | ||||
\(667\) | −21963.5 | −1.27501 | ||||||||
\(668\) | 800.442 | − | 1386.41i | 0.0463623 | − | 0.0803019i | ||||
\(669\) | 4487.71 | − | 13427.9i | 0.259350 | − | 0.776011i | ||||
\(670\) | 23395.6 | − | 13507.4i | 1.34903 | − | 0.778863i | ||||
\(671\) | −9407.45 | − | 16294.2i | −0.541238 | − | 0.937451i | ||||
\(672\) | 107.555 | − | 4144.89i | 0.00617415 | − | 0.237935i | ||||
\(673\) | 3370.28 | − | 5837.50i | 0.193038 | − | 0.334352i | −0.753217 | − | 0.657772i | \(-0.771499\pi\) |
0.946256 | + | 0.323420i | \(0.104833\pi\) | |||||||
\(674\) | − | 23522.2i | − | 1.34427i | ||||||
\(675\) | 16565.7 | − | 1321.15i | 0.944616 | − | 0.0753352i | ||||
\(676\) | −1018.78 | −0.0579641 | ||||||||
\(677\) | −2209.63 | + | 3827.20i | −0.125440 | + | 0.217269i | −0.921905 | − | 0.387416i | \(-0.873368\pi\) |
0.796465 | + | 0.604685i | \(0.206701\pi\) | |||||||
\(678\) | −1000.79 | − | 4910.28i | −0.0566888 | − | 0.278139i | ||||
\(679\) | 3946.91 | + | 12914.9i | 0.223076 | + | 0.729938i | ||||
\(680\) | −12403.7 | + | 7161.30i | −0.699502 | + | 0.403858i | ||||
\(681\) | 27920.4 | + | 9331.25i | 1.57109 | + | 0.525072i | ||||
\(682\) | 9823.06 | + | 5671.35i | 0.551532 | + | 0.318427i | ||||
\(683\) | − | 25188.7i | − | 1.41115i | −0.708633 | − | 0.705577i | \(-0.750688\pi\) | ||
0.708633 | − | 0.705577i | \(-0.249312\pi\) | |||||||
\(684\) | −501.074 | + | 665.911i | −0.0280103 | + | 0.0372248i | ||||
\(685\) | − | 15483.5i | − | 0.863640i | ||||||
\(686\) | 17751.3 | − | 6807.29i | 0.987970 | − | 0.378868i | ||||
\(687\) | −1458.97 | − | 1647.91i | −0.0810237 | − | 0.0915165i | ||||
\(688\) | 17959.9 | + | 31107.5i | 0.995225 | + | 1.72378i | ||||
\(689\) | −3591.00 | − | 6219.79i | −0.198558 | − | 0.343912i | ||||
\(690\) | −27126.2 | + | 24016.1i | −1.49664 | + | 1.32504i | ||||
\(691\) | 21.1593 | + | 12.2163i | 0.00116489 | + | 0.000672548i | 0.500582 | − | 0.865689i | \(-0.333119\pi\) |
−0.499417 | + | 0.866361i | \(0.666453\pi\) | |||||||
\(692\) | 950.111 | 0.0521933 | ||||||||
\(693\) | 17259.3 | + | 20544.4i | 0.946070 | + | 1.12614i | ||||
\(694\) | 3948.18 | 0.215952 | ||||||||
\(695\) | −11267.8 | − | 6505.49i | −0.614983 | − | 0.355061i | ||||
\(696\) | −15280.3 | − | 5106.81i | −0.832183 | − | 0.278122i | ||||
\(697\) | 7815.02 | + | 13536.0i | 0.424699 | + | 0.735600i | ||||
\(698\) | 7414.57 | + | 12842.4i | 0.402071 | + | 0.696408i | ||||
\(699\) | −1195.50 | + | 243.660i | −0.0646893 | + | 0.0131846i | ||||
\(700\) | 1535.27 | + | 1431.98i | 0.0828970 | + | 0.0773199i | ||||
\(701\) | − | 5989.84i | − | 0.322729i | −0.986895 | − | 0.161365i | \(-0.948411\pi\) | ||
0.986895 | − | 0.161365i | \(-0.0515895\pi\) | |||||||
\(702\) | −8015.38 | − | 11636.4i | −0.430941 | − | 0.625624i | ||||
\(703\) | − | 1301.52i | − | 0.0698259i | ||||||
\(704\) | −20306.2 | − | 11723.8i | −1.08710 | − | 0.627639i | ||||
\(705\) | −7388.50 | − | 36251.1i | −0.394705 | − | 1.93659i | ||||
\(706\) | −13948.2 | + | 8052.98i | −0.743550 | + | 0.429289i | ||||
\(707\) | −10156.7 | + | 3103.97i | −0.540284 | + | 0.165116i | ||||
\(708\) | −1505.38 | − | 503.112i | −0.0799094 | − | 0.0267064i | ||||
\(709\) | −2214.14 | + | 3835.00i | −0.117283 | + | 0.203140i | −0.918690 | − | 0.394979i | \(-0.870752\pi\) |
0.801407 | + | 0.598119i | \(0.204085\pi\) | |||||||
\(710\) | −36761.8 | −1.94316 | ||||||||
\(711\) | 1263.55 | − | 10350.3i | 0.0666480 | − | 0.545945i | ||||
\(712\) | − | 12563.2i | − | 0.661271i | ||||||
\(713\) | 5273.02 | − | 9133.15i | 0.276965 | − | 0.479718i | ||||
\(714\) | −11021.2 | + | 5987.41i | −0.577673 | + | 0.313828i | ||||
\(715\) | 14087.3 | + | 24400.0i | 0.736835 | + | 1.27624i | ||||
\(716\) | −120.814 | + | 69.7521i | −0.00630592 | + | 0.00364073i | ||||
\(717\) | 6267.78 | + | 7079.48i | 0.326464 | + | 0.368742i | ||||
\(718\) | 5707.36 | − | 9885.44i | 0.296653 | − | 0.513818i | ||||
\(719\) | 28053.6 | 1.45511 | 0.727554 | − | 0.686050i | \(-0.240657\pi\) | ||||
0.727554 | + | 0.686050i | \(0.240657\pi\) | |||||||
\(720\) | −27424.2 | + | 11663.4i | −1.41950 | + | 0.603708i | ||||
\(721\) | −29589.0 | − | 6834.61i | −1.52836 | − | 0.353030i | ||||
\(722\) | 15081.5 | + | 8707.30i | 0.777389 | + | 0.448826i | ||||
\(723\) | 4485.40 | − | 13421.0i | 0.230725 | − | 0.690361i | ||||
\(724\) | −1867.73 | + | 1078.34i | −0.0958753 | + | 0.0553536i | ||||
\(725\) | 15089.6 | − | 8711.98i | 0.772984 | − | 0.446282i | ||||
\(726\) | −23592.7 | + | 4808.53i | −1.20607 | + | 0.245814i | ||||
\(727\) | 13620.1 | + | 7863.54i | 0.694828 | + | 0.401159i | 0.805418 | − | 0.592707i | \(-0.201941\pi\) |
−0.110590 | + | 0.993866i | \(0.535274\pi\) | |||||||
\(728\) | −2956.60 | + | 12800.0i | −0.150521 | + | 0.651646i | ||||
\(729\) | −7015.38 | + | 18390.4i | −0.356418 | + | 0.934327i | ||||
\(730\) | 6835.18 | 0.346550 | ||||||||
\(731\) | 11056.4 | − | 19150.3i | 0.559420 | − | 0.968945i | ||||
\(732\) | 1708.51 | − | 348.219i | 0.0862682 | − | 0.0175827i | ||||
\(733\) | −28543.9 | + | 16479.8i | −1.43833 | + | 0.830418i | −0.997734 | − | 0.0672892i | \(-0.978565\pi\) |
−0.440593 | + | 0.897707i | \(0.645232\pi\) | |||||||
\(734\) | 18805.0 | + | 32571.3i | 0.945649 | + | 1.63791i | ||||
\(735\) | −19837.1 | − | 19489.0i | −0.995514 | − | 0.978043i | ||||
\(736\) | 3216.60 | − | 5571.32i | 0.161094 | − | 0.279024i | ||||
\(737\) | − | 31042.6i | − | 1.55152i | ||||||
\(738\) | 11350.6 | + | 26688.7i | 0.566153 | + | 1.33120i | ||||
\(739\) | 18483.4 | 0.920056 | 0.460028 | − | 0.887905i | \(-0.347839\pi\) | ||||
0.460028 | + | 0.887905i | \(0.347839\pi\) | |||||||
\(740\) | −301.285 | + | 521.841i | −0.0149668 | + | 0.0259233i | ||||
\(741\) | 4222.57 | − | 3738.43i | 0.209339 | − | 0.185337i | ||||
\(742\) | −11312.9 | + | 3457.33i | −0.559718 | + | 0.171055i | ||||
\(743\) | 27952.9 | − | 16138.6i | 1.38020 | − | 0.796861i | 0.388020 | − | 0.921651i | \(-0.373159\pi\) |
0.992183 | + | 0.124790i | \(0.0398257\pi\) | |||||||
\(744\) | 5792.09 | − | 5128.00i | 0.285415 | − | 0.252691i | ||||
\(745\) | 20658.8 | + | 11927.3i | 1.01594 | + | 0.586555i | ||||
\(746\) | 13998.0i | 0.687004i | ||||||||
\(747\) | −647.194 | + | 5301.47i | −0.0316996 | + | 0.259666i | ||||
\(748\) | − | 2236.31i | − | 0.109315i | ||||||
\(749\) | −4769.90 | + | 5113.95i | −0.232695 | + | 0.249479i | ||||
\(750\) | −503.626 | + | 1506.92i | −0.0245198 | + | 0.0733667i | ||||
\(751\) | 12875.3 | + | 22300.7i | 0.625601 | + | 1.08357i | 0.988424 | + | 0.151715i | \(0.0484796\pi\) |
−0.362823 | + | 0.931858i | \(0.618187\pi\) | |||||||
\(752\) | 16140.1 | + | 27955.5i | 0.782672 | + | 1.35563i | ||||
\(753\) | 4373.62 | + | 21458.8i | 0.211665 | + | 1.03852i | ||||
\(754\) | −12830.0 | − | 7407.41i | −0.619683 | − | 0.357774i | ||||
\(755\) | −11657.6 | −0.561939 | ||||||||
\(756\) | −2312.73 | + | 913.501i | −0.111261 | + | 0.0439467i | ||||
\(757\) | 14678.2 | 0.704741 | 0.352371 | − | 0.935861i | \(-0.385376\pi\) | ||||
0.352371 | + | 0.935861i | \(0.385376\pi\) | |||||||
\(758\) | −12575.0 | − | 7260.16i | −0.602564 | − | 0.347890i | ||||
\(759\) | 8314.18 | + | 40792.8i | 0.397609 | + | 1.95084i | ||||
\(760\) | −5303.68 | − | 9186.25i | −0.253138 | − | 0.438448i | ||||
\(761\) | −15248.7 | − | 26411.6i | −0.726369 | − | 1.25811i | −0.958408 | − | 0.285401i | \(-0.907873\pi\) |
0.232039 | − | 0.972706i | \(-0.425460\pi\) | |||||||
\(762\) | −6685.71 | + | 20004.6i | −0.317845 | + | 0.951037i | ||||
\(763\) | 15792.5 | + | 14730.1i | 0.749316 | + | 0.698905i | ||||
\(764\) | 3537.77i | 0.167529i | ||||||||
\(765\) | 14659.6 | + | 11030.8i | 0.692837 | + | 0.521334i | ||||
\(766\) | − | 14701.8i | − | 0.693470i | ||||||
\(767\) | 9302.19 | + | 5370.62i | 0.437917 | + | 0.252832i | ||||
\(768\) | 5640.29 | − | 4993.60i | 0.265008 | − | 0.234624i | ||||
\(769\) | 30619.6 | − | 17678.2i | 1.43585 | − | 0.828989i | 0.438294 | − | 0.898832i | \(-0.355583\pi\) |
0.997558 | + | 0.0698425i | \(0.0222497\pi\) | |||||||
\(770\) | 44380.1 | − | 13563.0i | 2.07708 | − | 0.634774i | ||||
\(771\) | −10807.7 | + | 9568.56i | −0.504838 | + | 0.446956i | ||||
\(772\) | −2100.39 | + | 3637.98i | −0.0979205 | + | 0.169603i | ||||
\(773\) | 4097.47 | 0.190654 | 0.0953272 | − | 0.995446i | \(-0.469610\pi\) | ||||
0.0953272 | + | 0.995446i | \(0.469610\pi\) | |||||||
\(774\) | 24670.3 | − | 32786.1i | 1.14568 | − | 1.52257i | ||||
\(775\) | 8366.32i | 0.387777i | ||||||||
\(776\) | −7684.95 | + | 13310.7i | −0.355507 | + | 0.615757i | ||||
\(777\) | 2028.30 | − | 3311.65i | 0.0936487 | − | 0.152902i | ||||
\(778\) | −7986.30 | − | 13832.7i | −0.368024 | − | 0.637436i | ||||
\(779\) | −10024.8 | + | 5787.84i | −0.461074 | + | 0.266201i | ||||
\(780\) | −2558.44 | + | 521.447i | −0.117444 | + | 0.0239369i | ||||
\(781\) | −21121.3 | + | 36583.2i | −0.967709 | + | 1.67612i | ||||
\(782\) | −19460.6 | −0.889908 | ||||||||
\(783\) | 1640.65 | + | 20571.9i | 0.0748813 | + | 0.938925i | ||||
\(784\) | 21805.9 | + | 10641.4i | 0.993343 | + | 0.484759i | ||||
\(785\) | −18617.6 | − | 10748.9i | −0.846484 | − | 0.488718i | ||||
\(786\) | −29835.8 | + | 6080.97i | −1.35395 | + | 0.275956i | ||||
\(787\) | −29205.4 | + | 16861.7i | −1.32282 | + | 0.763730i | −0.984178 | − | 0.177185i | \(-0.943301\pi\) |
−0.338642 | + | 0.940915i | \(0.609968\pi\) | |||||||
\(788\) | −1749.04 | + | 1009.81i | −0.0790696 | + | 0.0456509i | ||||
\(789\) | 5206.13 | − | 15577.5i | 0.234909 | − | 0.702881i | ||||
\(790\) | −15617.8 | − | 9016.95i | −0.703363 | − | 0.406087i | ||||
\(791\) | 5814.88 | + | 1343.15i | 0.261382 | + | 0.0603754i | ||||
\(792\) | −3700.59 | + | 30313.3i | −0.166029 | + | 1.36002i | ||||
\(793\) | −11799.7 | −0.528396 | ||||||||
\(794\) | 1957.56 | − | 3390.59i | 0.0874950 | − | 0.151546i | ||||
\(795\) | 11469.9 | + | 12955.3i | 0.511692 | + | 0.577957i | ||||
\(796\) | −2853.69 | + | 1647.58i | −0.127068 | + | 0.0733628i | ||||
\(797\) | 7132.81 | + | 12354.4i | 0.317010 | + | 0.549077i | 0.979863 | − | 0.199672i | \(-0.0639878\pi\) |
−0.662853 | + | 0.748750i | \(0.730654\pi\) | |||||||
\(798\) | −4434.30 | − | 8162.35i | −0.196707 | − | 0.362085i | ||||
\(799\) | 9936.12 | − | 17209.9i | 0.439943 | − | 0.762004i | ||||
\(800\) | 5103.54i | 0.225547i | ||||||||
\(801\) | −14808.9 | + | 6298.16i | −0.653241 | + | 0.277821i | ||||
\(802\) | −6020.75 | −0.265087 | ||||||||
\(803\) | 3927.12 | − | 6801.97i | 0.172584 | − | 0.298925i | ||||
\(804\) | 2728.46 | + | 911.876i | 0.119683 | + | 0.0399992i | ||||
\(805\) | −12610.4 | − | 41263.1i | −0.552122 | − | 1.80663i | ||||
\(806\) | 6160.48 | − | 3556.75i | 0.269223 | − | 0.155436i | ||||
\(807\) | −4500.91 | − | 22083.3i | −0.196332 | − | 0.963284i | ||||
\(808\) | −10468.0 | − | 6043.68i | −0.455770 | − | 0.263139i | ||||
\(809\) | 13916.9i | 0.604812i | 0.953179 | + | 0.302406i | \(0.0977898\pi\) | ||||
−0.953179 | + | 0.302406i | \(0.902210\pi\) | |||||||
\(810\) | 24520.7 | + | 23613.5i | 1.06367 | + | 1.02431i | ||||
\(811\) | 7296.14i | 0.315909i | 0.987446 | + | 0.157954i | \(0.0504899\pi\) | ||||
−0.987446 | + | 0.157954i | \(0.949510\pi\) | |||||||
\(812\) | −1778.28 | + | 1906.55i | −0.0768541 | + | 0.0823975i | ||||
\(813\) | −42766.6 | + | 8716.46i | −1.84488 | + | 0.376014i | ||||
\(814\) | 3240.27 | + | 5612.31i | 0.139523 | + | 0.241660i | ||||
\(815\) | 14825.0 | + | 25677.7i | 0.637175 | + | 1.10362i | ||||
\(816\) | −15182.1 | − | 5073.98i | −0.651323 | − | 0.217678i | ||||
\(817\) | 14182.8 | + | 8188.42i | 0.607334 | + | 0.350645i | ||||
\(818\) | −212.619 | −0.00908809 | ||||||||
\(819\) | 16570.2 | − | 2931.76i | 0.706971 | − | 0.125084i | ||||
\(820\) | 5359.26 | 0.228236 | ||||||||
\(821\) | 30269.4 | + | 17476.0i | 1.28673 | + | 0.742897i | 0.978070 | − | 0.208274i | \(-0.0667846\pi\) |
0.308664 | + | 0.951171i | \(0.400118\pi\) | |||||||
\(822\) | 11554.4 | − | 10229.7i | 0.490275 | − | 0.434063i | ||||
\(823\) | −11765.3 | − | 20378.1i | −0.498314 | − | 0.863105i | 0.501684 | − | 0.865051i | \(-0.332714\pi\) |
−0.999998 | + | 0.00194598i | \(0.999381\pi\) | |||||||
\(824\) | −17281.4 | − | 29932.2i | −0.730614 | − | 1.26546i | ||||
\(825\) | −21892.8 | − | 24728.0i | −0.923891 | − | 1.04354i | ||||
\(826\) | 12067.2 | − | 12937.7i | 0.508321 | − | 0.544986i | ||||
\(827\) | 40158.9i | 1.68859i | 0.535880 | + | 0.844294i | \(0.319980\pi\) | ||||
−0.535880 | + | 0.844294i | \(0.680020\pi\) | |||||||
\(828\) | −3829.68 | − | 467.521i | −0.160738 | − | 0.0196226i | ||||
\(829\) | − | 10739.4i | − | 0.449934i | −0.974366 | − | 0.224967i | \(-0.927773\pi\) | ||
0.974366 | − | 0.224967i | \(-0.0722275\pi\) | |||||||
\(830\) | 7999.52 | + | 4618.52i | 0.334539 | + | 0.193146i | ||||
\(831\) | 18002.2 | + | 6016.50i | 0.751493 | + | 0.251155i | ||||
\(832\) | −12734.9 | + | 7352.52i | −0.530654 | + | 0.306373i | ||||
\(833\) | −1038.66 | − | 14901.1i | −0.0432022 | − | 0.619799i | ||||
\(834\) | −2589.79 | − | 12706.6i | −0.107526 | − | 0.527569i | ||||
\(835\) | 13050.4 | − | 22603.9i | 0.540870 | − | 0.936814i | ||||
\(836\) | 1656.22 | 0.0685187 | ||||||||
\(837\) | −8948.34 | − | 4256.68i | −0.369534 | − | 0.175785i | ||||
\(838\) | 10924.7i | 0.450343i | ||||||||
\(839\) | 9285.04 | − | 16082.2i | 0.382068 | − | 0.661762i | −0.609289 | − | 0.792948i | \(-0.708545\pi\) |
0.991358 | + | 0.131186i | \(0.0418786\pi\) | |||||||
\(840\) | 821.007 | − | 31639.4i | 0.0337231 | − | 1.29960i | ||||
\(841\) | −1375.69 | − | 2382.76i | −0.0564062 | − | 0.0976983i | ||||
\(842\) | −15396.3 | + | 8889.05i | −0.630156 | + | 0.363821i | ||||
\(843\) | 13691.2 | − | 40966.0i | 0.559370 | − | 1.67372i | ||||
\(844\) | 1784.89 | − | 3091.52i | 0.0727944 | − | 0.126084i | ||||
\(845\) | −16610.1 | −0.676218 | ||||||||
\(846\) | 22170.6 | − | 29464.0i | 0.900993 | − | 1.19739i | ||||
\(847\) | 6453.50 | − | 27939.0i | 0.261801 | − | 1.13341i | ||||
\(848\) | −13074.7 | − | 7548.69i | −0.529466 | − | 0.305688i | ||||
\(849\) | −5149.13 | − | 5815.95i | −0.208148 | − | 0.235104i | ||||
\(850\) | 13370.0 | − | 7719.16i | 0.539513 | − | 0.311488i | ||||
\(851\) | 5218.13 | − | 3012.69i | 0.210194 | − | 0.121356i | ||||
\(852\) | −2595.01 | − | 2931.07i | −0.104347 | − | 0.117860i | ||||
\(853\) | −4663.07 | − | 2692.22i | −0.187175 | − | 0.108066i | 0.403484 | − | 0.914987i | \(-0.367799\pi\) |
−0.590659 | + | 0.806921i | \(0.701132\pi\) | |||||||
\(854\) | −4374.06 | + | 18936.5i | −0.175266 | + | 0.758776i | ||||
\(855\) | −8169.48 | + | 10857.0i | −0.326772 | + | 0.434270i | ||||
\(856\) | −7959.13 | −0.317801 | ||||||||
\(857\) | 5528.79 | − | 9576.15i | 0.220373 | − | 0.381698i | −0.734548 | − | 0.678557i | \(-0.762606\pi\) |
0.954921 | + | 0.296859i | \(0.0959391\pi\) | |||||||
\(858\) | −8901.03 | + | 26633.2i | −0.354168 | + | 1.05972i | ||||
\(859\) | −14136.9 | + | 8161.94i | −0.561519 | + | 0.324193i | −0.753755 | − | 0.657156i | \(-0.771759\pi\) |
0.192236 | + | 0.981349i | \(0.438426\pi\) | |||||||
\(860\) | −3791.04 | − | 6566.28i | −0.150318 | − | 0.260358i | ||||
\(861\) | −34527.6 | − | 895.953i | −1.36666 | − | 0.0354634i | ||||
\(862\) | −11235.2 | + | 19459.9i | −0.443935 | + | 0.768917i | ||||
\(863\) | − | 37617.5i | − | 1.48379i | −0.670515 | − | 0.741896i | \(-0.733927\pi\) | ||
0.670515 | − | 0.741896i | \(-0.266073\pi\) | |||||||
\(864\) | −5458.58 | − | 2596.62i | −0.214936 | − | 0.102244i | ||||
\(865\) | 15490.5 | 0.608895 | ||||||||
\(866\) | 10296.7 | − | 17834.5i | 0.404039 | − | 0.699816i | ||||
\(867\) | −3130.28 | − | 15358.4i | −0.122618 | − | 0.601615i | ||||
\(868\) | −365.874 | − | 1197.19i | −0.0143071 | − | 0.0468150i | ||||
\(869\) | −17946.3 | + | 10361.3i | −0.700560 | + | 0.404468i | ||||
\(870\) | 33851.8 | + | 11313.6i | 1.31918 | + | 0.440880i | ||||
\(871\) | −16859.9 | − | 9734.08i | −0.655886 | − | 0.378676i | ||||
\(872\) | 24578.8i | 0.954523i | ||||||||
\(873\) | 19542.7 | + | 2385.73i | 0.757639 | + | 0.0924912i | ||||
\(874\) | − | 14412.6i | − | 0.557794i | ||||||
\(875\) | −1383.73 | − | 1290.63i | −0.0534611 | − | 0.0498644i | ||||
\(876\) | 482.495 | + | 544.979i | 0.0186096 | + | 0.0210196i | ||||
\(877\) | −21070.2 | − | 36494.6i | −0.811275 | − | 1.40517i | −0.911972 | − | 0.410253i | \(-0.865440\pi\) |
0.100696 | − | 0.994917i | \(-0.467893\pi\) | |||||||
\(878\) | −7767.19 | − | 13453.2i | −0.298553 | − | 0.517110i | ||||
\(879\) | −1088.08 | + | 963.326i | −0.0417520 | + | 0.0369649i | ||||
\(880\) | 51291.6 | + | 29613.2i | 1.96482 | + | 1.13439i | ||||
\(881\) | −17255.0 | −0.659861 | −0.329930 | − | 0.944005i | \(-0.607025\pi\) | ||||
−0.329930 | + | 0.944005i | \(0.607025\pi\) | |||||||
\(882\) | 1437.46 | − | 27679.3i | 0.0548773 | − | 1.05670i | ||||
\(883\) | −26461.1 | −1.00848 | −0.504240 | − | 0.863564i | \(-0.668227\pi\) | ||||
−0.504240 | + | 0.863564i | \(0.668227\pi\) | |||||||
\(884\) | −1214.59 | − | 701.246i | −0.0462118 | − | 0.0266804i | ||||
\(885\) | −24543.7 | − | 8202.71i | −0.932235 | − | 0.311561i | ||||
\(886\) | −1517.98 | − | 2629.23i | −0.0575595 | − | 0.0996959i | ||||
\(887\) | 9683.24 | + | 16771.9i | 0.366552 | + | 0.634886i | 0.989024 | − | 0.147756i | \(-0.0472050\pi\) |
−0.622472 | + | 0.782642i | \(0.713872\pi\) | |||||||
\(888\) | 4330.82 | − | 882.684i | 0.163663 | − | 0.0333569i | ||||
\(889\) | −18369.2 | − | 17133.3i | −0.693005 | − | 0.646382i | ||||
\(890\) | 27832.3i | 1.04825i | ||||||||
\(891\) | 37587.0 | − | 10834.5i | 1.41326 | − | 0.407375i | ||||
\(892\) | − | 2607.55i | − | 0.0978780i | ||||||
\(893\) | 12745.7 | + | 7358.72i | 0.477624 | + | 0.275756i | ||||
\(894\) | 4748.18 | + | 23296.6i | 0.177632 | + | 0.871537i | ||||
\(895\) | −1969.75 | + | 1137.23i | −0.0735658 | + | 0.0424732i | ||||
\(896\) | 8944.55 | + | 29267.9i | 0.333500 | + | 1.09126i | ||||
\(897\) | 24762.6 | + | 8275.87i | 0.921738 | + | 0.308053i | ||||
\(898\) | 9518.76 | − | 16487.0i | 0.353725 | − | 0.612670i | ||||
\(899\) | −10389.6 | −0.385441 | ||||||||
\(900\) | 2816.55 | − | 1197.87i | 0.104317 | − | 0.0443655i | ||||
\(901\) | 9294.19i | 0.343656i | ||||||||
\(902\) | 28818.9 | − | 49915.9i | 1.06382 | − | 1.84259i | ||||
\(903\) | 23326.5 | + | 42937.8i | 0.859642 | + | 1.58237i | ||||
\(904\) | 3396.17 | + | 5882.34i | 0.124950 | + | 0.216420i | ||||
\(905\) | −30451.4 | + | 17581.1i | −1.11850 | + | 0.645764i | ||||
\(906\) | −7701.97 | − | 8699.39i | −0.282429 | − | 0.319004i | ||||
\(907\) | 569.688 | − | 986.728i | 0.0208558 | − | 0.0361232i | −0.855409 | − | 0.517953i | \(-0.826694\pi\) |
0.876265 | + | 0.481830i | \(0.160028\pi\) | |||||||
\(908\) | 5421.85 | 0.198161 | ||||||||
\(909\) | −1876.21 | + | 15369.0i | −0.0684600 | + | 0.560788i | ||||
\(910\) | 6550.01 | − | 28356.8i | 0.238605 | − | 1.03299i | ||||
\(911\) | −7531.25 | − | 4348.17i | −0.273898 | − | 0.158135i | 0.356760 | − | 0.934196i | \(-0.383882\pi\) |
−0.630658 | + | 0.776061i | \(0.717215\pi\) | |||||||
\(912\) | 3757.81 | − | 11243.9i | 0.136440 | − | 0.408249i | ||||
\(913\) | 9192.18 | − | 5307.10i | 0.333205 | − | 0.192376i | ||||
\(914\) | −14556.1 | + | 8403.95i | −0.526775 | + | 0.304133i | ||||
\(915\) | 27855.4 | − | 5677.34i | 1.00642 | − | 0.205123i | ||||
\(916\) | −351.055 | − | 202.682i | −0.0126629 | − | 0.00731090i | ||||
\(917\) | 8161.24 | − | 35332.3i | 0.293902 | − | 1.27238i | ||||
\(918\) | 1453.68 | + | 18227.5i | 0.0522643 | + | 0.655334i | ||||
\(919\) | −2297.46 | −0.0824659 | −0.0412330 | − | 0.999150i | \(-0.513129\pi\) | ||||
−0.0412330 | + | 0.999150i | \(0.513129\pi\) | |||||||
\(920\) | 24553.5 | − | 42527.8i | 0.879895 | − | 1.52402i | ||||
\(921\) | 54618.8 | − | 11132.1i | 1.95413 | − | 0.398279i | ||||
\(922\) | −11982.3 | + | 6917.99i | −0.428000 | + | 0.247106i | ||||
\(923\) | 13246.1 | + | 22942.9i | 0.472374 | + | 0.818176i | ||||
\(924\) | 4214.19 | + | 2581.09i | 0.150040 | + | 0.0918956i | ||||
\(925\) | −2390.01 | + | 4139.61i | −0.0849545 | + | 0.147146i | ||||
\(926\) | 13048.9i | 0.463083i | ||||||||
\(927\) | −26619.2 | + | 35376.1i | −0.943139 | + | 1.25340i | ||||
\(928\) | −6337.74 | −0.224188 | ||||||||
\(929\) | −24197.9 | + | 41911.9i | −0.854581 | + | 1.48018i | 0.0224522 | + | 0.999748i | \(0.492853\pi\) |
−0.877033 | + | 0.480430i | \(0.840481\pi\) | |||||||
\(930\) | −12831.7 | + | 11360.5i | −0.452439 | + | 0.400565i | ||||
\(931\) | 11035.8 | − | 769.235i | 0.388490 | − | 0.0270791i | ||||
\(932\) | −194.603 | + | 112.354i | −0.00683951 | + | 0.00394879i | ||||
\(933\) | −37164.6 | + | 32903.6i | −1.30409 | + | 1.15457i | ||||
\(934\) | 28313.1 | + | 16346.6i | 0.991900 | + | 0.572673i | ||||
\(935\) | − | 36460.7i | − | 1.27529i | ||||||
\(936\) | 15303.4 | + | 11515.3i | 0.534410 | + | 0.402124i | ||||
\(937\) | − | 23667.6i | − | 0.825172i | −0.910919 | − | 0.412586i | \(-0.864626\pi\) | ||
0.910919 | − | 0.412586i | \(-0.135374\pi\) | |||||||
\(938\) | −21871.5 | + | 23449.1i | −0.761333 | + | 0.816247i | ||||
\(939\) | 6077.10 | − | 18183.6i | 0.211202 | − | 0.631947i | ||||
\(940\) | −3406.91 | − | 5900.94i | −0.118214 | − | 0.204753i | ||||
\(941\) | −5099.48 | − | 8832.56i | −0.176661 | − | 0.305987i | 0.764074 | − | 0.645129i | \(-0.223196\pi\) |
−0.940735 | + | 0.339143i | \(0.889863\pi\) | |||||||
\(942\) | −4279.04 | − | 20994.8i | −0.148003 | − | 0.726164i | ||||
\(943\) | −46410.0 | − | 26794.9i | −1.60267 | − | 0.925303i | ||||
\(944\) | 22579.3 | 0.778489 | ||||||||
\(945\) | −37706.6 | + | 14893.7i | −1.29799 | + | 0.512689i | ||||
\(946\) | −81544.0 | −2.80256 | ||||||||
\(947\) | −2943.58 | − | 1699.47i | −0.101007 | − | 0.0583163i | 0.448646 | − | 0.893710i | \(-0.351907\pi\) |
−0.549652 | + | 0.835393i | \(0.685240\pi\) | |||||||
\(948\) | −383.526 | − | 1881.74i | −0.0131396 | − | 0.0644684i | ||||
\(949\) | −2462.87 | − | 4265.82i | −0.0842447 | − | 0.145916i | ||||
\(950\) | 5716.84 | + | 9901.85i | 0.195241 | + | 0.338167i | ||||
\(951\) | 1240.93 | − | 3713.03i | 0.0423131 | − | 0.126607i | ||||
\(952\) | 11595.7 | − | 12432.1i | 0.394768 | − | 0.423243i | ||||
\(953\) | 27410.8i | 0.931714i | 0.884860 | + | 0.465857i | \(0.154254\pi\) | ||||
−0.884860 | + | 0.465857i | \(0.845746\pi\) | |||||||
\(954\) | −2089.81 | + | 17118.6i | −0.0709225 | + | 0.580959i | ||||
\(955\) | 57679.7i | 1.95442i | ||||||||
\(956\) | 1508.14 | + | 870.725i | 0.0510217 | + | 0.0294574i | ||||
\(957\) | 30708.0 | − | 27187.2i | 1.03725 | − | 0.918325i | ||||
\(958\) | −24869.3 | + | 14358.3i | −0.838716 | + | 0.484233i | ||||
\(959\) | 5371.39 | + | 17576.0i | 0.180867 | + | 0.591824i | ||||
\(960\) | 26525.7 | − | 23484.4i | 0.891785 | − | 0.789538i | ||||
\(961\) | −12401.2 | + | 21479.4i | −0.416272 | + | 0.721005i | ||||
\(962\) | 4064.23 | 0.136212 | ||||||||
\(963\) | 3990.07 | + | 9381.85i | 0.133518 | + | 0.313942i | ||||
\(964\) | − | 2606.21i | − | 0.0870750i | ||||||
\(965\) | −34244.6 | + | 59313.4i | −1.14236 | + | 1.97862i | ||||
\(966\) | 22460.8 | − | 36672.2i | 0.748099 | − | 1.22144i | ||||
\(967\) | 18511.5 | + | 32062.9i | 0.615606 | + | 1.06626i | 0.990278 | + | 0.139103i | \(0.0444221\pi\) |
−0.374672 | + | 0.927158i | \(0.622245\pi\) | |||||||
\(968\) | 28263.2 | − | 16317.8i | 0.938443 | − | 0.541810i | ||||
\(969\) | −7151.26 | + | 1457.53i | −0.237081 | + | 0.0483206i | ||||
\(970\) | 17025.1 | − | 29488.4i | 0.563550 | − | 0.976098i | ||||
\(971\) | 17050.2 | 0.563509 | 0.281754 | − | 0.959487i | \(-0.409084\pi\) | ||||
0.281754 | + | 0.959487i | \(0.409084\pi\) | |||||||
\(972\) | −151.825 | + | 3621.95i | −0.00501006 | + | 0.119521i | ||||
\(973\) | 15047.5 | + | 3475.74i | 0.495786 | + | 0.114519i | ||||
\(974\) | −21358.2 | − | 12331.1i | −0.702628 | − | 0.405662i | ||||
\(975\) | −20295.3 | + | 4136.48i | −0.666636 | + | 0.135870i | ||||
\(976\) | −21481.1 | + | 12402.1i | −0.704501 | + | 0.406744i | ||||
\(977\) | −14180.0 | + | 8186.83i | −0.464338 | + | 0.268086i | −0.713867 | − | 0.700282i | \(-0.753058\pi\) |
0.249528 | + | 0.968367i | \(0.419724\pi\) | |||||||
\(978\) | −9367.12 | + | 28027.8i | −0.306265 | + | 0.916390i | ||||
\(979\) | 27697.1 | + | 15990.9i | 0.904190 | + | 0.522034i | ||||
\(980\) | −4602.86 | − | 2246.23i | −0.150034 | − | 0.0732176i | ||||
\(981\) | 28972.4 | − | 12321.8i | 0.942932 | − | 0.401026i | ||||
\(982\) | 6021.56 | 0.195678 | ||||||||
\(983\) | −10769.1 | + | 18652.7i | −0.349423 | + | 0.605218i | −0.986147 | − | 0.165874i | \(-0.946956\pi\) |
0.636724 | + | 0.771092i | \(0.280289\pi\) | |||||||
\(984\) | −26057.9 | − | 29432.5i | −0.844204 | − | 0.953530i | ||||
\(985\) | −28516.2 | + | 16463.8i | −0.922438 | + | 0.532570i | ||||
\(986\) | 9585.89 | + | 16603.3i | 0.309612 | + | 0.536263i | ||||
\(987\) | 20962.9 | + | 38587.1i | 0.676045 | + | 1.24442i | ||||
\(988\) | 519.345 | − | 899.533i | 0.0167233 | − | 0.0289655i | ||||
\(989\) | 75816.8i | 2.43765i | ||||||||
\(990\) | 8198.23 | − | 67155.6i | 0.263189 | − | 2.15590i | ||||
\(991\) | 39248.1 | 1.25808 | 0.629040 | − | 0.777373i | \(-0.283448\pi\) | ||||
0.629040 | + | 0.777373i | \(0.283448\pi\) | |||||||
\(992\) | 1521.57 | − | 2635.44i | 0.0486995 | − | 0.0843500i | ||||
\(993\) | −30745.5 | − | 10275.4i | −0.982557 | − | 0.328379i | ||||
\(994\) | 41730.0 | − | 12753.1i | 1.33158 | − | 0.406944i | ||||
\(995\) | −46526.3 | + | 26862.0i | −1.48240 | + | 0.855862i | ||||
\(996\) | 196.444 | + | 963.836i | 0.00624956 | + | 0.0306630i | ||||
\(997\) | −3452.73 | − | 1993.43i | −0.109678 | − | 0.0633226i | 0.444158 | − | 0.895949i | \(-0.353503\pi\) |
−0.553836 | + | 0.832626i | \(0.686836\pi\) | |||||||
\(998\) | − | 43015.9i | − | 1.36437i | ||||||
\(999\) | −3211.59 | − | 4662.45i | −0.101712 | − | 0.147661i |
(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 | 63.4.o.a.20.18 | yes | 44 | |
3.2 | odd | 2 | 189.4.o.a.62.5 | 44 | |||
7.6 | odd | 2 | inner | 63.4.o.a.20.17 | ✓ | 44 | |
9.2 | odd | 6 | 567.4.c.c.566.38 | 44 | |||
9.4 | even | 3 | 189.4.o.a.125.6 | 44 | |||
9.5 | odd | 6 | inner | 63.4.o.a.41.17 | yes | 44 | |
9.7 | even | 3 | 567.4.c.c.566.7 | 44 | |||
21.20 | even | 2 | 189.4.o.a.62.6 | 44 | |||
63.13 | odd | 6 | 189.4.o.a.125.5 | 44 | |||
63.20 | even | 6 | 567.4.c.c.566.8 | 44 | |||
63.34 | odd | 6 | 567.4.c.c.566.37 | 44 | |||
63.41 | even | 6 | inner | 63.4.o.a.41.18 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.o.a.20.17 | ✓ | 44 | 7.6 | odd | 2 | inner | |
63.4.o.a.20.18 | yes | 44 | 1.1 | even | 1 | trivial | |
63.4.o.a.41.17 | yes | 44 | 9.5 | odd | 6 | inner | |
63.4.o.a.41.18 | yes | 44 | 63.41 | even | 6 | inner | |
189.4.o.a.62.5 | 44 | 3.2 | odd | 2 | |||
189.4.o.a.62.6 | 44 | 21.20 | even | 2 | |||
189.4.o.a.125.5 | 44 | 63.13 | odd | 6 | |||
189.4.o.a.125.6 | 44 | 9.4 | even | 3 | |||
567.4.c.c.566.7 | 44 | 9.7 | even | 3 | |||
567.4.c.c.566.8 | 44 | 63.20 | even | 6 | |||
567.4.c.c.566.37 | 44 | 63.34 | odd | 6 | |||
567.4.c.c.566.38 | 44 | 9.2 | odd | 6 |