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 | 20.15 | ||
Character | \(\chi\) | \(=\) | 63.20 |
Dual form | 63.4.o.a.41.15 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93743 | + | 1.11857i | 0.684983 | + | 0.395475i | 0.801730 | − | 0.597686i | \(-0.203913\pi\) |
−0.116747 | + | 0.993162i | \(0.537247\pi\) | |||||||
\(3\) | −5.00204 | − | 1.40697i | −0.962644 | − | 0.270771i | ||||
\(4\) | −1.49759 | − | 2.59390i | −0.187198 | − | 0.324237i | ||||
\(5\) | −2.75758 | − | 4.77627i | −0.246645 | − | 0.427202i | 0.715948 | − | 0.698154i | \(-0.245995\pi\) |
−0.962593 | + | 0.270952i | \(0.912662\pi\) | |||||||
\(6\) | −8.11730 | − | 8.32104i | −0.552312 | − | 0.566175i | ||||
\(7\) | −17.8859 | − | 4.80585i | −0.965745 | − | 0.259491i | ||||
\(8\) | − | 24.5978i | − | 1.08708i | ||||||
\(9\) | 23.0409 | + | 14.0754i | 0.853367 | + | 0.521311i | ||||
\(10\) | − | 12.3382i | − | 0.390169i | ||||||
\(11\) | −30.2441 | − | 17.4614i | −0.828995 | − | 0.478620i | 0.0245137 | − | 0.999699i | \(-0.492196\pi\) |
−0.853508 | + | 0.521079i | \(0.825530\pi\) | |||||||
\(12\) | 3.84148 | + | 15.0818i | 0.0924115 | + | 0.362813i | ||||
\(13\) | 23.1532 | − | 13.3675i | 0.493965 | − | 0.285191i | −0.232253 | − | 0.972656i | \(-0.574610\pi\) |
0.726218 | + | 0.687464i | \(0.241276\pi\) | |||||||
\(14\) | −29.2768 | − | 29.3176i | −0.558897 | − | 0.559676i | ||||
\(15\) | 7.07349 | + | 27.7709i | 0.121758 | + | 0.478028i | ||||
\(16\) | 15.5338 | − | 26.9053i | 0.242715 | − | 0.420395i | ||||
\(17\) | 35.9093 | 0.512311 | 0.256156 | − | 0.966636i | \(-0.417544\pi\) | ||||
0.256156 | + | 0.966636i | \(0.417544\pi\) | |||||||
\(18\) | 28.8957 | + | 53.0430i | 0.378376 | + | 0.694575i | ||||
\(19\) | 78.0198i | 0.942051i | 0.882120 | + | 0.471025i | \(0.156116\pi\) | ||||
−0.882120 | + | 0.471025i | \(0.843884\pi\) | |||||||
\(20\) | −8.25943 | + | 14.3058i | −0.0923432 | + | 0.159943i | ||||
\(21\) | 82.7042 | + | 49.2038i | 0.859406 | + | 0.511293i | ||||
\(22\) | −39.0638 | − | 67.6605i | −0.378565 | − | 0.655694i | ||||
\(23\) | −50.1284 | + | 28.9416i | −0.454456 | + | 0.262380i | −0.709710 | − | 0.704494i | \(-0.751174\pi\) |
0.255254 | + | 0.966874i | \(0.417841\pi\) | |||||||
\(24\) | −34.6083 | + | 123.039i | −0.294349 | + | 1.04647i | ||||
\(25\) | 47.2915 | − | 81.9113i | 0.378332 | − | 0.655291i | ||||
\(26\) | 59.8102 | 0.451144 | ||||||||
\(27\) | −95.4480 | − | 102.824i | −0.680332 | − | 0.732904i | ||||
\(28\) | 14.3198 | + | 53.5913i | 0.0966493 | + | 0.361707i | ||||
\(29\) | −192.066 | − | 110.889i | −1.22985 | − | 0.710056i | −0.262854 | − | 0.964836i | \(-0.584664\pi\) |
−0.966999 | + | 0.254779i | \(0.917997\pi\) | |||||||
\(30\) | −17.3594 | + | 61.7163i | −0.105646 | + | 0.375593i | ||||
\(31\) | 126.002 | − | 72.7471i | 0.730018 | − | 0.421476i | −0.0884105 | − | 0.996084i | \(-0.528179\pi\) |
0.818429 | + | 0.574608i | \(0.194845\pi\) | |||||||
\(32\) | −110.228 | + | 63.6400i | −0.608928 | + | 0.351564i | ||||
\(33\) | 126.715 | + | 129.895i | 0.668430 | + | 0.685208i | ||||
\(34\) | 69.5717 | + | 40.1672i | 0.350925 | + | 0.202607i | ||||
\(35\) | 26.3676 | + | 98.6801i | 0.127341 | + | 0.476571i | ||||
\(36\) | 2.00440 | − | 80.8449i | 0.00927964 | − | 0.374282i | ||||
\(37\) | 290.956 | 1.29278 | 0.646390 | − | 0.763008i | \(-0.276278\pi\) | ||||
0.646390 | + | 0.763008i | \(0.276278\pi\) | |||||||
\(38\) | −87.2708 | + | 151.158i | −0.372558 | + | 0.645289i | ||||
\(39\) | −134.621 | + | 34.2892i | −0.552734 | + | 0.140786i | ||||
\(40\) | −117.486 | + | 67.8304i | −0.464403 | + | 0.268123i | ||||
\(41\) | −54.0606 | − | 93.6357i | −0.205923 | − | 0.356669i | 0.744503 | − | 0.667619i | \(-0.232686\pi\) |
−0.950426 | + | 0.310949i | \(0.899353\pi\) | |||||||
\(42\) | 105.195 | + | 187.839i | 0.386475 | + | 0.690101i | ||||
\(43\) | 174.061 | − | 301.482i | 0.617303 | − | 1.06920i | −0.372673 | − | 0.927963i | \(-0.621559\pi\) |
0.989976 | − | 0.141238i | \(-0.0451082\pi\) | |||||||
\(44\) | 104.600i | 0.358388i | ||||||||
\(45\) | 3.69080 | − | 148.863i | 0.0122265 | − | 0.493139i | ||||
\(46\) | −129.493 | −0.415060 | ||||||||
\(47\) | 125.545 | − | 217.450i | 0.389630 | − | 0.674858i | −0.602770 | − | 0.797915i | \(-0.705936\pi\) |
0.992400 | + | 0.123057i | \(0.0392697\pi\) | |||||||
\(48\) | −115.555 | + | 112.726i | −0.347479 | + | 0.338970i | ||||
\(49\) | 296.808 | + | 171.913i | 0.865328 | + | 0.501205i | ||||
\(50\) | 183.248 | − | 105.798i | 0.518303 | − | 0.299242i | ||||
\(51\) | −179.620 | − | 50.5232i | −0.493173 | − | 0.138719i | ||||
\(52\) | −69.3480 | − | 40.0381i | −0.184939 | − | 0.106775i | ||||
\(53\) | 160.173i | 0.415122i | 0.978222 | + | 0.207561i | \(0.0665525\pi\) | ||||
−0.978222 | + | 0.207561i | \(0.933448\pi\) | |||||||
\(54\) | −69.9077 | − | 305.979i | −0.176171 | − | 0.771082i | ||||
\(55\) | 192.605i | 0.472198i | ||||||||
\(56\) | −118.213 | + | 439.953i | −0.282088 | + | 1.04984i | ||||
\(57\) | 109.771 | − | 390.258i | 0.255080 | − | 0.906859i | ||||
\(58\) | −248.076 | − | 429.680i | −0.561620 | − | 0.972754i | ||||
\(59\) | −367.425 | − | 636.398i | −0.810756 | − | 1.40427i | −0.912336 | − | 0.409443i | \(-0.865723\pi\) |
0.101580 | − | 0.994827i | \(-0.467610\pi\) | |||||||
\(60\) | 61.4417 | − | 59.9373i | 0.132202 | − | 0.128964i | ||||
\(61\) | −581.350 | − | 335.643i | −1.22023 | − | 0.704502i | −0.255266 | − | 0.966871i | \(-0.582163\pi\) |
−0.964968 | + | 0.262368i | \(0.915496\pi\) | |||||||
\(62\) | 325.492 | 0.666734 | ||||||||
\(63\) | −344.462 | − | 362.482i | −0.688859 | − | 0.724895i | ||||
\(64\) | −533.284 | −1.04157 | ||||||||
\(65\) | −127.694 | − | 73.7240i | −0.243669 | − | 0.140682i | ||||
\(66\) | 100.203 | + | 393.402i | 0.186881 | + | 0.733704i | ||||
\(67\) | 344.364 | + | 596.455i | 0.627921 | + | 1.08759i | 0.987968 | + | 0.154657i | \(0.0494273\pi\) |
−0.360047 | + | 0.932934i | \(0.617239\pi\) | |||||||
\(68\) | −53.7774 | − | 93.1452i | −0.0959039 | − | 0.166110i | ||||
\(69\) | 291.464 | − | 74.2385i | 0.508524 | − | 0.129526i | ||||
\(70\) | −59.2956 | + | 220.680i | −0.101245 | + | 0.376804i | ||||
\(71\) | − | 577.396i | − | 0.965130i | −0.875860 | − | 0.482565i | \(-0.839705\pi\) | ||
0.875860 | − | 0.482565i | \(-0.160295\pi\) | |||||||
\(72\) | 346.224 | − | 566.756i | 0.566707 | − | 0.927678i | ||||
\(73\) | − | 37.4543i | − | 0.0600506i | −0.999549 | − | 0.0300253i | \(-0.990441\pi\) | ||
0.999549 | − | 0.0300253i | \(-0.00955879\pi\) | |||||||
\(74\) | 563.705 | + | 325.455i | 0.885532 | + | 0.511262i | ||||
\(75\) | −351.801 | + | 343.187i | −0.541633 | + | 0.528370i | ||||
\(76\) | 202.375 | − | 116.841i | 0.305448 | − | 0.176350i | ||||
\(77\) | 457.025 | + | 457.661i | 0.676400 | + | 0.677342i | ||||
\(78\) | −299.173 | − | 84.1509i | −0.434291 | − | 0.122157i | ||||
\(79\) | −428.000 | + | 741.317i | −0.609541 | + | 1.05576i | 0.381775 | + | 0.924255i | \(0.375313\pi\) |
−0.991316 | + | 0.131501i | \(0.958020\pi\) | |||||||
\(80\) | −171.342 | −0.239458 | ||||||||
\(81\) | 332.766 | + | 648.620i | 0.456469 | + | 0.889739i | ||||
\(82\) | − | 241.883i | − | 0.325750i | ||||||
\(83\) | −616.129 | + | 1067.17i | −0.814806 | + | 1.41129i | 0.0946603 | + | 0.995510i | \(0.469824\pi\) |
−0.909467 | + | 0.415777i | \(0.863510\pi\) | |||||||
\(84\) | 3.77299 | − | 288.213i | 0.00490079 | − | 0.374365i | ||||
\(85\) | −99.0228 | − | 171.513i | −0.126359 | − | 0.218861i | ||||
\(86\) | 674.460 | − | 389.400i | 0.845685 | − | 0.488256i | ||||
\(87\) | 804.705 | + | 824.903i | 0.991649 | + | 1.01654i | ||||
\(88\) | −429.513 | + | 743.939i | −0.520299 | + | 0.901184i | ||||
\(89\) | 1505.64 | 1.79323 | 0.896615 | − | 0.442811i | \(-0.146019\pi\) | ||||
0.896615 | + | 0.442811i | \(0.146019\pi\) | |||||||
\(90\) | 173.665 | − | 284.284i | 0.203399 | − | 0.332957i | ||||
\(91\) | −478.358 | + | 127.819i | −0.551050 | + | 0.147242i | ||||
\(92\) | 150.143 | + | 86.6853i | 0.170147 | + | 0.0982344i | ||||
\(93\) | −732.619 | + | 186.604i | −0.816871 | + | 0.208064i | ||||
\(94\) | 486.467 | − | 280.862i | 0.533780 | − | 0.308178i | ||||
\(95\) | 372.643 | − | 215.146i | 0.402446 | − | 0.232352i | ||||
\(96\) | 640.903 | − | 163.243i | 0.681374 | − | 0.173552i | ||||
\(97\) | 1002.35 | + | 578.705i | 1.04921 | + | 0.605759i | 0.922427 | − | 0.386172i | \(-0.126203\pi\) |
0.126778 | + | 0.991931i | \(0.459536\pi\) | |||||||
\(98\) | 382.745 | + | 665.071i | 0.394521 | + | 0.685533i | ||||
\(99\) | −451.074 | − | 828.025i | −0.457926 | − | 0.840603i | ||||
\(100\) | −283.293 | −0.283293 | ||||||||
\(101\) | 77.7834 | − | 134.725i | 0.0766311 | − | 0.132729i | −0.825163 | − | 0.564894i | \(-0.808917\pi\) |
0.901794 | + | 0.432165i | \(0.142250\pi\) | |||||||
\(102\) | −291.487 | − | 298.803i | −0.282956 | − | 0.290058i | ||||
\(103\) | −1640.73 | + | 947.276i | −1.56957 | + | 0.906193i | −0.573354 | + | 0.819307i | \(0.694358\pi\) |
−0.996218 | + | 0.0868857i | \(0.972309\pi\) | |||||||
\(104\) | −328.812 | − | 569.519i | −0.310026 | − | 0.536980i | ||||
\(105\) | 6.94737 | − | 530.701i | 0.00645709 | − | 0.493248i | ||||
\(106\) | −179.165 | + | 310.323i | −0.164170 | + | 0.284351i | ||||
\(107\) | − | 507.467i | − | 0.458492i | −0.973369 | − | 0.229246i | \(-0.926374\pi\) | ||
0.973369 | − | 0.229246i | \(-0.0736260\pi\) | |||||||
\(108\) | −123.772 | + | 401.570i | −0.110278 | + | 0.357787i | ||||
\(109\) | 298.426 | 0.262239 | 0.131119 | − | 0.991367i | \(-0.458143\pi\) | ||||
0.131119 | + | 0.991367i | \(0.458143\pi\) | |||||||
\(110\) | −215.443 | + | 373.158i | −0.186743 | + | 0.323448i | ||||
\(111\) | −1455.37 | − | 409.365i | −1.24449 | − | 0.350047i | ||||
\(112\) | −407.137 | + | 406.571i | −0.343490 | + | 0.343012i | ||||
\(113\) | 216.173 | − | 124.808i | 0.179964 | − | 0.103902i | −0.407312 | − | 0.913289i | \(-0.633534\pi\) |
0.587276 | + | 0.809387i | \(0.300200\pi\) | |||||||
\(114\) | 649.206 | − | 633.310i | 0.533366 | − | 0.520306i | ||||
\(115\) | 276.466 | + | 159.618i | 0.224179 | + | 0.129430i | ||||
\(116\) | 664.266i | 0.531686i | ||||||||
\(117\) | 721.625 | + | 17.8914i | 0.570207 | + | 0.0141373i | ||||
\(118\) | − | 1643.97i | − | 1.28254i | ||||||
\(119\) | −642.269 | − | 172.575i | −0.494762 | − | 0.132940i | ||||
\(120\) | 683.104 | − | 173.992i | 0.519655 | − | 0.132360i | ||||
\(121\) | −55.6960 | − | 96.4683i | −0.0418452 | − | 0.0724781i | ||||
\(122\) | −750.882 | − | 1300.57i | −0.557227 | − | 0.965145i | ||||
\(123\) | 138.671 | + | 544.431i | 0.101655 | + | 0.399103i | ||||
\(124\) | −377.397 | − | 217.890i | −0.273317 | − | 0.157799i | ||||
\(125\) | −1211.03 | −0.866546 | ||||||||
\(126\) | −261.907 | − | 1087.59i | −0.185179 | − | 0.768968i | ||||
\(127\) | 1942.24 | 1.35706 | 0.678528 | − | 0.734574i | \(-0.262618\pi\) | ||||
0.678528 | + | 0.734574i | \(0.262618\pi\) | |||||||
\(128\) | −151.377 | − | 87.3976i | −0.104531 | − | 0.0603510i | ||||
\(129\) | −1294.84 | + | 1263.13i | −0.883751 | + | 0.862112i | ||||
\(130\) | −164.931 | − | 285.670i | −0.111273 | − | 0.192730i | ||||
\(131\) | −13.2642 | − | 22.9743i | −0.00884655 | − | 0.0153227i | 0.861568 | − | 0.507642i | \(-0.169483\pi\) |
−0.870415 | + | 0.492319i | \(0.836149\pi\) | |||||||
\(132\) | 147.169 | − | 523.215i | 0.0970409 | − | 0.345000i | ||||
\(133\) | 374.951 | − | 1395.45i | 0.244454 | − | 0.909781i | ||||
\(134\) | 1540.78i | 0.993309i | ||||||||
\(135\) | −227.907 | + | 739.429i | −0.145297 | + | 0.471407i | ||||
\(136\) | − | 883.291i | − | 0.556924i | ||||||
\(137\) | −230.946 | − | 133.337i | −0.144023 | − | 0.0831515i | 0.426257 | − | 0.904602i | \(-0.359832\pi\) |
−0.570280 | + | 0.821451i | \(0.693165\pi\) | |||||||
\(138\) | 647.732 | + | 182.193i | 0.399555 | + | 0.112386i | ||||
\(139\) | 444.807 | − | 256.810i | 0.271425 | − | 0.156707i | −0.358110 | − | 0.933679i | \(-0.616579\pi\) |
0.629535 | + | 0.776972i | \(0.283245\pi\) | |||||||
\(140\) | 216.478 | − | 216.177i | 0.130684 | − | 0.130502i | ||||
\(141\) | −933.925 | + | 911.057i | −0.557806 | + | 0.544148i | ||||
\(142\) | 645.859 | − | 1118.66i | 0.381685 | − | 0.661098i | ||||
\(143\) | −933.665 | −0.545993 | ||||||||
\(144\) | 736.614 | − | 401.277i | 0.426281 | − | 0.232221i | ||||
\(145\) | 1223.14i | 0.700528i | ||||||||
\(146\) | 41.8954 | − | 72.5650i | 0.0237486 | − | 0.0411337i | ||||
\(147\) | −1242.77 | − | 1277.52i | −0.697291 | − | 0.716788i | ||||
\(148\) | −435.732 | − | 754.709i | −0.242006 | − | 0.419167i | ||||
\(149\) | −1835.58 | + | 1059.77i | −1.00924 | + | 0.582683i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) |
−0.0982688 | + | 0.995160i | \(0.531331\pi\) | |||||||
\(150\) | −1065.47 | + | 271.384i | −0.579967 | + | 0.147723i | ||||
\(151\) | 1141.85 | − | 1977.74i | 0.615380 | − | 1.06587i | −0.374937 | − | 0.927050i | \(-0.622336\pi\) |
0.990318 | − | 0.138820i | \(-0.0443309\pi\) | |||||||
\(152\) | 1919.12 | 1.02408 | ||||||||
\(153\) | 827.383 | + | 505.439i | 0.437189 | + | 0.267074i | ||||
\(154\) | 373.524 | + | 1397.90i | 0.195451 | + | 0.731468i | ||||
\(155\) | −694.919 | − | 401.212i | −0.360111 | − | 0.207910i | ||||
\(156\) | 290.549 | + | 297.842i | 0.149119 | + | 0.152862i | ||||
\(157\) | 3179.20 | − | 1835.51i | 1.61610 | − | 0.933057i | 0.628186 | − | 0.778063i | \(-0.283798\pi\) |
0.987916 | − | 0.154993i | \(-0.0495356\pi\) | |||||||
\(158\) | −1658.44 | + | 957.498i | −0.835051 | + | 0.482117i | ||||
\(159\) | 225.358 | − | 801.192i | 0.112403 | − | 0.399614i | ||||
\(160\) | 607.923 | + | 350.984i | 0.300378 | + | 0.173423i | ||||
\(161\) | 1035.68 | − | 276.737i | 0.506974 | − | 0.135465i | ||||
\(162\) | −80.8198 | + | 1628.88i | −0.0391963 | + | 0.789979i | ||||
\(163\) | 169.826 | 0.0816063 | 0.0408032 | − | 0.999167i | \(-0.487008\pi\) | ||||
0.0408032 | + | 0.999167i | \(0.487008\pi\) | |||||||
\(164\) | −161.921 | + | 280.455i | −0.0770970 | + | 0.133536i | ||||
\(165\) | 270.989 | − | 963.420i | 0.127857 | − | 0.454558i | ||||
\(166\) | −2387.41 | + | 1378.37i | −1.11626 | + | 0.644472i | ||||
\(167\) | 218.313 | + | 378.129i | 0.101159 | + | 0.175213i | 0.912162 | − | 0.409829i | \(-0.134412\pi\) |
−0.811003 | + | 0.585041i | \(0.801078\pi\) | |||||||
\(168\) | 1210.31 | − | 2034.34i | 0.555817 | − | 0.934244i | ||||
\(169\) | −741.119 | + | 1283.66i | −0.337332 | + | 0.584276i | ||||
\(170\) | − | 443.057i | − | 0.199888i | ||||||
\(171\) | −1098.16 | + | 1797.65i | −0.491102 | + | 0.803915i | ||||
\(172\) | −1042.69 | −0.462233 | ||||||||
\(173\) | 827.732 | − | 1433.67i | 0.363765 | − | 0.630059i | −0.624812 | − | 0.780775i | \(-0.714825\pi\) |
0.988577 | + | 0.150716i | \(0.0481579\pi\) | |||||||
\(174\) | 636.341 | + | 2498.31i | 0.277247 | + | 1.08849i | ||||
\(175\) | −1239.50 | + | 1237.78i | −0.535415 | + | 0.534670i | ||||
\(176\) | −939.610 | + | 542.484i | −0.402419 | + | 0.232337i | ||||
\(177\) | 942.484 | + | 3700.24i | 0.400234 | + | 1.57134i | ||||
\(178\) | 2917.07 | + | 1684.17i | 1.22833 | + | 0.709178i | ||||
\(179\) | − | 4545.28i | − | 1.89793i | −0.315376 | − | 0.948967i | \(-0.602131\pi\) | ||
0.315376 | − | 0.948967i | \(-0.397869\pi\) | |||||||
\(180\) | −391.664 | + | 213.363i | −0.162183 | + | 0.0883506i | ||||
\(181\) | 69.4780i | 0.0285318i | 0.999898 | + | 0.0142659i | \(0.00454113\pi\) | ||||
−0.999898 | + | 0.0142659i | \(0.995459\pi\) | |||||||
\(182\) | −1069.76 | − | 287.439i | −0.435690 | − | 0.117068i | ||||
\(183\) | 2435.70 | + | 2496.84i | 0.983892 | + | 1.00859i | ||||
\(184\) | 711.901 | + | 1233.05i | 0.285229 | + | 0.494030i | ||||
\(185\) | −802.333 | − | 1389.68i | −0.318858 | − | 0.552278i | ||||
\(186\) | −1628.12 | − | 457.956i | −0.641827 | − | 0.180532i | ||||
\(187\) | −1086.05 | − | 627.029i | −0.424703 | − | 0.245203i | ||||
\(188\) | −752.057 | −0.291752 | ||||||||
\(189\) | 1213.01 | + | 2297.80i | 0.466846 | + | 0.884339i | ||||
\(190\) | 962.625 | 0.367559 | ||||||||
\(191\) | 1216.59 | + | 702.396i | 0.460885 | + | 0.266092i | 0.712416 | − | 0.701757i | \(-0.247601\pi\) |
−0.251531 | + | 0.967849i | \(0.580934\pi\) | |||||||
\(192\) | 2667.51 | + | 750.312i | 1.00266 | + | 0.282027i | ||||
\(193\) | −1156.04 | − | 2002.32i | −0.431158 | − | 0.746787i | 0.565815 | − | 0.824532i | \(-0.308561\pi\) |
−0.996973 | + | 0.0777446i | \(0.975228\pi\) | |||||||
\(194\) | 1294.65 | + | 2242.40i | 0.479125 | + | 0.829870i | ||||
\(195\) | 535.002 | + | 548.431i | 0.196473 | + | 0.201405i | ||||
\(196\) | 1.43036 | − | 1027.34i | 0.000521267 | − | 0.374397i | ||||
\(197\) | 1556.72i | 0.563005i | 0.959561 | + | 0.281502i | \(0.0908327\pi\) | ||||
−0.959561 | + | 0.281502i | \(0.909167\pi\) | |||||||
\(198\) | 52.2838 | − | 2108.80i | 0.0187659 | − | 0.756898i | ||||
\(199\) | − | 1187.87i | − | 0.423146i | −0.977362 | − | 0.211573i | \(-0.932141\pi\) | ||
0.977362 | − | 0.211573i | \(-0.0678585\pi\) | |||||||
\(200\) | −2014.84 | − | 1163.27i | −0.712353 | − | 0.411277i | ||||
\(201\) | −883.330 | − | 3468.00i | −0.309977 | − | 1.21699i | ||||
\(202\) | 301.399 | − | 174.013i | 0.104982 | − | 0.0606114i | ||||
\(203\) | 2902.35 | + | 2906.39i | 1.00347 | + | 1.00487i | ||||
\(204\) | 137.945 | + | 541.579i | 0.0473435 | + | 0.185873i | ||||
\(205\) | −298.153 | + | 516.416i | −0.101580 | + | 0.175942i | ||||
\(206\) | −4238.39 | −1.43351 | ||||||||
\(207\) | −1562.37 | − | 38.7361i | −0.524600 | − | 0.0130065i | ||||
\(208\) | − | 830.592i | − | 0.276881i | ||||||
\(209\) | 1362.34 | − | 2359.64i | 0.450885 | − | 0.780955i | ||||
\(210\) | 607.088 | − | 1020.42i | 0.199491 | − | 0.335313i | ||||
\(211\) | −122.996 | − | 213.035i | −0.0401298 | − | 0.0695069i | 0.845263 | − | 0.534351i | \(-0.179444\pi\) |
−0.885393 | + | 0.464844i | \(0.846110\pi\) | |||||||
\(212\) | 415.472 | − | 239.873i | 0.134598 | − | 0.0777101i | ||||
\(213\) | −812.376 | + | 2888.16i | −0.261329 | + | 0.929077i | ||||
\(214\) | 567.639 | − | 983.179i | 0.181322 | − | 0.314059i | ||||
\(215\) | −1919.95 | −0.609020 | ||||||||
\(216\) | −2529.24 | + | 2347.81i | −0.796725 | + | 0.739576i | ||||
\(217\) | −2603.26 | + | 695.599i | −0.814381 | + | 0.217605i | ||||
\(218\) | 578.178 | + | 333.811i | 0.179629 | + | 0.103709i | ||||
\(219\) | −52.6969 | + | 187.348i | −0.0162600 | + | 0.0578074i | ||||
\(220\) | 499.598 | − | 288.443i | 0.153104 | − | 0.0883947i | ||||
\(221\) | 831.417 | − | 480.019i | 0.253064 | − | 0.146107i | ||||
\(222\) | −2361.77 | − | 2421.06i | −0.714018 | − | 0.731940i | ||||
\(223\) | −951.393 | − | 549.287i | −0.285695 | − | 0.164946i | 0.350304 | − | 0.936636i | \(-0.386078\pi\) |
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(224\) | 2277.36 | − | 608.518i | 0.679297 | − | 0.181510i | ||||
\(225\) | 2242.57 | − | 1221.66i | 0.664466 | − | 0.361974i | ||||
\(226\) | 558.427 | 0.164363 | ||||||||
\(227\) | 2151.95 | − | 3727.29i | 0.629208 | − | 1.08982i | −0.358503 | − | 0.933528i | \(-0.616713\pi\) |
0.987711 | − | 0.156291i | \(-0.0499539\pi\) | |||||||
\(228\) | −1176.68 | + | 299.711i | −0.341788 | + | 0.0870564i | ||||
\(229\) | 2476.51 | − | 1429.81i | 0.714639 | − | 0.412597i | −0.0981371 | − | 0.995173i | \(-0.531288\pi\) |
0.812776 | + | 0.582576i | \(0.197955\pi\) | |||||||
\(230\) | 357.088 | + | 618.495i | 0.102373 | + | 0.177315i | ||||
\(231\) | −1642.14 | − | 2932.26i | −0.467728 | − | 0.835189i | ||||
\(232\) | −2727.64 | + | 4724.40i | −0.771888 | + | 1.33695i | ||||
\(233\) | 2256.65i | 0.634497i | 0.948342 | + | 0.317249i | \(0.102759\pi\) | ||||
−0.948342 | + | 0.317249i | \(0.897241\pi\) | |||||||
\(234\) | 1378.08 | + | 841.853i | 0.384991 | + | 0.235187i | ||||
\(235\) | −1384.80 | −0.384401 | ||||||||
\(236\) | −1100.50 | + | 1906.12i | −0.303545 | + | 0.525755i | ||||
\(237\) | 3183.88 | − | 3105.92i | 0.872639 | − | 0.851271i | ||||
\(238\) | −1051.31 | − | 1052.78i | −0.286329 | − | 0.286728i | ||||
\(239\) | 1367.09 | − | 789.292i | 0.370000 | − | 0.213620i | −0.303458 | − | 0.952845i | \(-0.598141\pi\) |
0.673458 | + | 0.739225i | \(0.264808\pi\) | |||||||
\(240\) | 857.062 | + | 241.073i | 0.230513 | + | 0.0648382i | ||||
\(241\) | −1248.30 | − | 720.708i | −0.333652 | − | 0.192634i | 0.323809 | − | 0.946122i | \(-0.395036\pi\) |
−0.657461 | + | 0.753488i | \(0.728370\pi\) | |||||||
\(242\) | − | 249.200i | − | 0.0661951i | ||||||
\(243\) | −751.924 | − | 3712.62i | −0.198502 | − | 0.980101i | ||||
\(244\) | 2010.62i | 0.527527i | ||||||||
\(245\) | 2.63378 | − | 1891.70i | 0.000686801 | − | 0.493290i | ||||
\(246\) | −340.321 | + | 1209.91i | −0.0882035 | + | 0.313581i | ||||
\(247\) | 1042.93 | + | 1806.41i | 0.268664 | + | 0.465341i | ||||
\(248\) | −1789.42 | − | 3099.37i | −0.458179 | − | 0.793589i | ||||
\(249\) | 4583.37 | − | 4471.14i | 1.16650 | − | 1.13794i | ||||
\(250\) | −2346.29 | − | 1354.63i | −0.593570 | − | 0.342698i | ||||
\(251\) | −2935.90 | −0.738296 | −0.369148 | − | 0.929371i | \(-0.620350\pi\) | ||||
−0.369148 | + | 0.929371i | \(0.620350\pi\) | |||||||
\(252\) | −424.379 | + | 1436.35i | −0.106085 | + | 0.359053i | ||||
\(253\) | 2021.45 | 0.502322 | ||||||||
\(254\) | 3762.95 | + | 2172.54i | 0.929562 | + | 0.536683i | ||||
\(255\) | 254.004 | + | 997.235i | 0.0623779 | + | 0.244899i | ||||
\(256\) | 1937.62 | + | 3356.05i | 0.473051 | + | 0.819348i | ||||
\(257\) | 3638.04 | + | 6301.27i | 0.883015 | + | 1.52943i | 0.847973 | + | 0.530040i | \(0.177823\pi\) |
0.0350420 | + | 0.999386i | \(0.488843\pi\) | |||||||
\(258\) | −3921.55 | + | 998.853i | −0.946299 | + | 0.241030i | ||||
\(259\) | −5203.99 | − | 1398.29i | −1.24850 | − | 0.335465i | ||||
\(260\) | 441.632i | 0.105342i | ||||||||
\(261\) | −2864.56 | − | 5258.40i | −0.679355 | − | 1.24707i | ||||
\(262\) | − | 59.3479i | − | 0.0139944i | ||||||
\(263\) | 5830.68 | + | 3366.35i | 1.36705 | + | 0.789269i | 0.990551 | − | 0.137146i | \(-0.0437930\pi\) |
0.376503 | + | 0.926415i | \(0.377126\pi\) | |||||||
\(264\) | 3195.14 | − | 3116.91i | 0.744876 | − | 0.726637i | ||||
\(265\) | 765.029 | − | 441.689i | 0.177341 | − | 0.102388i | ||||
\(266\) | 2287.35 | − | 2284.17i | 0.527243 | − | 0.526509i | ||||
\(267\) | −7531.28 | − | 2118.38i | −1.72624 | − | 0.485554i | ||||
\(268\) | 1031.43 | − | 1786.49i | 0.235092 | − | 0.407191i | ||||
\(269\) | −7501.34 | −1.70024 | −0.850121 | − | 0.526588i | \(-0.823471\pi\) | ||||
−0.850121 | + | 0.526588i | \(0.823471\pi\) | |||||||
\(270\) | −1268.66 | + | 1177.66i | −0.285956 | + | 0.265444i | ||||
\(271\) | 4621.90i | 1.03602i | 0.855376 | + | 0.518008i | \(0.173326\pi\) | ||||
−0.855376 | + | 0.518008i | \(0.826674\pi\) | |||||||
\(272\) | 557.807 | − | 966.150i | 0.124346 | − | 0.215373i | ||||
\(273\) | 2572.60 | + | 33.6778i | 0.570333 | + | 0.00746620i | ||||
\(274\) | −298.294 | − | 516.661i | −0.0657687 | − | 0.113915i | ||||
\(275\) | −2860.58 | + | 1651.56i | −0.627271 | + | 0.362155i | ||||
\(276\) | −629.060 | − | 644.850i | −0.137192 | − | 0.140636i | ||||
\(277\) | 982.366 | − | 1701.51i | 0.213085 | − | 0.369075i | −0.739593 | − | 0.673054i | \(-0.764982\pi\) |
0.952679 | + | 0.303980i | \(0.0983154\pi\) | |||||||
\(278\) | 1149.04 | 0.247895 | ||||||||
\(279\) | 3927.14 | + | 97.3663i | 0.842694 | + | 0.0208931i | ||||
\(280\) | 2427.32 | − | 648.586i | 0.518071 | − | 0.138430i | ||||
\(281\) | 1702.23 | + | 982.785i | 0.361376 | + | 0.208641i | 0.669684 | − | 0.742646i | \(-0.266429\pi\) |
−0.308308 | + | 0.951287i | \(0.599763\pi\) | |||||||
\(282\) | −2828.50 | + | 720.442i | −0.597285 | + | 0.152134i | ||||
\(283\) | 4621.27 | − | 2668.09i | 0.970692 | − | 0.560429i | 0.0712447 | − | 0.997459i | \(-0.477303\pi\) |
0.899447 | + | 0.437030i | \(0.143970\pi\) | |||||||
\(284\) | −1497.71 | + | 864.701i | −0.312931 | + | 0.180671i | ||||
\(285\) | −2166.68 | + | 551.872i | −0.450327 | + | 0.114702i | ||||
\(286\) | −1808.91 | − | 1044.37i | −0.373996 | − | 0.215927i | ||||
\(287\) | 516.921 | + | 1934.56i | 0.106317 | + | 0.397887i | ||||
\(288\) | −3435.50 | − | 85.1771i | −0.702913 | − | 0.0174275i | ||||
\(289\) | −3623.52 | −0.737537 | ||||||||
\(290\) | −1368.18 | + | 2369.75i | −0.277042 | + | 0.479850i | ||||
\(291\) | −4199.57 | − | 4304.98i | −0.845989 | − | 0.867224i | ||||
\(292\) | −97.1527 | + | 56.0911i | −0.0194707 | + | 0.0112414i | ||||
\(293\) | −1032.50 | − | 1788.34i | −0.205867 | − | 0.356572i | 0.744542 | − | 0.667576i | \(-0.232668\pi\) |
−0.950409 | + | 0.311004i | \(0.899335\pi\) | |||||||
\(294\) | −978.776 | − | 3865.22i | −0.194161 | − | 0.766749i | ||||
\(295\) | −2026.40 | + | 3509.83i | −0.399938 | + | 0.692713i | ||||
\(296\) | − | 7156.88i | − | 1.40535i | ||||||
\(297\) | 1091.29 | + | 4776.47i | 0.213209 | + | 0.933194i | ||||
\(298\) | −4741.73 | −0.921748 | ||||||||
\(299\) | −773.756 | + | 1340.18i | −0.149657 | + | 0.259214i | ||||
\(300\) | 1417.04 | + | 398.583i | 0.272710 | + | 0.0767074i | ||||
\(301\) | −4562.11 | + | 4555.76i | −0.873606 | + | 0.872391i | ||||
\(302\) | 4424.50 | − | 2554.49i | 0.843051 | − | 0.486736i | ||||
\(303\) | −578.629 | + | 564.461i | −0.109708 | + | 0.107021i | ||||
\(304\) | 2099.14 | + | 1211.94i | 0.396033 | + | 0.228650i | ||||
\(305\) | 3702.24i | 0.695049i | ||||||||
\(306\) | 1037.62 | + | 1904.74i | 0.193846 | + | 0.355839i | ||||
\(307\) | 395.602i | 0.0735446i | 0.999324 | + | 0.0367723i | \(0.0117076\pi\) | ||||
−0.999324 | + | 0.0367723i | \(0.988292\pi\) | |||||||
\(308\) | 502.692 | − | 1870.86i | 0.0929986 | − | 0.346111i | ||||
\(309\) | 9539.79 | − | 2429.87i | 1.75631 | − | 0.447347i | ||||
\(310\) | −897.569 | − | 1554.64i | −0.164447 | − | 0.284830i | ||||
\(311\) | 3155.13 | + | 5464.85i | 0.575277 | + | 0.996409i | 0.996011 | + | 0.0892250i | \(0.0284390\pi\) |
−0.420735 | + | 0.907184i | \(0.638228\pi\) | |||||||
\(312\) | 843.438 | + | 3311.39i | 0.153046 | + | 0.600866i | ||||
\(313\) | 8787.97 | + | 5073.73i | 1.58698 | + | 0.916244i | 0.993801 | + | 0.111175i | \(0.0354613\pi\) |
0.593180 | + | 0.805070i | \(0.297872\pi\) | |||||||
\(314\) | 8212.62 | 1.47600 | ||||||||
\(315\) | −781.428 | + | 2644.81i | −0.139773 | + | 0.473074i | ||||
\(316\) | 2563.87 | 0.456421 | ||||||||
\(317\) | 1537.07 | + | 887.426i | 0.272335 | + | 0.157233i | 0.629948 | − | 0.776637i | \(-0.283076\pi\) |
−0.357613 | + | 0.933870i | \(0.616409\pi\) | |||||||
\(318\) | 1332.81 | − | 1300.17i | 0.235032 | − | 0.229277i | ||||
\(319\) | 3872.58 | + | 6707.50i | 0.679695 | + | 1.17727i | ||||
\(320\) | 1470.57 | + | 2547.11i | 0.256898 | + | 0.444961i | ||||
\(321\) | −713.988 | + | 2538.37i | −0.124146 | + | 0.441365i | ||||
\(322\) | 2316.10 | + | 622.325i | 0.400842 | + | 0.107704i | ||||
\(323\) | 2801.64i | 0.482623i | ||||||||
\(324\) | 1184.11 | − | 1834.53i | 0.203036 | − | 0.314562i | ||||
\(325\) | − | 2528.68i | − | 0.431588i | ||||||
\(326\) | 329.026 | + | 189.963i | 0.0558990 | + | 0.0322733i | ||||
\(327\) | −1492.74 | − | 419.875i | −0.252443 | − | 0.0710065i | ||||
\(328\) | −2303.23 | + | 1329.77i | −0.387728 | + | 0.223855i | ||||
\(329\) | −3290.51 | + | 3285.93i | −0.551403 | + | 0.550636i | ||||
\(330\) | 1602.68 | − | 1563.43i | 0.267347 | − | 0.260801i | ||||
\(331\) | −2397.72 | + | 4152.98i | −0.398160 | + | 0.689633i | −0.993499 | − | 0.113842i | \(-0.963684\pi\) |
0.595339 | + | 0.803474i | \(0.297018\pi\) | |||||||
\(332\) | 3690.83 | 0.610122 | ||||||||
\(333\) | 6703.88 | + | 4095.32i | 1.10321 | + | 0.673940i | ||||
\(334\) | 976.796i | 0.160024i | ||||||||
\(335\) | 1899.22 | − | 3289.54i | 0.309748 | − | 0.536498i | ||||
\(336\) | 2608.55 | − | 1460.86i | 0.423536 | − | 0.237191i | ||||
\(337\) | −3694.91 | − | 6399.77i | −0.597253 | − | 1.03447i | −0.993225 | − | 0.116210i | \(-0.962925\pi\) |
0.395971 | − | 0.918263i | \(-0.370408\pi\) | |||||||
\(338\) | −2871.72 | + | 1657.99i | −0.462134 | + | 0.266813i | ||||
\(339\) | −1256.91 | + | 320.146i | −0.201374 | + | 0.0512918i | ||||
\(340\) | −296.591 | + | 513.710i | −0.0473085 | + | 0.0819407i | ||||
\(341\) | −5081.08 | −0.806908 | ||||||||
\(342\) | −4138.40 | + | 2254.43i | −0.654325 | + | 0.356450i | ||||
\(343\) | −4482.47 | − | 4501.23i | −0.705628 | − | 0.708582i | ||||
\(344\) | −7415.81 | − | 4281.52i | −1.16231 | − | 0.671058i | ||||
\(345\) | −1158.32 | − | 1187.39i | −0.180759 | − | 0.185296i | ||||
\(346\) | 3207.34 | − | 1851.76i | 0.498346 | − | 0.287720i | ||||
\(347\) | 1565.28 | − | 903.715i | 0.242157 | − | 0.139810i | −0.374010 | − | 0.927424i | \(-0.622018\pi\) |
0.616168 | + | 0.787615i | \(0.288684\pi\) | |||||||
\(348\) | 934.599 | − | 3322.69i | 0.143965 | − | 0.511824i | ||||
\(349\) | −5094.40 | − | 2941.25i | −0.781367 | − | 0.451122i | 0.0555477 | − | 0.998456i | \(-0.482310\pi\) |
−0.836914 | + | 0.547334i | \(0.815643\pi\) | |||||||
\(350\) | −3785.99 | + | 1011.63i | −0.578199 | + | 0.154497i | ||||
\(351\) | −3584.43 | − | 1104.79i | −0.545078 | − | 0.168004i | ||||
\(352\) | 4444.98 | 0.673064 | ||||||||
\(353\) | −1196.54 | + | 2072.48i | −0.180413 | + | 0.312484i | −0.942021 | − | 0.335554i | \(-0.891077\pi\) |
0.761609 | + | 0.648037i | \(0.224410\pi\) | |||||||
\(354\) | −2313.00 | + | 8223.19i | −0.347273 | + | 1.23463i | ||||
\(355\) | −2757.80 | + | 1592.21i | −0.412306 | + | 0.238045i | ||||
\(356\) | −2254.83 | − | 3905.48i | −0.335690 | − | 0.581432i | ||||
\(357\) | 2969.85 | + | 1766.88i | 0.440284 | + | 0.261941i | ||||
\(358\) | 5084.23 | − | 8806.14i | 0.750586 | − | 1.30005i | ||||
\(359\) | − | 10728.4i | − | 1.57723i | −0.614887 | − | 0.788615i | \(-0.710798\pi\) | ||
0.614887 | − | 0.788615i | \(-0.289202\pi\) | |||||||
\(360\) | −3661.72 | − | 90.7857i | −0.536082 | − | 0.0132912i | ||||
\(361\) | 771.915 | 0.112540 | ||||||||
\(362\) | −77.7162 | + | 134.608i | −0.0112836 | + | 0.0195438i | ||||
\(363\) | 142.866 | + | 560.901i | 0.0206571 | + | 0.0811011i | ||||
\(364\) | 1047.93 | + | 1049.39i | 0.150897 | + | 0.151107i | ||||
\(365\) | −178.892 | + | 103.283i | −0.0256538 | + | 0.0148112i | ||||
\(366\) | 1926.09 | + | 7561.95i | 0.275078 | + | 1.07997i | ||||
\(367\) | 4743.12 | + | 2738.44i | 0.674630 | + | 0.389498i | 0.797829 | − | 0.602884i | \(-0.205982\pi\) |
−0.123199 | + | 0.992382i | \(0.539315\pi\) | |||||||
\(368\) | 1798.29i | 0.254735i | ||||||||
\(369\) | 72.3559 | − | 2918.38i | 0.0102078 | − | 0.411720i | ||||
\(370\) | − | 3589.87i | − | 0.504402i | ||||||
\(371\) | 769.767 | − | 2864.83i | 0.107721 | − | 0.400902i | ||||
\(372\) | 1581.19 | + | 1620.88i | 0.220379 | + | 0.225911i | ||||
\(373\) | −6052.38 | − | 10483.0i | −0.840162 | − | 1.45520i | −0.889757 | − | 0.456434i | \(-0.849127\pi\) |
0.0495956 | − | 0.998769i | \(-0.484207\pi\) | |||||||
\(374\) | −1402.76 | − | 2429.64i | −0.193943 | − | 0.335920i | ||||
\(375\) | 6057.65 | + | 1703.88i | 0.834175 | + | 0.234635i | ||||
\(376\) | −5348.80 | − | 3088.13i | −0.733625 | − | 0.423559i | ||||
\(377\) | −5929.26 | −0.810007 | ||||||||
\(378\) | −220.127 | + | 5808.65i | −0.0299527 | + | 0.790383i | ||||
\(379\) | 2.33509 | 0.000316479 | 0.000158240 | − | 1.00000i | \(-0.499950\pi\) | ||||
0.000158240 | 1.00000i | \(0.499950\pi\) | ||||||||
\(380\) | −1116.13 | − | 644.399i | −0.150675 | − | 0.0869920i | ||||
\(381\) | −9715.19 | − | 2732.67i | −1.30636 | − | 0.367451i | ||||
\(382\) | 1571.36 | + | 2721.68i | 0.210466 | + | 0.364537i | ||||
\(383\) | −4098.57 | − | 7098.93i | −0.546807 | − | 0.947097i | −0.998491 | − | 0.0549191i | \(-0.982510\pi\) |
0.451684 | − | 0.892178i | \(-0.350823\pi\) | |||||||
\(384\) | 634.230 | + | 650.149i | 0.0842849 | + | 0.0864005i | ||||
\(385\) | 925.631 | − | 3444.91i | 0.122531 | − | 0.456023i | ||||
\(386\) | − | 5172.45i | − | 0.682049i | ||||||
\(387\) | 8254.01 | − | 4496.45i | 1.08417 | − | 0.590613i | ||||
\(388\) | − | 3466.65i | − | 0.453588i | ||||||
\(389\) | −4487.63 | − | 2590.94i | −0.584915 | − | 0.337701i | 0.178169 | − | 0.984000i | \(-0.442983\pi\) |
−0.763084 | + | 0.646299i | \(0.776316\pi\) | |||||||
\(390\) | 423.067 | + | 1660.98i | 0.0549303 | + | 0.215660i | ||||
\(391\) | −1800.08 | + | 1039.28i | −0.232823 | + | 0.134420i | ||||
\(392\) | 4228.69 | − | 7300.82i | 0.544850 | − | 0.940681i | ||||
\(393\) | 34.0241 | + | 133.580i | 0.00436715 | + | 0.0171457i | ||||
\(394\) | −1741.31 | + | 3016.04i | −0.222655 | + | 0.385649i | ||||
\(395\) | 4720.97 | 0.601362 | ||||||||
\(396\) | −1472.29 | + | 2410.08i | −0.186832 | + | 0.305836i | ||||
\(397\) | − | 6757.41i | − | 0.854269i | −0.904188 | − | 0.427135i | \(-0.859523\pi\) | ||
0.904188 | − | 0.427135i | \(-0.140477\pi\) | |||||||
\(398\) | 1328.72 | − | 2301.41i | 0.167344 | − | 0.289848i | ||||
\(399\) | −3838.87 | + | 6452.56i | −0.481664 | + | 0.809604i | ||||
\(400\) | −1469.23 | − | 2544.78i | −0.183654 | − | 0.318098i | ||||
\(401\) | −7670.47 | + | 4428.55i | −0.955225 | + | 0.551499i | −0.894700 | − | 0.446667i | \(-0.852611\pi\) |
−0.0605248 | + | 0.998167i | \(0.519277\pi\) | |||||||
\(402\) | 2167.83 | − | 7707.07i | 0.268959 | − | 0.956203i | ||||
\(403\) | 1944.90 | − | 3368.66i | 0.240403 | − | 0.416389i | ||||
\(404\) | −465.950 | −0.0573809 | ||||||||
\(405\) | 2180.35 | − | 3378.00i | 0.267513 | − | 0.414455i | ||||
\(406\) | 2372.07 | + | 8877.40i | 0.289960 | + | 1.08517i | ||||
\(407\) | −8799.70 | − | 5080.51i | −1.07171 | − | 0.618750i | ||||
\(408\) | −1242.76 | + | 4418.26i | −0.150799 | + | 0.536119i | ||||
\(409\) | −9564.59 | + | 5522.12i | −1.15633 | + | 0.667607i | −0.950421 | − | 0.310965i | \(-0.899348\pi\) |
−0.205907 | + | 0.978571i | \(0.566015\pi\) | |||||||
\(410\) | −1155.30 | + | 667.011i | −0.139161 | + | 0.0803447i | ||||
\(411\) | 967.604 | + | 991.891i | 0.116127 | + | 0.119042i | ||||
\(412\) | 4914.28 | + | 2837.26i | 0.587643 | + | 0.339276i | ||||
\(413\) | 3513.27 | + | 13148.3i | 0.418588 | + | 1.56655i | ||||
\(414\) | −2983.64 | − | 1822.67i | −0.354198 | − | 0.216375i | ||||
\(415\) | 6796.10 | 0.803873 | ||||||||
\(416\) | −1701.42 | + | 2946.94i | −0.200526 | + | 0.347321i | ||||
\(417\) | −2586.27 | + | 658.745i | −0.303717 | + | 0.0773594i | ||||
\(418\) | 5278.86 | − | 3047.75i | 0.617697 | − | 0.356628i | ||||
\(419\) | 4827.28 | + | 8361.09i | 0.562835 | + | 0.974859i | 0.997247 | + | 0.0741448i | \(0.0236227\pi\) |
−0.434412 | + | 0.900714i | \(0.643044\pi\) | |||||||
\(420\) | −1386.99 | + | 776.750i | −0.161138 | + | 0.0902417i | ||||
\(421\) | 1311.18 | − | 2271.02i | 0.151788 | − | 0.262905i | −0.780097 | − | 0.625659i | \(-0.784830\pi\) |
0.931885 | + | 0.362754i | \(0.118164\pi\) | |||||||
\(422\) | − | 550.320i | − | 0.0634814i | ||||||
\(423\) | 5953.36 | − | 3243.15i | 0.684308 | − | 0.372783i | ||||
\(424\) | 3939.91 | 0.451271 | ||||||||
\(425\) | 1698.21 | − | 2941.38i | 0.193824 | − | 0.335713i | ||||
\(426\) | −4804.53 | + | 4686.89i | −0.546433 | + | 0.533053i | ||||
\(427\) | 8784.90 | + | 8797.14i | 0.995623 | + | 0.997010i | ||||
\(428\) | −1316.32 | + | 759.976i | −0.148660 | + | 0.0858290i | ||||
\(429\) | 4670.23 | + | 1313.63i | 0.525597 | + | 0.147839i | ||||
\(430\) | −3719.75 | − | 2147.60i | −0.417168 | − | 0.240852i | ||||
\(431\) | − | 2142.38i | − | 0.239431i | −0.992808 | − | 0.119716i | \(-0.961802\pi\) | ||
0.992808 | − | 0.119716i | \(-0.0381983\pi\) | |||||||
\(432\) | −4249.16 | + | 970.817i | −0.473236 | + | 0.108121i | ||||
\(433\) | 8576.98i | 0.951925i | 0.879466 | + | 0.475962i | \(0.157900\pi\) | ||||
−0.879466 | + | 0.475962i | \(0.842100\pi\) | |||||||
\(434\) | −5821.70 | − | 1564.26i | −0.643895 | − | 0.173012i | ||||
\(435\) | 1720.92 | − | 6118.22i | 0.189682 | − | 0.674359i | ||||
\(436\) | −446.919 | − | 774.086i | −0.0490907 | − | 0.0850276i | ||||
\(437\) | −2258.02 | − | 3911.01i | −0.247176 | − | 0.428121i | ||||
\(438\) | −311.659 | + | 304.028i | −0.0339992 | + | 0.0331667i | ||||
\(439\) | 6408.01 | + | 3699.67i | 0.696669 | + | 0.402222i | 0.806106 | − | 0.591772i | \(-0.201571\pi\) |
−0.109437 | + | 0.993994i | \(0.534905\pi\) | |||||||
\(440\) | 4737.67 | 0.513317 | ||||||||
\(441\) | 4418.96 | + | 8138.73i | 0.477158 | + | 0.878817i | ||||
\(442\) | 2147.75 | 0.231126 | ||||||||
\(443\) | 12279.2 | + | 7089.41i | 1.31694 | + | 0.760334i | 0.983235 | − | 0.182345i | \(-0.0583687\pi\) |
0.333702 | + | 0.942679i | \(0.391702\pi\) | |||||||
\(444\) | 1117.70 | + | 4388.15i | 0.119468 | + | 0.469037i | ||||
\(445\) | −4151.92 | − | 7191.33i | −0.442292 | − | 0.766072i | ||||
\(446\) | −1228.84 | − | 2128.41i | −0.130464 | − | 0.225971i | ||||
\(447\) | 10672.7 | − | 2718.43i | 1.12931 | − | 0.287645i | ||||
\(448\) | 9538.24 | + | 2562.88i | 1.00589 | + | 0.270279i | ||||
\(449\) | 6800.58i | 0.714787i | 0.933954 | + | 0.357393i | \(0.116334\pi\) | ||||
−0.933954 | + | 0.357393i | \(0.883666\pi\) | |||||||
\(450\) | 5711.34 | + | 141.602i | 0.598300 | + | 0.0148338i | ||||
\(451\) | 3775.90i | 0.394236i | ||||||||
\(452\) | −647.477 | − | 373.821i | −0.0673778 | − | 0.0389006i | ||||
\(453\) | −8494.20 | + | 8286.21i | −0.880998 | + | 0.859426i | ||||
\(454\) | 8338.50 | − | 4814.23i | 0.861994 | − | 0.497672i | ||||
\(455\) | 1929.60 | + | 1932.29i | 0.198816 | + | 0.199093i | ||||
\(456\) | −9599.50 | − | 2700.13i | −0.985829 | − | 0.277292i | ||||
\(457\) | 1885.91 | − | 3266.49i | 0.193040 | − | 0.334355i | −0.753216 | − | 0.657773i | \(-0.771499\pi\) |
0.946256 | + | 0.323418i | \(0.104832\pi\) | |||||||
\(458\) | 6397.41 | 0.652688 | ||||||||
\(459\) | −3427.47 | − | 3692.33i | −0.348542 | − | 0.375475i | ||||
\(460\) | − | 956.166i | − | 0.0969162i | ||||||
\(461\) | −7807.12 | + | 13522.3i | −0.788750 | + | 1.36616i | 0.137983 | + | 0.990435i | \(0.455938\pi\) |
−0.926733 | + | 0.375721i | \(0.877395\pi\) | |||||||
\(462\) | 98.4164 | − | 7517.90i | 0.00991070 | − | 0.757065i | ||||
\(463\) | −4055.66 | − | 7024.62i | −0.407090 | − | 0.705101i | 0.587472 | − | 0.809244i | \(-0.300123\pi\) |
−0.994562 | + | 0.104144i | \(0.966790\pi\) | |||||||
\(464\) | −5967.01 | + | 3445.06i | −0.597008 | + | 0.344683i | ||||
\(465\) | 2911.52 | + | 2984.61i | 0.290363 | + | 0.297651i | ||||
\(466\) | −2524.23 | + | 4372.09i | −0.250928 | + | 0.434620i | ||||
\(467\) | 6607.80 | 0.654759 | 0.327380 | − | 0.944893i | \(-0.393834\pi\) | ||||
0.327380 | + | 0.944893i | \(0.393834\pi\) | |||||||
\(468\) | −1034.29 | − | 1898.61i | −0.102158 | − | 0.187529i | ||||
\(469\) | −3292.76 | − | 12323.1i | −0.324191 | − | 1.21328i | ||||
\(470\) | −2682.94 | − | 1549.00i | −0.263309 | − | 0.152021i | ||||
\(471\) | −18485.0 | + | 4708.29i | −1.80837 | + | 0.460608i | ||||
\(472\) | −15654.0 | + | 9037.84i | −1.52655 | + | 0.881357i | ||||
\(473\) | −10528.6 | + | 6078.71i | −1.02348 | + | 0.590908i | ||||
\(474\) | 9642.74 | − | 2456.09i | 0.934400 | − | 0.238000i | ||||
\(475\) | 6390.70 | + | 3689.67i | 0.617317 | + | 0.356408i | ||||
\(476\) | 514.213 | + | 1924.43i | 0.0495145 | + | 0.185307i | ||||
\(477\) | −2254.50 | + | 3690.53i | −0.216408 | + | 0.354251i | ||||
\(478\) | 3531.53 | 0.337925 | ||||||||
\(479\) | 4138.13 | − | 7167.45i | 0.394731 | − | 0.683694i | −0.598336 | − | 0.801245i | \(-0.704171\pi\) |
0.993067 | + | 0.117552i | \(0.0375045\pi\) | |||||||
\(480\) | −2547.03 | − | 2610.97i | −0.242199 | − | 0.248279i | ||||
\(481\) | 6736.57 | − | 3889.36i | 0.638588 | − | 0.368689i | ||||
\(482\) | −1612.33 | − | 2792.64i | −0.152364 | − | 0.263903i | ||||
\(483\) | −5569.87 | − | 72.9149i | −0.524716 | − | 0.00686903i | ||||
\(484\) | −166.819 | + | 288.940i | −0.0156667 | + | 0.0271356i | ||||
\(485\) | − | 6383.30i | − | 0.597630i | ||||||
\(486\) | 2696.04 | − | 8034.00i | 0.251635 | − | 0.749855i | ||||
\(487\) | 229.243 | 0.0213306 | 0.0106653 | − | 0.999943i | \(-0.496605\pi\) | ||||
0.0106653 | + | 0.999943i | \(0.496605\pi\) | |||||||
\(488\) | −8256.08 | + | 14299.9i | −0.765851 | + | 1.32649i | ||||
\(489\) | −849.479 | − | 238.940i | −0.0785578 | − | 0.0220966i | ||||
\(490\) | 2121.10 | − | 3662.08i | 0.195555 | − | 0.337624i | ||||
\(491\) | 17923.6 | − | 10348.2i | 1.64742 | − | 0.951138i | 0.669326 | − | 0.742969i | \(-0.266583\pi\) |
0.978093 | − | 0.208169i | \(-0.0667505\pi\) | |||||||
\(492\) | 1204.53 | − | 1175.03i | 0.110375 | − | 0.107672i | ||||
\(493\) | −6896.96 | − | 3981.96i | −0.630068 | − | 0.363770i | ||||
\(494\) | 4666.38i | 0.425001i | ||||||||
\(495\) | −2711.00 | + | 4437.80i | −0.246162 | + | 0.402958i | ||||
\(496\) | − | 4520.14i | − | 0.409195i | ||||||
\(497\) | −2774.88 | + | 10327.2i | −0.250443 | + | 0.932070i | ||||
\(498\) | 13881.2 | − | 3535.67i | 1.24906 | − | 0.318147i | ||||
\(499\) | 6552.36 | + | 11349.0i | 0.587824 | + | 1.01814i | 0.994517 | + | 0.104576i | \(0.0333485\pi\) |
−0.406693 | + | 0.913565i | \(0.633318\pi\) | |||||||
\(500\) | 1813.63 | + | 3141.30i | 0.162216 | + | 0.280966i | ||||
\(501\) | −559.997 | − | 2198.58i | −0.0499377 | − | 0.196058i | ||||
\(502\) | −5688.08 | − | 3284.02i | −0.505720 | − | 0.291978i | ||||
\(503\) | −7415.97 | −0.657379 | −0.328690 | − | 0.944438i | \(-0.606607\pi\) | ||||
−0.328690 | + | 0.944438i | \(0.606607\pi\) | |||||||
\(504\) | −8916.26 | + | 8473.01i | −0.788019 | + | 0.748845i | ||||
\(505\) | −857.975 | −0.0756028 | ||||||||
\(506\) | 3916.41 | + | 2261.14i | 0.344082 | + | 0.198656i | ||||
\(507\) | 5513.17 | − | 5378.17i | 0.482936 | − | 0.471110i | ||||
\(508\) | −2908.68 | − | 5037.98i | −0.254039 | − | 0.440008i | ||||
\(509\) | −10536.9 | − | 18250.5i | −0.917565 | − | 1.58927i | −0.803103 | − | 0.595841i | \(-0.796819\pi\) |
−0.114462 | − | 0.993428i | \(-0.536514\pi\) | |||||||
\(510\) | −623.366 | + | 2216.19i | −0.0541237 | + | 0.192421i | ||||
\(511\) | −180.000 | + | 669.903i | −0.0155826 | + | 0.0579936i | ||||
\(512\) | 10067.8i | 0.869021i | ||||||||
\(513\) | 8022.27 | − | 7446.83i | 0.690433 | − | 0.640908i | ||||
\(514\) | 16277.7i | 1.39684i | ||||||||
\(515\) | 9048.89 | + | 5224.38i | 0.774255 | + | 0.447017i | ||||
\(516\) | 5215.56 | + | 1467.02i | 0.444966 | + | 0.125159i | ||||
\(517\) | −7593.98 | + | 4384.39i | −0.646002 | + | 0.372969i | ||||
\(518\) | −8518.26 | − | 8530.13i | −0.722531 | − | 0.723537i | ||||
\(519\) | −6157.48 | + | 6006.71i | −0.520777 | + | 0.508026i | ||||
\(520\) | −1813.45 | + | 3140.99i | −0.152933 | + | 0.264887i | ||||
\(521\) | 19991.7 | 1.68110 | 0.840548 | − | 0.541736i | \(-0.182233\pi\) | ||||
0.840548 | + | 0.541736i | \(0.182233\pi\) | |||||||
\(522\) | 332.030 | − | 13392.0i | 0.0278401 | − | 1.12289i | ||||
\(523\) | − | 3604.15i | − | 0.301336i | −0.988584 | − | 0.150668i | \(-0.951858\pi\) | ||
0.988584 | − | 0.150668i | \(-0.0481424\pi\) | |||||||
\(524\) | −39.7286 | + | 68.8119i | −0.00331212 | + | 0.00573676i | ||||
\(525\) | 7941.56 | − | 4447.48i | 0.660187 | − | 0.369722i | ||||
\(526\) | 7531.01 | + | 13044.1i | 0.624273 | + | 1.08127i | ||||
\(527\) | 4524.64 | − | 2612.30i | 0.373997 | − | 0.215927i | ||||
\(528\) | 5463.22 | − | 1391.53i | 0.450296 | − | 0.114694i | ||||
\(529\) | −4408.26 | + | 7635.34i | −0.362313 | + | 0.627545i | ||||
\(530\) | 1976.25 | 0.161967 | ||||||||
\(531\) | 491.769 | − | 19834.8i | 0.0401901 | − | 1.62101i | ||||
\(532\) | −4181.18 | + | 1117.22i | −0.340746 | + | 0.0910485i | ||||
\(533\) | −2503.35 | − | 1445.31i | −0.203438 | − | 0.117455i | ||||
\(534\) | −12221.7 | − | 12528.5i | −0.990423 | − | 1.01528i | ||||
\(535\) | −2423.80 | + | 1399.38i | −0.195869 | + | 0.113085i | ||||
\(536\) | 14671.5 | − | 8470.59i | 1.18230 | − | 0.682601i | ||||
\(537\) | −6395.05 | + | 22735.7i | −0.513905 | + | 1.82703i | ||||
\(538\) | −14533.3 | − | 8390.80i | −1.16464 | − | 0.672404i | ||||
\(539\) | −5974.83 | − | 10382.1i | −0.477466 | − | 0.829660i | ||||
\(540\) | 2259.31 | − | 516.191i | 0.180047 | − | 0.0411358i | ||||
\(541\) | −13211.0 | −1.04988 | −0.524939 | − | 0.851140i | \(-0.675912\pi\) | ||||
−0.524939 | + | 0.851140i | \(0.675912\pi\) | |||||||
\(542\) | −5169.93 | + | 8954.58i | −0.409719 | + | 0.709654i | ||||
\(543\) | 97.7531 | − | 347.532i | 0.00772557 | − | 0.0274660i | ||||
\(544\) | −3958.20 | + | 2285.27i | −0.311961 | + | 0.180111i | ||||
\(545\) | −822.933 | − | 1425.36i | −0.0646799 | − | 0.112029i | ||||
\(546\) | 4946.56 | + | 2942.89i | 0.387716 | + | 0.230667i | ||||
\(547\) | −8858.54 | + | 15343.4i | −0.692439 | + | 1.19934i | 0.278598 | + | 0.960408i | \(0.410130\pi\) |
−0.971037 | + | 0.238931i | \(0.923203\pi\) | |||||||
\(548\) | 798.735i | 0.0622633i | ||||||||
\(549\) | −8670.52 | − | 15916.3i | −0.674042 | − | 1.23732i | ||||
\(550\) | −7389.55 | −0.572893 | ||||||||
\(551\) | 8651.56 | − | 14984.9i | 0.668909 | − | 1.15858i | ||||
\(552\) | −1826.10 | − | 7169.39i | −0.140805 | − | 0.552807i | ||||
\(553\) | 11217.8 | − | 11202.2i | 0.862621 | − | 0.861421i | ||||
\(554\) | 3806.52 | − | 2197.70i | 0.291920 | − | 0.168540i | ||||
\(555\) | 2058.07 | + | 8080.11i | 0.157406 | + | 0.617984i | ||||
\(556\) | −1332.28 | − | 769.190i | −0.101621 | − | 0.0586707i | ||||
\(557\) | − | 13013.3i | − | 0.989933i | −0.868912 | − | 0.494966i | \(-0.835180\pi\) | ||
0.868912 | − | 0.494966i | \(-0.164820\pi\) | |||||||
\(558\) | 7499.62 | + | 4581.43i | 0.568968 | + | 0.347576i | ||||
\(559\) | − | 9307.05i | − | 0.704198i | ||||||
\(560\) | 3064.60 | + | 823.445i | 0.231256 | + | 0.0621373i | ||||
\(561\) | 4550.24 | + | 4664.46i | 0.342445 | + | 0.351040i | ||||
\(562\) | 2198.63 | + | 3808.14i | 0.165024 | + | 0.285831i | ||||
\(563\) | 7866.96 | + | 13626.0i | 0.588904 | + | 1.02001i | 0.994376 | + | 0.105904i | \(0.0337736\pi\) |
−0.405473 | + | 0.914107i | \(0.632893\pi\) | |||||||
\(564\) | 3761.82 | + | 1058.12i | 0.280854 | + | 0.0789979i | ||||
\(565\) | −1192.23 | − | 688.335i | −0.0887744 | − | 0.0512539i | ||||
\(566\) | 11937.8 | 0.886544 | ||||||||
\(567\) | −2834.63 | − | 13200.3i | −0.209953 | − | 0.977711i | ||||
\(568\) | −14202.7 | −1.04917 | ||||||||
\(569\) | 5395.51 | + | 3115.10i | 0.397524 | + | 0.229511i | 0.685415 | − | 0.728152i | \(-0.259621\pi\) |
−0.287891 | + | 0.957663i | \(0.592954\pi\) | |||||||
\(570\) | −4815.09 | − | 1354.38i | −0.353828 | − | 0.0995241i | ||||
\(571\) | 1182.19 | + | 2047.62i | 0.0866432 | + | 0.150070i | 0.906090 | − | 0.423084i | \(-0.139053\pi\) |
−0.819447 | + | 0.573155i | \(0.805719\pi\) | |||||||
\(572\) | 1398.25 | + | 2421.83i | 0.102209 | + | 0.177031i | ||||
\(573\) | −5097.17 | − | 5225.11i | −0.371618 | − | 0.380946i | ||||
\(574\) | −1162.45 | + | 4326.28i | −0.0845293 | + | 0.314592i | ||||
\(575\) | 5474.78i | 0.397068i | ||||||||
\(576\) | −12287.3 | − | 7506.19i | −0.888841 | − | 0.542983i | ||||
\(577\) | − | 4194.43i | − | 0.302628i | −0.988486 | − | 0.151314i | \(-0.951650\pi\) | ||
0.988486 | − | 0.151314i | \(-0.0483505\pi\) | |||||||
\(578\) | −7020.30 | − | 4053.17i | −0.505201 | − | 0.291678i | ||||
\(579\) | 2965.36 | + | 11642.2i | 0.212843 | + | 0.835635i | ||||
\(580\) | 3172.71 | − | 1831.77i | 0.227137 | − | 0.131138i | ||||
\(581\) | 16148.6 | − | 16126.2i | 1.15311 | − | 1.15151i | ||||
\(582\) | −3320.91 | − | 13038.1i | −0.236523 | − | 0.928602i | ||||
\(583\) | 2796.85 | − | 4844.29i | 0.198686 | − | 0.344134i | ||||
\(584\) | −921.295 | −0.0652799 | ||||||||
\(585\) | −1904.48 | − | 3496.01i | −0.134599 | − | 0.247081i | ||||
\(586\) | − | 4619.69i | − | 0.325662i | ||||||
\(587\) | −6703.36 | + | 11610.6i | −0.471341 | + | 0.816387i | −0.999463 | − | 0.0327817i | \(-0.989563\pi\) |
0.528121 | + | 0.849169i | \(0.322897\pi\) | |||||||
\(588\) | −1452.59 | + | 5136.81i | −0.101877 | + | 0.360269i | ||||
\(589\) | 5675.71 | + | 9830.62i | 0.397052 | + | 0.687714i | ||||
\(590\) | −7852.01 | + | 4533.36i | −0.547902 | + | 0.316332i | ||||
\(591\) | 2190.26 | − | 7786.80i | 0.152445 | − | 0.541973i | ||||
\(592\) | 4519.64 | − | 7828.24i | 0.313777 | − | 0.543478i | ||||
\(593\) | −4672.62 | −0.323577 | −0.161789 | − | 0.986825i | \(-0.551726\pi\) | ||||
−0.161789 | + | 0.986825i | \(0.551726\pi\) | |||||||
\(594\) | −3228.53 | + | 10474.7i | −0.223010 | + | 0.723542i | ||||
\(595\) | 946.845 | + | 3543.54i | 0.0652384 | + | 0.244153i | ||||
\(596\) | 5497.87 | + | 3174.20i | 0.377855 | + | 0.218155i | ||||
\(597\) | −1671.29 | + | 5941.79i | −0.114575 | + | 0.407339i | ||||
\(598\) | −2998.19 | + | 1731.01i | −0.205025 | + | 0.118371i | ||||
\(599\) | 5611.71 | − | 3239.92i | 0.382785 | − | 0.221001i | −0.296244 | − | 0.955112i | \(-0.595734\pi\) |
0.679029 | + | 0.734111i | \(0.262401\pi\) | |||||||
\(600\) | 8441.64 | + | 8653.53i | 0.574381 | + | 0.588798i | ||||
\(601\) | 2243.61 | + | 1295.35i | 0.152277 | + | 0.0879174i | 0.574203 | − | 0.818713i | \(-0.305312\pi\) |
−0.421925 | + | 0.906631i | \(0.638646\pi\) | |||||||
\(602\) | −13934.7 | + | 3723.39i | −0.943415 | + | 0.252083i | ||||
\(603\) | −460.904 | + | 18589.9i | −0.0311268 | + | 1.25546i | ||||
\(604\) | −6840.08 | −0.460793 | ||||||||
\(605\) | −307.172 | + | 532.038i | −0.0206419 | + | 0.0357528i | ||||
\(606\) | −1752.44 | + | 446.362i | −0.117472 | + | 0.0299211i | ||||
\(607\) | 1869.60 | − | 1079.41i | 0.125016 | − | 0.0721781i | −0.436188 | − | 0.899856i | \(-0.643672\pi\) |
0.561204 | + | 0.827678i | \(0.310338\pi\) | |||||||
\(608\) | −4965.18 | − | 8599.94i | −0.331192 | − | 0.573641i | ||||
\(609\) | −10428.5 | − | 18621.4i | −0.693897 | − | 1.23904i | ||||
\(610\) | −4141.23 | + | 7172.82i | −0.274875 | + | 0.476097i | ||||
\(611\) | − | 6712.89i | − | 0.444476i | ||||||
\(612\) | 71.9768 | − | 2903.09i | 0.00475407 | − | 0.191749i | ||||
\(613\) | 6333.20 | 0.417285 | 0.208642 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208642 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(614\) | −442.510 | + | 766.449i | −0.0290851 | + | 0.0503768i | ||||
\(615\) | 2217.95 | − | 2163.64i | 0.145425 | − | 0.141864i | ||||
\(616\) | 11257.5 | − | 11241.8i | 0.736325 | − | 0.735301i | ||||
\(617\) | 1802.84 | − | 1040.87i | 0.117633 | − | 0.0679157i | −0.440029 | − | 0.897984i | \(-0.645032\pi\) |
0.557662 | + | 0.830068i | \(0.311698\pi\) | |||||||
\(618\) | 21200.6 | + | 5963.27i | 1.37996 | + | 0.388152i | ||||
\(619\) | −20384.1 | − | 11768.8i | −1.32360 | − | 0.764179i | −0.339296 | − | 0.940680i | \(-0.610189\pi\) |
−0.984301 | + | 0.176501i | \(0.943522\pi\) | |||||||
\(620\) | 2403.40i | 0.155682i | ||||||||
\(621\) | 7760.54 | + | 2391.96i | 0.501481 | + | 0.154567i | ||||
\(622\) | 14117.0i | 0.910031i | ||||||||
\(623\) | −26929.7 | − | 7235.88i | −1.73180 | − | 0.465328i | ||||
\(624\) | −1168.61 | + | 4154.66i | −0.0749711 | + | 0.266537i | ||||
\(625\) | −2571.92 | − | 4454.69i | −0.164603 | − | 0.285100i | ||||
\(626\) | 11350.7 | + | 19660.0i | 0.724704 | + | 1.25522i | ||||
\(627\) | −10134.4 | + | 9886.25i | −0.645501 | + | 0.629695i | ||||
\(628\) | −9522.27 | − | 5497.68i | −0.605063 | − | 0.349333i | ||||
\(629\) | 10448.0 | 0.662306 | ||||||||
\(630\) | −4472.38 | + | 4250.04i | −0.282831 | + | 0.268771i | ||||
\(631\) | 13465.2 | 0.849510 | 0.424755 | − | 0.905308i | \(-0.360360\pi\) | ||||
0.424755 | + | 0.905308i | \(0.360360\pi\) | |||||||
\(632\) | 18234.8 | + | 10527.9i | 1.14769 | + | 0.662620i | ||||
\(633\) | 315.498 | + | 1238.66i | 0.0198103 | + | 0.0777763i | ||||
\(634\) | 1985.30 | + | 3438.64i | 0.124363 | + | 0.215404i | ||||
\(635\) | −5355.89 | − | 9276.67i | −0.334712 | − | 0.579738i | ||||
\(636\) | −2415.70 | + | 615.300i | −0.150611 | + | 0.0383620i | ||||
\(637\) | 9170.11 | + | 12.7674i | 0.570382 | + | 0.000794135i | ||||
\(638\) | 17327.0i | 1.07521i | ||||||||
\(639\) | 8127.08 | − | 13303.7i | 0.503133 | − | 0.823610i | ||||
\(640\) | 964.023i | 0.0595412i | ||||||||
\(641\) | −2697.97 | − | 1557.67i | −0.166246 | − | 0.0959819i | 0.414569 | − | 0.910018i | \(-0.363932\pi\) |
−0.580814 | + | 0.814036i | \(0.697266\pi\) | |||||||
\(642\) | −4222.65 | + | 4119.26i | −0.259587 | + | 0.253231i | ||||
\(643\) | −138.508 | + | 79.9675i | −0.00849489 | + | 0.00490452i | −0.504241 | − | 0.863563i | \(-0.668228\pi\) |
0.495747 | + | 0.868467i | \(0.334894\pi\) | |||||||
\(644\) | −2268.85 | − | 2272.01i | −0.138828 | − | 0.139021i | ||||
\(645\) | 9603.66 | + | 2701.30i | 0.586269 | + | 0.164905i | ||||
\(646\) | −3133.84 | + | 5427.97i | −0.190866 | + | 0.330589i | ||||
\(647\) | 11705.0 | 0.711239 | 0.355619 | − | 0.934631i | \(-0.384270\pi\) | ||||
0.355619 | + | 0.934631i | \(0.384270\pi\) | |||||||
\(648\) | 15954.6 | − | 8185.31i | 0.967218 | − | 0.496218i | ||||
\(649\) | 25663.1i | 1.55218i | ||||||||
\(650\) | 2828.52 | − | 4899.13i | 0.170682 | − | 0.295631i | ||||
\(651\) | 14000.3 | + | 183.277i | 0.842880 | + | 0.0110341i | ||||
\(652\) | −254.330 | − | 440.512i | −0.0152766 | − | 0.0264598i | ||||
\(653\) | −23280.1 | + | 13440.8i | −1.39513 | + | 0.805479i | −0.993878 | − | 0.110487i | \(-0.964759\pi\) |
−0.401254 | + | 0.915967i | \(0.631425\pi\) | |||||||
\(654\) | −2422.41 | − | 2483.22i | −0.144838 | − | 0.148473i | ||||
\(655\) | −73.1541 | + | 126.707i | −0.00436392 | + | 0.00755853i | ||||
\(656\) | −3359.06 | −0.199923 | ||||||||
\(657\) | 527.185 | − | 862.981i | 0.0313051 | − | 0.0512452i | ||||
\(658\) | −10050.7 | + | 2685.57i | −0.595465 | + | 0.159110i | ||||
\(659\) | −7188.85 | − | 4150.48i | −0.424943 | − | 0.245341i | 0.272247 | − | 0.962227i | \(-0.412233\pi\) |
−0.697190 | + | 0.716886i | \(0.745567\pi\) | |||||||
\(660\) | −2904.84 | + | 739.888i | −0.171319 | + | 0.0436365i | ||||
\(661\) | −1248.35 | + | 720.734i | −0.0734571 | + | 0.0424105i | −0.536279 | − | 0.844041i | \(-0.680170\pi\) |
0.462822 | + | 0.886451i | \(0.346837\pi\) | |||||||
\(662\) | −9290.83 | + | 5364.06i | −0.545466 | + | 0.314925i | ||||
\(663\) | −4834.16 | + | 1231.30i | −0.283172 | + | 0.0721264i | ||||
\(664\) | 26250.0 | + | 15155.4i | 1.53418 | + | 0.885760i | ||||
\(665\) | −7699.00 | + | 2057.20i | −0.448954 | + | 0.119962i | ||||
\(666\) | 8407.36 | + | 15433.2i | 0.489157 | + | 0.897932i | ||||
\(667\) | 12837.3 | 0.745219 | ||||||||
\(668\) | 653.886 | − | 1132.56i | 0.0378736 | − | 0.0655991i | ||||
\(669\) | 3986.08 | + | 4086.13i | 0.230360 | + | 0.236142i | ||||
\(670\) | 7359.19 | − | 4248.83i | 0.424344 | − | 0.244995i | ||||
\(671\) | 11721.6 | + | 20302.4i | 0.674378 | + | 1.16806i | ||||
\(672\) | −12247.6 | − | 160.333i | −0.703069 | − | 0.00920384i | ||||
\(673\) | 8012.16 | − | 13877.5i | 0.458909 | − | 0.794854i | −0.539994 | − | 0.841669i | \(-0.681574\pi\) |
0.998904 | + | 0.0468146i | \(0.0149070\pi\) | |||||||
\(674\) | − | 16532.1i | − | 0.944796i | ||||||
\(675\) | −12936.3 | + | 2955.59i | −0.737657 | + | 0.168534i | ||||
\(676\) | 4439.56 | 0.252592 | ||||||||
\(677\) | 13755.2 | − | 23824.7i | 0.780880 | − | 1.35252i | −0.150549 | − | 0.988602i | \(-0.548104\pi\) |
0.931430 | − | 0.363922i | \(-0.118562\pi\) | |||||||
\(678\) | −2793.28 | − | 785.687i | −0.158223 | − | 0.0445046i | ||||
\(679\) | −15146.7 | − | 15167.8i | −0.856076 | − | 0.857269i | ||||
\(680\) | −4218.83 | + | 2435.75i | −0.237919 | + | 0.137363i | ||||
\(681\) | −16008.3 | + | 15616.4i | −0.900794 | + | 0.878737i | ||||
\(682\) | −9844.21 | − | 5683.56i | −0.552719 | − | 0.319112i | ||||
\(683\) | 2208.68i | 0.123738i | 0.998084 | + | 0.0618688i | \(0.0197060\pi\) | ||||
−0.998084 | + | 0.0618688i | \(0.980294\pi\) | |||||||
\(684\) | 6307.50 | + | 156.383i | 0.352592 | + | 0.00874190i | ||||
\(685\) | 1470.75i | 0.0820357i | ||||||||
\(686\) | −3649.49 | − | 13734.8i | −0.203117 | − | 0.764426i | ||||
\(687\) | −14399.3 | + | 3667.63i | −0.799662 | + | 0.203681i | ||||
\(688\) | −5407.64 | − | 9366.31i | −0.299658 | − | 0.519022i | ||||
\(689\) | 2141.12 | + | 3708.52i | 0.118389 | + | 0.205056i | ||||
\(690\) | −915.970 | − | 3596.15i | −0.0505368 | − | 0.198410i | ||||
\(691\) | 20410.4 | + | 11784.0i | 1.12366 | + | 0.648746i | 0.942333 | − | 0.334676i | \(-0.108627\pi\) |
0.181328 | + | 0.983423i | \(0.441960\pi\) | |||||||
\(692\) | −4958.40 | −0.272385 | ||||||||
\(693\) | 4088.49 | + | 16977.7i | 0.224111 | + | 0.930636i | ||||
\(694\) | 4043.48 | 0.221165 | ||||||||
\(695\) | −2453.18 | − | 1416.35i | −0.133891 | − | 0.0773022i | ||||
\(696\) | 20290.8 | − | 19794.0i | 1.10506 | − | 1.07800i | ||||
\(697\) | −1941.28 | − | 3362.40i | −0.105497 | − | 0.182726i | ||||
\(698\) | −6580.02 | − | 11396.9i | −0.356816 | − | 0.618023i | ||||
\(699\) | 3175.03 | − | 11287.9i | 0.171803 | − | 0.610795i | ||||
\(700\) | 5066.93 | + | 1361.46i | 0.273589 | + | 0.0735120i | ||||
\(701\) | 18383.9i | 0.990516i | 0.868746 | + | 0.495258i | \(0.164926\pi\) | ||||
−0.868746 | + | 0.495258i | \(0.835074\pi\) | |||||||
\(702\) | −5708.77 | − | 6149.90i | −0.306928 | − | 0.330645i | ||||
\(703\) | 22700.3i | 1.21786i | ||||||||
\(704\) | 16128.7 | + | 9311.91i | 0.863456 | + | 0.498517i | ||||
\(705\) | 6926.82 | + | 1948.36i | 0.370042 | + | 0.104085i | ||||
\(706\) | −4636.43 | + | 2676.85i | −0.247159 | + | 0.142697i | ||||
\(707\) | −2038.69 | + | 2035.85i | −0.108448 | + | 0.108297i | ||||
\(708\) | 8186.60 | − | 7986.15i | 0.434564 | − | 0.423923i | ||||
\(709\) | 11608.4 | − | 20106.3i | 0.614895 | − | 1.06503i | −0.375508 | − | 0.926819i | \(-0.622532\pi\) |
0.990403 | − | 0.138211i | \(-0.0441351\pi\) | |||||||
\(710\) | −7124.03 | −0.376564 | ||||||||
\(711\) | −20295.8 | + | 11056.3i | −1.07054 | + | 0.583186i | ||||
\(712\) | − | 37035.5i | − | 1.94939i | ||||||
\(713\) | −4210.84 | + | 7293.39i | −0.221174 | + | 0.383085i | ||||
\(714\) | 3777.49 | + | 6745.19i | 0.197996 | + | 0.353547i | ||||
\(715\) | 2574.65 | + | 4459.43i | 0.134667 | + | 0.233249i | ||||
\(716\) | −11790.0 | + | 6806.95i | −0.615381 | + | 0.355290i | ||||
\(717\) | −7948.77 | + | 2024.62i | −0.414020 | + | 0.105454i | ||||
\(718\) | 12000.6 | − | 20785.6i | 0.623756 | − | 1.08038i | ||||
\(719\) | −24589.3 | −1.27542 | −0.637709 | − | 0.770278i | \(-0.720118\pi\) | ||||
−0.637709 | + | 0.770278i | \(0.720118\pi\) | |||||||
\(720\) | −3947.88 | − | 2411.71i | −0.204346 | − | 0.124832i | ||||
\(721\) | 33898.3 | − | 9057.74i | 1.75096 | − | 0.467861i | ||||
\(722\) | 1495.53 | + | 863.443i | 0.0770883 | + | 0.0445070i | ||||
\(723\) | 5230.05 | + | 5361.33i | 0.269029 | + | 0.275781i | ||||
\(724\) | 180.219 | − | 104.049i | 0.00925107 | − | 0.00534111i | ||||
\(725\) | −18166.2 | + | 10488.3i | −0.930586 | + | 0.537274i | ||||
\(726\) | −350.616 | + | 1246.51i | −0.0179237 | + | 0.0637223i | ||||
\(727\) | −14219.3 | − | 8209.54i | −0.725400 | − | 0.418810i | 0.0913367 | − | 0.995820i | \(-0.470886\pi\) |
−0.816737 | + | 0.577010i | \(0.804219\pi\) | |||||||
\(728\) | 3144.06 | + | 11766.6i | 0.160064 | + | 0.599035i | ||||
\(729\) | −1462.36 | + | 19628.6i | −0.0742958 | + | 0.997236i | ||||
\(730\) | −462.119 | −0.0234299 | ||||||||
\(731\) | 6250.41 | − | 10826.0i | 0.316252 | − | 0.547764i | ||||
\(732\) | 2828.87 | − | 10057.2i | 0.142839 | − | 0.507821i | ||||
\(733\) | −1654.43 | + | 955.186i | −0.0833667 | + | 0.0481318i | −0.541104 | − | 0.840956i | \(-0.681993\pi\) |
0.457737 | + | 0.889088i | \(0.348660\pi\) | |||||||
\(734\) | 6126.30 | + | 10611.1i | 0.308073 | + | 0.533599i | ||||
\(735\) | −2674.73 | + | 9458.65i | −0.134230 | + | 0.474677i | ||||
\(736\) | 3683.69 | − | 6380.34i | 0.184487 | − | 0.319541i | ||||
\(737\) | − | 24052.3i | − | 1.20214i | ||||||
\(738\) | 3404.60 | − | 5573.20i | 0.169817 | − | 0.277984i | ||||
\(739\) | 10538.9 | 0.524601 | 0.262300 | − | 0.964986i | \(-0.415519\pi\) | ||||
0.262300 | + | 0.964986i | \(0.415519\pi\) | |||||||
\(740\) | −2403.13 | + | 4162.34i | −0.119379 | + | 0.206771i | ||||
\(741\) | −2675.23 | − | 10503.1i | −0.132628 | − | 0.520704i | ||||
\(742\) | 4695.89 | − | 4689.36i | 0.232334 | − | 0.232010i | ||||
\(743\) | −9283.92 | + | 5360.07i | −0.458404 | + | 0.264660i | −0.711373 | − | 0.702815i | \(-0.751926\pi\) |
0.252969 | + | 0.967474i | \(0.418593\pi\) | |||||||
\(744\) | 4590.06 | + | 18020.8i | 0.226182 | + | 0.888004i | ||||
\(745\) | 10123.5 | + | 5844.80i | 0.497847 | + | 0.287432i | ||||
\(746\) | − | 27080.1i | − | 1.32905i | ||||||
\(747\) | −29217.0 | + | 15916.2i | −1.43105 | + | 0.779577i | ||||
\(748\) | 3756.12i | 0.183606i | ||||||||
\(749\) | −2438.81 | + | 9076.47i | −0.118975 | + | 0.442787i | ||||
\(750\) | 9830.33 | + | 10077.1i | 0.478604 | + | 0.490617i | ||||
\(751\) | 16974.5 | + | 29400.7i | 0.824779 | + | 1.42856i | 0.902088 | + | 0.431552i | \(0.142034\pi\) |
−0.0773094 | + | 0.997007i | \(0.524633\pi\) | |||||||
\(752\) | −3900.37 | − | 6755.63i | −0.189138 | − | 0.327597i | ||||
\(753\) | 14685.5 | + | 4130.71i | 0.710716 | + | 0.199909i | ||||
\(754\) | −11487.5 | − | 6632.32i | −0.554841 | − | 0.320338i | ||||
\(755\) | −12595.0 | −0.607123 | ||||||||
\(756\) | 4143.65 | − | 6587.59i | 0.199343 | − | 0.316916i | ||||
\(757\) | −4201.14 | −0.201708 | −0.100854 | − | 0.994901i | \(-0.532158\pi\) | ||||
−0.100854 | + | 0.994901i | \(0.532158\pi\) | |||||||
\(758\) | 4.52407 | + | 2.61197i | 0.000216783 | + | 0.000125160i | ||||
\(759\) | −10111.4 | − | 2844.11i | −0.483557 | − | 0.136014i | ||||
\(760\) | −5292.11 | − | 9166.21i | −0.252586 | − | 0.437491i | ||||
\(761\) | −1844.61 | − | 3194.96i | −0.0878674 | − | 0.152191i | 0.818742 | − | 0.574161i | \(-0.194672\pi\) |
−0.906609 | + | 0.421971i | \(0.861339\pi\) | |||||||
\(762\) | −15765.8 | − | 16161.5i | −0.749519 | − | 0.768332i | ||||
\(763\) | −5337.60 | − | 1434.19i | −0.253256 | − | 0.0680487i | ||||
\(764\) | − | 4207.60i | − | 0.199248i | ||||||
\(765\) | 132.534 | − | 5345.59i | 0.00626377 | − | 0.252641i | ||||
\(766\) | − | 18338.2i | − | 0.864994i | ||||||
\(767\) | −17014.1 | − | 9823.11i | −0.800971 | − | 0.462441i | ||||
\(768\) | −4970.19 | − | 19513.3i | −0.233524 | − | 0.916828i | ||||
\(769\) | −2527.18 | + | 1459.07i | −0.118508 | + | 0.0684204i | −0.558082 | − | 0.829786i | \(-0.688463\pi\) |
0.439574 | + | 0.898206i | \(0.355129\pi\) | |||||||
\(770\) | 5646.72 | − | 5638.87i | 0.264278 | − | 0.263910i | ||||
\(771\) | −9331.97 | − | 36637.8i | −0.435905 | − | 1.71139i | ||||
\(772\) | −3462.54 | + | 5997.29i | −0.161424 | + | 0.279595i | ||||
\(773\) | 6902.85 | 0.321188 | 0.160594 | − | 0.987021i | \(-0.448659\pi\) | ||||
0.160594 | + | 0.987021i | \(0.448659\pi\) | |||||||
\(774\) | 21021.1 | + | 521.181i | 0.976213 | + | 0.0242034i | ||||
\(775\) | − | 13761.3i | − | 0.637832i | ||||||
\(776\) | 14234.9 | − | 24655.5i | 0.658509 | − | 1.14057i | ||||
\(777\) | 24063.3 | + | 14316.1i | 1.11102 | + | 0.660989i | ||||
\(778\) | −5796.31 | − | 10039.5i | −0.267105 | − | 0.462639i | ||||
\(779\) | 7305.44 | − | 4217.80i | 0.336001 | − | 0.193990i | ||||
\(780\) | 621.362 | − | 2209.07i | 0.0285235 | − | 0.101407i | ||||
\(781\) | −10082.2 | + | 17462.8i | −0.461931 | + | 0.800088i | ||||
\(782\) | −4650.02 | −0.212640 | ||||||||
\(783\) | 6930.27 | + | 30333.1i | 0.316306 | + | 1.38444i | ||||
\(784\) | 9235.92 | − | 5315.23i | 0.420732 | − | 0.242130i | ||||
\(785\) | −17533.8 | − | 10123.1i | −0.797208 | − | 0.460268i | ||||
\(786\) | −83.5004 | + | 296.861i | −0.00378926 | + | 0.0134716i | ||||
\(787\) | −29189.2 | + | 16852.4i | −1.32209 | + | 0.763308i | −0.984061 | − | 0.177829i | \(-0.943093\pi\) |
−0.338026 | + | 0.941137i | \(0.609759\pi\) | |||||||
\(788\) | 4037.98 | − | 2331.33i | 0.182547 | − | 0.105394i | ||||
\(789\) | −24429.0 | − | 25042.2i | −1.10228 | − | 1.12994i | ||||
\(790\) | 9146.53 | + | 5280.75i | 0.411923 | + | 0.237824i | ||||
\(791\) | −4466.25 | + | 1193.40i | −0.200761 | + | 0.0536439i | ||||
\(792\) | −20367.6 | + | 11095.4i | −0.913803 | + | 0.497802i | ||||
\(793\) | −17946.8 | −0.803671 | ||||||||
\(794\) | 7558.66 | − | 13092.0i | 0.337842 | − | 0.585160i | ||||
\(795\) | −4448.15 | + | 1132.98i | −0.198440 | + | 0.0505443i | ||||
\(796\) | −3081.22 | + | 1778.94i | −0.137200 | + | 0.0792122i | ||||
\(797\) | −2571.40 | − | 4453.80i | −0.114283 | − | 0.197944i | 0.803210 | − | 0.595696i | \(-0.203124\pi\) |
−0.917493 | + | 0.397752i | \(0.869790\pi\) | |||||||
\(798\) | −14655.2 | + | 8207.30i | −0.650111 | + | 0.364079i | ||||
\(799\) | 4508.23 | − | 7808.49i | 0.199612 | − | 0.345738i | ||||
\(800\) | 12038.5i | 0.532033i | ||||||||
\(801\) | 34691.3 | + | 21192.5i | 1.53028 | + | 0.934831i | ||||
\(802\) | −19814.6 | −0.872418 | ||||||||
\(803\) | −654.007 | + | 1132.77i | −0.0287415 | + | 0.0497817i | ||||
\(804\) | −7672.78 | + | 7484.91i | −0.336565 | + | 0.328324i | ||||
\(805\) | −4177.73 | − | 4183.55i | −0.182914 | − | 0.183169i | ||||
\(806\) | 7536.19 | − | 4351.02i | 0.329344 | − | 0.190147i | ||||
\(807\) | 37522.1 | + | 10554.1i | 1.63673 | + | 0.460375i | ||||
\(808\) | −3313.94 | − | 1913.30i | −0.144287 | − | 0.0833041i | ||||
\(809\) | 4644.84i | 0.201859i | 0.994894 | + | 0.100930i | \(0.0321817\pi\) | ||||
−0.994894 | + | 0.100930i | \(0.967818\pi\) | |||||||
\(810\) | 8002.81 | − | 4105.74i | 0.347148 | − | 0.178100i | ||||
\(811\) | − | 8124.92i | − | 0.351794i | −0.984409 | − | 0.175897i | \(-0.943717\pi\) | ||
0.984409 | − | 0.175897i | \(-0.0562825\pi\) | |||||||
\(812\) | 3192.36 | − | 11881.0i | 0.137968 | − | 0.513473i | ||||
\(813\) | 6502.85 | − | 23118.9i | 0.280523 | − | 0.997314i | ||||
\(814\) | −11365.8 | − | 19686.2i | −0.489401 | − | 0.847668i | ||||
\(815\) | −468.310 | − | 811.136i | −0.0201278 | − | 0.0348624i | ||||
\(816\) | −4149.52 | + | 4047.91i | −0.178017 | + | 0.173658i | ||||
\(817\) | 23521.6 | + | 13580.2i | 1.00724 | + | 0.581531i | ||||
\(818\) | −24707.6 | −1.05609 | ||||||||
\(819\) | −12820.9 | − | 3788.02i | −0.547006 | − | 0.161617i | ||||
\(820\) | 1786.04 | 0.0760624 | ||||||||
\(821\) | 2253.56 | + | 1301.09i | 0.0957976 | + | 0.0553088i | 0.547133 | − | 0.837045i | \(-0.315719\pi\) |
−0.451336 | + | 0.892354i | \(0.649052\pi\) | |||||||
\(822\) | 765.158 | + | 3004.05i | 0.0324671 | + | 0.127468i | ||||
\(823\) | −9500.29 | − | 16455.0i | −0.402381 | − | 0.696944i | 0.591632 | − | 0.806208i | \(-0.298484\pi\) |
−0.994013 | + | 0.109264i | \(0.965150\pi\) | |||||||
\(824\) | 23300.9 | + | 40358.4i | 0.985105 | + | 1.70625i | ||||
\(825\) | 16632.4 | − | 4236.42i | 0.701899 | − | 0.178780i | ||||
\(826\) | −7900.65 | + | 29403.7i | −0.332807 | + | 1.23860i | ||||
\(827\) | − | 20997.3i | − | 0.882886i | −0.897289 | − | 0.441443i | \(-0.854467\pi\) | ||
0.897289 | − | 0.441443i | \(-0.145533\pi\) | |||||||
\(828\) | 2239.31 | + | 4110.63i | 0.0939870 | + | 0.172529i | ||||
\(829\) | 5441.05i | 0.227956i | 0.993483 | + | 0.113978i | \(0.0363594\pi\) | ||||
−0.993483 | + | 0.113978i | \(0.963641\pi\) | |||||||
\(830\) | 13166.9 | + | 7601.93i | 0.550640 | + | 0.317912i | ||||
\(831\) | −7307.80 | + | 7128.86i | −0.305060 | + | 0.297590i | ||||
\(832\) | −12347.2 | + | 7128.69i | −0.514500 | + | 0.297047i | ||||
\(833\) | 10658.2 | + | 6173.30i | 0.443318 | + | 0.256773i | ||||
\(834\) | −5747.56 | − | 1616.66i | −0.238635 | − | 0.0671228i | ||||
\(835\) | 1204.03 | − | 2085.44i | 0.0499008 | − | 0.0864307i | ||||
\(836\) | −8160.88 | −0.337620 | ||||||||
\(837\) | −19506.7 | − | 6012.38i | −0.805557 | − | 0.248289i | ||||
\(838\) | 21598.6i | 0.890350i | ||||||||
\(839\) | 15441.7 | − | 26745.7i | 0.635406 | − | 1.10055i | −0.351024 | − | 0.936367i | \(-0.614166\pi\) |
0.986429 | − | 0.164188i | \(-0.0525004\pi\) | |||||||
\(840\) | −13054.1 | − | 170.890i | −0.536201 | − | 0.00701937i | ||||
\(841\) | 12398.4 | + | 21474.6i | 0.508360 | + | 0.880505i | ||||
\(842\) | 5080.61 | − | 2933.29i | 0.207945 | − | 0.120057i | ||||
\(843\) | −7131.90 | − | 7310.91i | −0.291383 | − | 0.298697i | ||||
\(844\) | −368.394 | + | 638.078i | −0.0150245 | + | 0.0260232i | ||||
\(845\) | 8174.77 | 0.332805 | ||||||||
\(846\) | 15161.9 | + | 375.912i | 0.616166 | + | 0.0152767i | ||||
\(847\) | 532.559 | + | 1993.09i | 0.0216044 | + | 0.0808539i | ||||
\(848\) | 4309.50 | + | 2488.09i | 0.174515 | + | 0.100756i | ||||
\(849\) | −26869.7 | + | 6843.94i | −1.08618 | + | 0.276659i | ||||
\(850\) | 6580.30 | − | 3799.14i | 0.265532 | − | 0.153305i | ||||
\(851\) | −14585.1 | + | 8420.74i | −0.587511 | + | 0.339200i | ||||
\(852\) | 8708.19 | − | 2218.05i | 0.350162 | − | 0.0891892i | ||||
\(853\) | −6988.53 | − | 4034.83i | −0.280519 | − | 0.161958i | 0.353139 | − | 0.935571i | \(-0.385114\pi\) |
−0.633658 | + | 0.773613i | \(0.718448\pi\) | |||||||
\(854\) | 7179.85 | + | 26870.4i | 0.287692 | + | 1.07668i | ||||
\(855\) | 11614.3 | + | 287.955i | 0.464562 | + | 0.0115180i | ||||
\(856\) | −12482.6 | −0.498418 | ||||||||
\(857\) | −14248.6 | + | 24679.3i | −0.567938 | + | 0.983697i | 0.428832 | + | 0.903384i | \(0.358925\pi\) |
−0.996770 | + | 0.0803127i | \(0.974408\pi\) | |||||||
\(858\) | 7578.84 | + | 7769.07i | 0.301558 | + | 0.309128i | ||||
\(859\) | 31536.5 | − | 18207.6i | 1.25263 | − | 0.723208i | 0.281001 | − | 0.959707i | \(-0.409334\pi\) |
0.971632 | + | 0.236500i | \(0.0760002\pi\) | |||||||
\(860\) | 2875.29 | + | 4980.14i | 0.114008 | + | 0.197467i | ||||
\(861\) | 136.199 | − | 10404.1i | 0.00539100 | − | 0.411811i | ||||
\(862\) | 2396.41 | − | 4150.71i | 0.0946892 | − | 0.164006i | ||||
\(863\) | 784.791i | 0.0309555i | 0.999880 | + | 0.0154778i | \(0.00492692\pi\) | ||||
−0.999880 | + | 0.0154778i | \(0.995073\pi\) | |||||||
\(864\) | 17064.7 | + | 5259.69i | 0.671936 | + | 0.207105i | ||||
\(865\) | −9130.14 | −0.358883 | ||||||||
\(866\) | −9593.98 | + | 16617.3i | −0.376463 | + | 0.652053i | ||||
\(867\) | 18125.0 | + | 5098.17i | 0.709985 | + | 0.199703i | ||||
\(868\) | 5702.92 | + | 5710.87i | 0.223007 | + | 0.223317i | ||||
\(869\) | 25888.9 | − | 14947.0i | 1.01061 | − | 0.583477i | ||||
\(870\) | 10177.8 | − | 9928.62i | 0.396622 | − | 0.386910i | ||||
\(871\) | 15946.3 | + | 9206.58i | 0.620343 | + | 0.358155i | ||||
\(872\) | − | 7340.63i | − | 0.285075i | ||||||
\(873\) | 14949.5 | + | 27442.3i | 0.579568 | + | 1.06390i | ||||
\(874\) | − | 10103.0i | − | 0.391008i | ||||||
\(875\) | 21660.4 | + | 5820.05i | 0.836863 | + | 0.224861i | ||||
\(876\) | 564.880 | − | 143.880i | 0.0217871 | − | 0.00554937i | ||||
\(877\) | 7678.68 | + | 13299.9i | 0.295656 | + | 0.512092i | 0.975137 | − | 0.221601i | \(-0.0711284\pi\) |
−0.679481 | + | 0.733693i | \(0.737795\pi\) | |||||||
\(878\) | 8276.70 | + | 14335.7i | 0.318138 | + | 0.551031i | ||||
\(879\) | 2648.47 | + | 10398.0i | 0.101627 | + | 0.398995i | ||||
\(880\) | 5182.09 | + | 2991.88i | 0.198509 | + | 0.114610i | ||||
\(881\) | 40911.2 | 1.56451 | 0.782254 | − | 0.622959i | \(-0.214070\pi\) | ||||
0.782254 | + | 0.622959i | \(0.214070\pi\) | |||||||
\(882\) | −542.349 | + | 20711.1i | −0.0207050 | + | 0.790680i | ||||
\(883\) | −33904.8 | −1.29217 | −0.646086 | − | 0.763265i | \(-0.723595\pi\) | ||||
−0.646086 | + | 0.763265i | \(0.723595\pi\) | |||||||
\(884\) | −2490.24 | − | 1437.74i | −0.0947464 | − | 0.0547019i | ||||
\(885\) | 15074.4 | − | 14705.3i | 0.572565 | − | 0.558545i | ||||
\(886\) | 15860.0 | + | 27470.4i | 0.601387 | + | 1.04163i | ||||
\(887\) | 8641.25 | + | 14967.1i | 0.327108 | + | 0.566568i | 0.981937 | − | 0.189210i | \(-0.0605925\pi\) |
−0.654829 | + | 0.755777i | \(0.727259\pi\) | |||||||
\(888\) | −10069.5 | + | 35799.0i | −0.380529 | + | 1.35286i | ||||
\(889\) | −34738.7 | − | 9334.13i | −1.31057 | − | 0.352145i | ||||
\(890\) | − | 18576.9i | − | 0.699662i | ||||||
\(891\) | 1261.63 | − | 25427.5i | 0.0474369 | − | 0.956064i | ||||
\(892\) | 3290.42i | 0.123511i | ||||||||
\(893\) | 16965.4 | + | 9794.98i | 0.635751 | + | 0.367051i | ||||
\(894\) | 23718.3 | + | 6671.44i | 0.887315 | + | 0.249582i | ||||
\(895\) | −21709.5 | + | 12534.0i | −0.810801 | + | 0.468116i | ||||
\(896\) | 2287.49 | + | 2290.68i | 0.0852898 | + | 0.0854086i | ||||
\(897\) | 5755.96 | − | 5615.02i | 0.214254 | − | 0.209008i | ||||
\(898\) | −7606.95 | + | 13175.6i | −0.282681 | + | 0.489617i | ||||
\(899\) | −32267.5 | −1.19709 | ||||||||
\(900\) | −6527.32 | − | 3987.46i | −0.241753 | − | 0.147684i | ||||
\(901\) | 5751.71i | 0.212672i | ||||||||
\(902\) | −4223.63 | + | 7315.53i | −0.155911 | + | 0.270045i | ||||
\(903\) | 29229.7 | − | 16369.4i | 1.07719 | − | 0.603255i | ||||
\(904\) | −3070.00 | − | 5317.40i | −0.112950 | − | 0.195635i | ||||
\(905\) | 331.845 | − | 191.591i | 0.0121888 | − | 0.00703723i | ||||
\(906\) | −25725.6 | + | 6552.53i | −0.943351 | + | 0.240280i | ||||
\(907\) | −23198.5 | + | 40181.0i | −0.849276 | + | 1.47099i | 0.0325796 | + | 0.999469i | \(0.489628\pi\) |
−0.881855 | + | 0.471520i | \(0.843706\pi\) | |||||||
\(908\) | −12891.0 | −0.471147 | ||||||||
\(909\) | 3688.51 | − | 2009.35i | 0.134587 | − | 0.0733178i | ||||
\(910\) | 1577.05 | + | 5902.08i | 0.0574493 | + | 0.215002i | ||||
\(911\) | −6266.99 | − | 3618.25i | −0.227919 | − | 0.131589i | 0.381692 | − | 0.924289i | \(-0.375341\pi\) |
−0.609612 | + | 0.792700i | \(0.708675\pi\) | |||||||
\(912\) | −8794.85 | − | 9015.60i | −0.319327 | − | 0.327343i | ||||
\(913\) | 37268.5 | − | 21517.0i | 1.35094 | − | 0.779966i | ||||
\(914\) | 7307.62 | − | 4219.06i | 0.264458 | − | 0.152685i | ||||
\(915\) | 5208.93 | − | 18518.8i | 0.188199 | − | 0.669085i | ||||
\(916\) | −7417.58 | − | 4282.54i | −0.267559 | − | 0.154475i | ||||
\(917\) | 126.831 | + | 474.660i | 0.00456741 | + | 0.0170934i | ||||
\(918\) | −2510.34 | − | 10987.5i | −0.0902544 | − | 0.395034i | ||||
\(919\) | 4016.19 | 0.144159 | 0.0720793 | − | 0.997399i | \(-0.477037\pi\) | ||||
0.0720793 | + | 0.997399i | \(0.477037\pi\) | |||||||
\(920\) | 3926.25 | − | 6800.46i | 0.140701 | − | 0.243701i | ||||
\(921\) | 556.598 | − | 1978.82i | 0.0199137 | − | 0.0707973i | ||||
\(922\) | −30251.4 | + | 17465.7i | −1.08056 | + | 0.623863i | ||||
\(923\) | −7718.35 | − | 13368.6i | −0.275247 | − | 0.476741i | ||||
\(924\) | −5146.73 | + | 8650.87i | −0.183241 | + | 0.308001i | ||||
\(925\) | 13759.7 | − | 23832.6i | 0.489100 | − | 0.847146i | ||||
\(926\) | − | 18146.2i | − | 0.643976i | ||||||
\(927\) | −51137.2 | − | 1267.85i | −1.81183 | − | 0.0449210i | ||||
\(928\) | 28228.0 | 0.998522 | ||||||||
\(929\) | −6595.59 | + | 11423.9i | −0.232932 | + | 0.403451i | −0.958670 | − | 0.284521i | \(-0.908165\pi\) |
0.725737 | + | 0.687972i | \(0.241499\pi\) | |||||||
\(930\) | 2302.36 | + | 9039.20i | 0.0811801 | + | 0.318717i | ||||
\(931\) | −13412.6 | + | 23156.9i | −0.472161 | + | 0.815183i | ||||
\(932\) | 5853.51 | − | 3379.53i | 0.205728 | − | 0.118777i | ||||
\(933\) | −8093.26 | − | 31774.6i | −0.283989 | − | 1.11495i | ||||
\(934\) | 12802.1 | + | 7391.31i | 0.448499 | + | 0.258941i | ||||
\(935\) | 6916.33i | 0.241912i | ||||||||
\(936\) | 440.089 | − | 17750.4i | 0.0153683 | − | 0.619861i | ||||
\(937\) | − | 35573.0i | − | 1.24025i | −0.784502 | − | 0.620127i | \(-0.787081\pi\) | ||
0.784502 | − | 0.620127i | \(-0.212919\pi\) | |||||||
\(938\) | 7404.77 | − | 27558.2i | 0.257755 | − | 0.959284i | ||||
\(939\) | −36819.2 | − | 37743.4i | −1.27961 | − | 1.31172i | ||||
\(940\) | 2073.86 | + | 3592.03i | 0.0719593 | + | 0.124637i | ||||
\(941\) | −13592.7 | − | 23543.3i | −0.470893 | − | 0.815610i | 0.528553 | − | 0.848900i | \(-0.322735\pi\) |
−0.999446 | + | 0.0332901i | \(0.989401\pi\) | |||||||
\(942\) | −41079.9 | − | 11554.9i | −1.42087 | − | 0.399658i | ||||
\(943\) | 5419.94 | + | 3129.20i | 0.187166 | + | 0.108060i | ||||
\(944\) | −22829.9 | −0.787131 | ||||||||
\(945\) | 7629.90 | − | 12130.0i | 0.262646 | − | 0.417555i | ||||
\(946\) | −27197.9 | −0.934758 | ||||||||
\(947\) | 47661.0 | + | 27517.1i | 1.63545 | + | 0.944229i | 0.982371 | + | 0.186940i | \(0.0598570\pi\) |
0.653081 | + | 0.757288i | \(0.273476\pi\) | |||||||
\(948\) | −12824.6 | − | 3607.27i | −0.439370 | − | 0.123585i | ||||
\(949\) | −500.672 | − | 867.189i | −0.0171259 | − | 0.0296629i | ||||
\(950\) | 8254.34 | + | 14296.9i | 0.281901 | + | 0.488267i | ||||
\(951\) | −6439.90 | − | 6601.55i | −0.219588 | − | 0.225100i | ||||
\(952\) | −4244.96 | + | 15798.4i | −0.144517 | + | 0.537846i | ||||
\(953\) | 29456.0i | 1.00123i | 0.865670 | + | 0.500615i | \(0.166893\pi\) | ||||
−0.865670 | + | 0.500615i | \(0.833107\pi\) | |||||||
\(954\) | −8496.05 | + | 4628.30i | −0.288333 | + | 0.157072i | ||||
\(955\) | − | 7747.65i | − | 0.262521i | ||||||
\(956\) | −4094.69 | − | 2364.07i | −0.138527 | − | 0.0799785i | ||||
\(957\) | −9933.58 | − | 38999.8i | −0.335535 | − | 1.31733i | ||||
\(958\) | 16034.6 | − | 9257.61i | 0.540768 | − | 0.312213i | ||||
\(959\) | 3489.88 | + | 3494.74i | 0.117512 | + | 0.117676i | ||||
\(960\) | −3772.18 | − | 14809.8i | −0.126819 | − | 0.497900i | ||||
\(961\) | −4311.22 | + | 7467.25i | −0.144715 | + | 0.250655i | ||||
\(962\) | 17402.1 | 0.583230 | ||||||||
\(963\) | 7142.80 | − | 11692.5i | 0.239017 | − | 0.391262i | ||||
\(964\) | 4317.29i | 0.144243i | ||||||||
\(965\) | −6375.73 | + | 11043.1i | −0.212686 | + | 0.368383i | ||||
\(966\) | −10709.6 | − | 6371.57i | −0.356705 | − | 0.212217i | ||||
\(967\) | −13886.7 | − | 24052.5i | −0.461806 | − | 0.799872i | 0.537245 | − | 0.843426i | \(-0.319465\pi\) |
−0.999051 | + | 0.0435547i | \(0.986132\pi\) | |||||||
\(968\) | −2372.91 | + | 1370.00i | −0.0787895 | + | 0.0454891i | ||||
\(969\) | 3941.81 | − | 14013.9i | 0.130680 | − | 0.464594i | ||||
\(970\) | 7140.19 | − | 12367.2i | 0.236348 | − | 0.409367i | ||||
\(971\) | 13906.7 | 0.459615 | 0.229807 | − | 0.973236i | \(-0.426190\pi\) | ||||
0.229807 | + | 0.973236i | \(0.426190\pi\) | |||||||
\(972\) | −8504.07 | + | 7510.38i | −0.280626 | + | 0.247835i | ||||
\(973\) | −9189.95 | + | 2455.58i | −0.302792 | + | 0.0809069i | ||||
\(974\) | 444.142 | + | 256.425i | 0.0146111 | + | 0.00843573i | ||||
\(975\) | −3557.77 | + | 12648.6i | −0.116861 | + | 0.415465i | ||||
\(976\) | −18061.1 | + | 10427.6i | −0.592338 | + | 0.341987i | ||||
\(977\) | 7241.30 | − | 4180.76i | 0.237123 | − | 0.136903i | −0.376730 | − | 0.926323i | \(-0.622952\pi\) |
0.613854 | + | 0.789420i | \(0.289618\pi\) | |||||||
\(978\) | −1378.53 | − | 1413.13i | −0.0450722 | − | 0.0462035i | ||||
\(979\) | −45536.7 | − | 26290.6i | −1.48658 | − | 0.858276i | ||||
\(980\) | −4910.81 | + | 2826.15i | −0.160072 | + | 0.0921205i | ||||
\(981\) | 6876.00 | + | 4200.47i | 0.223786 | + | 0.136708i | ||||
\(982\) | 46301.0 | 1.50461 | ||||||||
\(983\) | −4846.51 | + | 8394.40i | −0.157253 | + | 0.272370i | −0.933877 | − | 0.357594i | \(-0.883597\pi\) |
0.776624 | + | 0.629964i | \(0.216930\pi\) | |||||||
\(984\) | 13391.8 | − | 3411.01i | 0.433857 | − | 0.110507i | ||||
\(985\) | 7435.32 | − | 4292.79i | 0.240517 | − | 0.138862i | ||||
\(986\) | −8908.23 | − | 15429.5i | −0.287724 | − | 0.498353i | ||||
\(987\) | 21082.5 | − | 11806.7i | 0.679901 | − | 0.380762i | ||||
\(988\) | 3123.76 | − | 5410.51i | 0.100587 | − | 0.174222i | ||||
\(989\) | 20150.4i | 0.647873i | ||||||||
\(990\) | −10216.4 | + | 5565.45i | −0.327977 | + | 0.178668i | ||||
\(991\) | 31419.3 | 1.00713 | 0.503566 | − | 0.863957i | \(-0.332021\pi\) | ||||
0.503566 | + | 0.863957i | \(0.332021\pi\) | |||||||
\(992\) | −9259.25 | + | 16037.5i | −0.296352 | + | 0.513297i | ||||
\(993\) | 17836.6 | − | 17399.9i | 0.570018 | − | 0.556061i | ||||
\(994\) | −16927.9 | + | 16904.3i | −0.540160 | + | 0.539409i | ||||
\(995\) | −5673.59 | + | 3275.65i | −0.180769 | + | 0.104367i | ||||
\(996\) | −18461.7 | − | 5192.87i | −0.587330 | − | 0.165203i | ||||
\(997\) | 11388.3 | + | 6575.05i | 0.361757 | + | 0.208860i | 0.669851 | − | 0.742495i | \(-0.266358\pi\) |
−0.308094 | + | 0.951356i | \(0.599691\pi\) | |||||||
\(998\) | 29317.2i | 0.929880i | ||||||||
\(999\) | −27771.1 | − | 29917.1i | −0.879520 | − | 0.947483i |
(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.20.15 | ✓ | 44 | |
3.2 | odd | 2 | 189.4.o.a.62.8 | 44 | |||
7.6 | odd | 2 | inner | 63.4.o.a.20.16 | yes | 44 | |
9.2 | odd | 6 | 567.4.c.c.566.30 | 44 | |||
9.4 | even | 3 | 189.4.o.a.125.7 | 44 | |||
9.5 | odd | 6 | inner | 63.4.o.a.41.16 | yes | 44 | |
9.7 | even | 3 | 567.4.c.c.566.15 | 44 | |||
21.20 | even | 2 | 189.4.o.a.62.7 | 44 | |||
63.13 | odd | 6 | 189.4.o.a.125.8 | 44 | |||
63.20 | even | 6 | 567.4.c.c.566.16 | 44 | |||
63.34 | odd | 6 | 567.4.c.c.566.29 | 44 | |||
63.41 | even | 6 | inner | 63.4.o.a.41.15 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.o.a.20.15 | ✓ | 44 | 1.1 | even | 1 | trivial | |
63.4.o.a.20.16 | yes | 44 | 7.6 | odd | 2 | inner | |
63.4.o.a.41.15 | yes | 44 | 63.41 | even | 6 | inner | |
63.4.o.a.41.16 | yes | 44 | 9.5 | odd | 6 | inner | |
189.4.o.a.62.7 | 44 | 21.20 | even | 2 | |||
189.4.o.a.62.8 | 44 | 3.2 | odd | 2 | |||
189.4.o.a.125.7 | 44 | 9.4 | even | 3 | |||
189.4.o.a.125.8 | 44 | 63.13 | odd | 6 | |||
567.4.c.c.566.15 | 44 | 9.7 | even | 3 | |||
567.4.c.c.566.16 | 44 | 63.20 | even | 6 | |||
567.4.c.c.566.29 | 44 | 63.34 | odd | 6 | |||
567.4.c.c.566.30 | 44 | 9.2 | odd | 6 |