Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,5,Mod(7,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.g (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.41120878177\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Character | \(\chi\) | \(=\) | 33.19 |
Dual form | 33.5.g.a.7.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.37135 | − | 6.01665i | −1.09284 | − | 1.50416i | −0.844550 | − | 0.535476i | \(-0.820132\pi\) |
−0.248288 | − | 0.968686i | \(-0.579868\pi\) | |||||||
\(3\) | −1.60570 | − | 4.94183i | −0.178411 | − | 0.549093i | ||||
\(4\) | −12.1471 | + | 37.3849i | −0.759193 | + | 2.33656i | ||||
\(5\) | −24.8968 | − | 18.0886i | −0.995873 | − | 0.723544i | −0.0346733 | − | 0.999399i | \(-0.511039\pi\) |
−0.961199 | + | 0.275855i | \(0.911039\pi\) | |||||||
\(6\) | −22.7142 | + | 31.2634i | −0.630950 | + | 0.868429i | ||||
\(7\) | 40.6127 | + | 13.1959i | 0.828831 | + | 0.269304i | 0.692553 | − | 0.721367i | \(-0.256486\pi\) |
0.136278 | + | 0.990671i | \(0.456486\pi\) | |||||||
\(8\) | 164.863 | − | 53.5673i | 2.57599 | − | 0.836989i | ||||
\(9\) | −21.8435 | + | 15.8702i | −0.269672 | + | 0.195928i | ||||
\(10\) | 228.867i | 2.28867i | ||||||||
\(11\) | −55.8909 | + | 107.318i | −0.461908 | + | 0.886928i | ||||
\(12\) | 204.255 | 1.41843 | ||||||||
\(13\) | −92.9028 | − | 127.870i | −0.549721 | − | 0.756626i | 0.440253 | − | 0.897874i | \(-0.354889\pi\) |
−0.989974 | + | 0.141248i | \(0.954889\pi\) | |||||||
\(14\) | −98.1376 | − | 302.036i | −0.500702 | − | 1.54100i | ||||
\(15\) | −49.4140 | + | 152.081i | −0.219618 | + | 0.675915i | ||||
\(16\) | −534.147 | − | 388.080i | −2.08651 | − | 1.51594i | ||||
\(17\) | −52.6147 | + | 72.4180i | −0.182058 | + | 0.250581i | −0.890285 | − | 0.455403i | \(-0.849495\pi\) |
0.708227 | + | 0.705984i | \(0.249495\pi\) | |||||||
\(18\) | 190.971 | + | 62.0502i | 0.589416 | + | 0.191513i | ||||
\(19\) | −624.099 | + | 202.782i | −1.72881 | + | 0.561723i | −0.993276 | − | 0.115768i | \(-0.963067\pi\) |
−0.735531 | + | 0.677492i | \(0.763067\pi\) | |||||||
\(20\) | 978.664 | − | 711.041i | 2.44666 | − | 1.77760i | ||||
\(21\) | − | 221.890i | − | 0.503152i | ||||||
\(22\) | 890.015 | − | 132.850i | 1.83887 | − | 0.274484i | ||||
\(23\) | −292.602 | −0.553123 | −0.276561 | − | 0.960996i | \(-0.589195\pi\) | ||||
−0.276561 | + | 0.960996i | \(0.589195\pi\) | |||||||
\(24\) | −529.441 | − | 728.713i | −0.919169 | − | 1.26513i | ||||
\(25\) | 99.5185 | + | 306.287i | 0.159230 | + | 0.490058i | ||||
\(26\) | −363.237 | + | 1117.93i | −0.537333 | + | 1.65374i | ||||
\(27\) | 113.502 | + | 82.4640i | 0.155695 | + | 0.113119i | ||||
\(28\) | −986.653 | + | 1358.01i | −1.25849 | + | 1.73216i | ||||
\(29\) | −646.603 | − | 210.094i | −0.768850 | − | 0.249815i | −0.101777 | − | 0.994807i | \(-0.532453\pi\) |
−0.667073 | + | 0.744993i | \(0.732453\pi\) | |||||||
\(30\) | 1131.02 | − | 367.492i | 1.25669 | − | 0.408324i | ||||
\(31\) | 1421.82 | − | 1033.01i | 1.47952 | − | 1.07493i | 0.501809 | − | 0.864979i | \(-0.332668\pi\) |
0.977711 | − | 0.209955i | \(-0.0673319\pi\) | |||||||
\(32\) | 2136.65i | 2.08657i | ||||||||
\(33\) | 620.093 | + | 103.883i | 0.569415 | + | 0.0953926i | ||||
\(34\) | 665.711 | 0.575875 | ||||||||
\(35\) | −772.433 | − | 1063.16i | −0.630557 | − | 0.867888i | ||||
\(36\) | −327.971 | − | 1009.39i | −0.253064 | − | 0.778852i | ||||
\(37\) | 56.5273 | − | 173.973i | 0.0412909 | − | 0.127080i | −0.928286 | − | 0.371867i | \(-0.878718\pi\) |
0.969577 | + | 0.244786i | \(0.0787178\pi\) | |||||||
\(38\) | 3948.23 | + | 2868.55i | 2.73423 | + | 1.98653i | ||||
\(39\) | −482.737 | + | 664.431i | −0.317382 | + | 0.436838i | ||||
\(40\) | −5073.52 | − | 1648.49i | −3.17095 | − | 1.03030i | ||||
\(41\) | −553.714 | + | 179.912i | −0.329395 | + | 0.107027i | −0.469046 | − | 0.883174i | \(-0.655402\pi\) |
0.139650 | + | 0.990201i | \(0.455402\pi\) | |||||||
\(42\) | −1335.03 | + | 969.960i | −0.756822 | + | 0.549864i | ||||
\(43\) | 298.729i | 0.161563i | 0.996732 | + | 0.0807813i | \(0.0257415\pi\) | ||||
−0.996732 | + | 0.0807813i | \(0.974258\pi\) | |||||||
\(44\) | −3333.17 | − | 3393.08i | −1.72168 | − | 1.75262i | ||||
\(45\) | 830.902 | 0.410322 | ||||||||
\(46\) | 1279.07 | + | 1760.48i | 0.604474 | + | 0.831986i | ||||
\(47\) | −662.592 | − | 2039.25i | −0.299951 | − | 0.923154i | −0.981513 | − | 0.191394i | \(-0.938699\pi\) |
0.681562 | − | 0.731760i | \(-0.261301\pi\) | |||||||
\(48\) | −1060.15 | + | 3262.80i | −0.460134 | + | 1.41615i | ||||
\(49\) | −467.187 | − | 339.431i | −0.194580 | − | 0.141371i | ||||
\(50\) | 1407.79 | − | 1937.65i | 0.563115 | − | 0.775062i | ||||
\(51\) | 442.361 | + | 143.732i | 0.170073 | + | 0.0552602i | ||||
\(52\) | 5908.90 | − | 1919.92i | 2.18524 | − | 0.710029i | ||||
\(53\) | −1783.60 | + | 1295.86i | −0.634959 | + | 0.461325i | −0.858115 | − | 0.513458i | \(-0.828364\pi\) |
0.223156 | + | 0.974783i | \(0.428364\pi\) | |||||||
\(54\) | − | 1043.38i | − | 0.357812i | ||||||
\(55\) | 3332.74 | − | 1660.90i | 1.10173 | − | 0.549057i | ||||
\(56\) | 7402.41 | 2.36046 | ||||||||
\(57\) | 2004.23 | + | 2758.59i | 0.616876 | + | 0.849058i | ||||
\(58\) | 1562.47 | + | 4808.78i | 0.464467 | + | 1.42948i | ||||
\(59\) | 1495.28 | − | 4602.01i | 0.429556 | − | 1.32204i | −0.469008 | − | 0.883194i | \(-0.655389\pi\) |
0.898564 | − | 0.438843i | \(-0.144611\pi\) | |||||||
\(60\) | −5085.29 | − | 3694.68i | −1.41258 | − | 1.02630i | ||||
\(61\) | −1179.00 | + | 1622.76i | −0.316851 | + | 0.436108i | −0.937502 | − | 0.347979i | \(-0.886868\pi\) |
0.620652 | + | 0.784087i | \(0.286868\pi\) | |||||||
\(62\) | −12430.5 | − | 4038.93i | −3.23375 | − | 1.05071i | ||||
\(63\) | −1096.54 | + | 356.289i | −0.276277 | + | 0.0897679i | ||||
\(64\) | 4309.14 | − | 3130.77i | 1.05204 | − | 0.764349i | ||||
\(65\) | 4864.03i | 1.15125i | ||||||||
\(66\) | −2085.62 | − | 4184.99i | −0.478793 | − | 0.960742i | ||||
\(67\) | −4987.81 | −1.11112 | −0.555559 | − | 0.831477i | \(-0.687496\pi\) | ||||
−0.555559 | + | 0.831477i | \(0.687496\pi\) | |||||||
\(68\) | −2068.22 | − | 2846.66i | −0.447280 | − | 0.615628i | ||||
\(69\) | 469.831 | + | 1445.99i | 0.0986832 | + | 0.303716i | ||||
\(70\) | −3020.10 | + | 9294.92i | −0.616347 | + | 1.89692i | ||||
\(71\) | 4378.91 | + | 3181.46i | 0.868659 | + | 0.631118i | 0.930227 | − | 0.366985i | \(-0.119610\pi\) |
−0.0615677 | + | 0.998103i | \(0.519610\pi\) | |||||||
\(72\) | −2751.06 | + | 3786.51i | −0.530682 | + | 0.730422i | ||||
\(73\) | 1926.53 | + | 625.969i | 0.361519 | + | 0.117465i | 0.484144 | − | 0.874988i | \(-0.339131\pi\) |
−0.122625 | + | 0.992453i | \(0.539131\pi\) | |||||||
\(74\) | −1293.84 | + | 420.393i | −0.236274 | + | 0.0767701i | ||||
\(75\) | 1353.82 | − | 983.608i | 0.240679 | − | 0.174864i | ||||
\(76\) | − | 25795.1i | − | 4.46591i | ||||||
\(77\) | −3686.04 | + | 3620.96i | −0.621697 | + | 0.610720i | ||||
\(78\) | 6107.86 | 1.00392 | ||||||||
\(79\) | −1821.76 | − | 2507.43i | −0.291901 | − | 0.401768i | 0.637729 | − | 0.770261i | \(-0.279874\pi\) |
−0.929631 | + | 0.368493i | \(0.879874\pi\) | |||||||
\(80\) | 6278.72 | + | 19323.9i | 0.981051 | + | 3.01936i | ||||
\(81\) | 225.273 | − | 693.320i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 3502.95 | + | 2545.04i | 0.520962 | + | 0.378501i | ||||
\(83\) | −3443.51 | + | 4739.58i | −0.499856 | + | 0.687992i | −0.982168 | − | 0.188007i | \(-0.939797\pi\) |
0.482312 | + | 0.876000i | \(0.339797\pi\) | |||||||
\(84\) | 8295.34 | + | 2695.32i | 1.17564 | + | 0.381990i | ||||
\(85\) | 2619.88 | − | 851.250i | 0.362613 | − | 0.117820i | ||||
\(86\) | 1797.35 | − | 1305.85i | 0.243017 | − | 0.176562i | ||||
\(87\) | 3532.75i | 0.466740i | ||||||||
\(88\) | −3465.59 | + | 20686.7i | −0.447520 | + | 2.67133i | ||||
\(89\) | −1483.07 | −0.187233 | −0.0936166 | − | 0.995608i | \(-0.529843\pi\) | ||||
−0.0936166 | + | 0.995608i | \(0.529843\pi\) | |||||||
\(90\) | −3632.17 | − | 4999.25i | −0.448416 | − | 0.617191i | ||||
\(91\) | −2085.68 | − | 6419.08i | −0.251864 | − | 0.775157i | ||||
\(92\) | 3554.26 | − | 10938.9i | 0.419927 | − | 1.29240i | ||||
\(93\) | −7387.99 | − | 5367.69i | −0.854201 | − | 0.620613i | ||||
\(94\) | −9373.02 | + | 12900.9i | −1.06078 | + | 1.46003i | ||||
\(95\) | 19206.1 | + | 6240.45i | 2.12810 | + | 0.691463i | ||||
\(96\) | 10559.0 | − | 3430.82i | 1.14572 | − | 0.372268i | ||||
\(97\) | 5297.09 | − | 3848.56i | 0.562982 | − | 0.409030i | −0.269567 | − | 0.962982i | \(-0.586881\pi\) |
0.832549 | + | 0.553951i | \(0.186881\pi\) | |||||||
\(98\) | 4294.67i | 0.447175i | ||||||||
\(99\) | −482.313 | − | 3231.20i | −0.0492106 | − | 0.329681i | ||||
\(100\) | −12659.4 | −1.26594 | ||||||||
\(101\) | −750.623 | − | 1033.14i | −0.0735833 | − | 0.101279i | 0.770639 | − | 0.637272i | \(-0.219937\pi\) |
−0.844222 | + | 0.535993i | \(0.819937\pi\) | |||||||
\(102\) | −1068.93 | − | 3289.83i | −0.102742 | − | 0.316209i | ||||
\(103\) | 3389.37 | − | 10431.4i | 0.319480 | − | 0.983260i | −0.654390 | − | 0.756157i | \(-0.727075\pi\) |
0.973871 | − | 0.227103i | \(-0.0729253\pi\) | |||||||
\(104\) | −22165.9 | − | 16104.5i | −2.04936 | − | 1.48895i | ||||
\(105\) | −4013.68 | + | 5524.36i | −0.364053 | + | 0.501075i | ||||
\(106\) | 15593.5 | + | 5066.63i | 1.38781 | + | 0.450928i | ||||
\(107\) | 12517.4 | − | 4067.16i | 1.09332 | − | 0.355241i | 0.293792 | − | 0.955869i | \(-0.405083\pi\) |
0.799529 | + | 0.600628i | \(0.205083\pi\) | |||||||
\(108\) | −4461.63 | + | 3241.56i | −0.382513 | + | 0.277912i | ||||
\(109\) | 4675.96i | 0.393566i | 0.980447 | + | 0.196783i | \(0.0630495\pi\) | ||||
−0.980447 | + | 0.196783i | \(0.936950\pi\) | |||||||
\(110\) | −24561.6 | − | 12791.6i | −2.02989 | − | 1.05716i | ||||
\(111\) | −950.512 | −0.0771457 | ||||||||
\(112\) | −16572.1 | − | 22809.5i | −1.32112 | − | 1.81836i | ||||
\(113\) | −1784.80 | − | 5493.06i | −0.139776 | − | 0.430187i | 0.856526 | − | 0.516104i | \(-0.172618\pi\) |
−0.996302 | + | 0.0859167i | \(0.972618\pi\) | |||||||
\(114\) | 7836.26 | − | 24117.5i | 0.602975 | − | 1.85577i | ||||
\(115\) | 7284.85 | + | 5292.76i | 0.550840 | + | 0.400208i | ||||
\(116\) | 15708.7 | − | 21621.2i | 1.16741 | − | 1.60680i | ||||
\(117\) | 4058.64 | + | 1318.73i | 0.296489 | + | 0.0963351i | ||||
\(118\) | −34225.1 | + | 11120.4i | −2.45799 | + | 0.798650i | ||||
\(119\) | −3092.45 | + | 2246.79i | −0.218378 | + | 0.158661i | ||||
\(120\) | 27719.5i | 1.92496i | ||||||||
\(121\) | −8393.42 | − | 11996.2i | −0.573282 | − | 0.819358i | ||||
\(122\) | 14917.4 | 1.00224 | ||||||||
\(123\) | 1778.20 | + | 2447.48i | 0.117536 | + | 0.161774i | ||||
\(124\) | 21348.1 | + | 65702.6i | 1.38840 | + | 4.27306i | ||||
\(125\) | −2880.99 | + | 8866.77i | −0.184383 | + | 0.567473i | ||||
\(126\) | 6937.04 | + | 5040.06i | 0.436952 | + | 0.317464i | ||||
\(127\) | 7154.38 | − | 9847.15i | 0.443572 | − | 0.610525i | −0.527429 | − | 0.849599i | \(-0.676844\pi\) |
0.971001 | + | 0.239074i | \(0.0768440\pi\) | |||||||
\(128\) | −5160.31 | − | 1676.69i | −0.314961 | − | 0.102337i | ||||
\(129\) | 1476.27 | − | 479.670i | 0.0887129 | − | 0.0288246i | ||||
\(130\) | 29265.2 | − | 21262.4i | 1.73167 | − | 1.25813i | ||||
\(131\) | − | 17730.8i | − | 1.03320i | −0.856226 | − | 0.516601i | \(-0.827197\pi\) | ||
0.856226 | − | 0.516601i | \(-0.172803\pi\) | |||||||
\(132\) | −11416.0 | + | 21920.2i | −0.655186 | + | 1.25805i | ||||
\(133\) | −28022.3 | −1.58416 | ||||||||
\(134\) | 21803.5 | + | 30009.9i | 1.21427 | + | 1.67130i | ||||
\(135\) | −1334.18 | − | 4106.18i | −0.0732060 | − | 0.225305i | ||||
\(136\) | −4795.00 | + | 14757.5i | −0.259245 | + | 0.797874i | ||||
\(137\) | 12286.3 | + | 8926.54i | 0.654608 | + | 0.475600i | 0.864838 | − | 0.502052i | \(-0.167421\pi\) |
−0.210230 | + | 0.977652i | \(0.567421\pi\) | |||||||
\(138\) | 6646.22 | − | 9147.74i | 0.348993 | − | 0.480348i | ||||
\(139\) | −24706.7 | − | 8027.71i | −1.27875 | − | 0.415491i | −0.410611 | − | 0.911811i | \(-0.634684\pi\) |
−0.868140 | + | 0.496319i | \(0.834684\pi\) | |||||||
\(140\) | 49129.0 | − | 15963.0i | 2.50658 | − | 0.814438i | ||||
\(141\) | −9013.70 | + | 6548.84i | −0.453383 | + | 0.329402i | ||||
\(142\) | − | 40253.7i | − | 1.99631i | ||||||
\(143\) | 18915.2 | − | 2823.42i | 0.924993 | − | 0.138071i | ||||
\(144\) | 17826.5 | 0.859689 | ||||||||
\(145\) | 12298.0 | + | 16926.8i | 0.584925 | + | 0.805080i | ||||
\(146\) | −4655.32 | − | 14327.6i | −0.218396 | − | 0.672153i | ||||
\(147\) | −927.250 | + | 2853.78i | −0.0429104 | + | 0.132065i | ||||
\(148\) | 5817.32 | + | 4226.53i | 0.265583 | + | 0.192957i | ||||
\(149\) | −19082.2 | + | 26264.4i | −0.859522 | + | 1.18303i | 0.122162 | + | 0.992510i | \(0.461017\pi\) |
−0.981683 | + | 0.190520i | \(0.938983\pi\) | |||||||
\(150\) | −11836.1 | − | 3845.77i | −0.526047 | − | 0.170923i | ||||
\(151\) | −28481.7 | + | 9254.25i | −1.24914 | + | 0.405871i | −0.857613 | − | 0.514296i | \(-0.828053\pi\) |
−0.391528 | + | 0.920166i | \(0.628053\pi\) | |||||||
\(152\) | −92028.5 | + | 66862.6i | −3.98323 | + | 2.89398i | ||||
\(153\) | − | 2416.87i | − | 0.103245i | ||||||
\(154\) | 37899.0 | + | 6349.12i | 1.59804 | + | 0.267715i | ||||
\(155\) | −54084.5 | −2.25117 | ||||||||
\(156\) | −18975.8 | − | 26118.0i | −0.779743 | − | 1.07322i | ||||
\(157\) | 1589.28 | + | 4891.29i | 0.0644764 | + | 0.198438i | 0.978105 | − | 0.208112i | \(-0.0667318\pi\) |
−0.913629 | + | 0.406550i | \(0.866732\pi\) | |||||||
\(158\) | −7122.81 | + | 21921.7i | −0.285323 | + | 0.878134i | ||||
\(159\) | 9267.85 | + | 6733.49i | 0.366594 | + | 0.266346i | ||||
\(160\) | 38649.0 | − | 53195.8i | 1.50973 | − | 2.07796i | ||||
\(161\) | −11883.4 | − | 3861.14i | −0.458445 | − | 0.148958i | ||||
\(162\) | −5156.21 | + | 1675.36i | −0.196472 | + | 0.0638377i | ||||
\(163\) | 22862.3 | − | 16610.5i | 0.860489 | − | 0.625182i | −0.0675289 | − | 0.997717i | \(-0.521511\pi\) |
0.928018 | + | 0.372535i | \(0.121511\pi\) | |||||||
\(164\) | − | 22885.9i | − | 0.850905i | ||||||
\(165\) | −13559.3 | − | 13803.0i | −0.498044 | − | 0.506996i | ||||
\(166\) | 43569.2 | 1.58111 | ||||||||
\(167\) | 5521.70 | + | 7599.96i | 0.197988 | + | 0.272508i | 0.896455 | − | 0.443135i | \(-0.146134\pi\) |
−0.698466 | + | 0.715643i | \(0.746134\pi\) | |||||||
\(168\) | −11886.0 | − | 36581.5i | −0.421133 | − | 1.29611i | ||||
\(169\) | 1106.09 | − | 3404.19i | 0.0387272 | − | 0.119190i | ||||
\(170\) | −16574.1 | − | 12041.8i | −0.573498 | − | 0.416671i | ||||
\(171\) | 10414.3 | − | 14334.0i | 0.356154 | − | 0.490204i | ||||
\(172\) | −11168.0 | − | 3628.69i | −0.377500 | − | 0.122657i | ||||
\(173\) | 21544.3 | − | 7000.16i | 0.719847 | − | 0.233892i | 0.0738899 | − | 0.997266i | \(-0.476459\pi\) |
0.645957 | + | 0.763374i | \(0.276459\pi\) | |||||||
\(174\) | 21255.3 | − | 15442.9i | 0.702052 | − | 0.510071i | ||||
\(175\) | 13752.4i | 0.449057i | ||||||||
\(176\) | 71502.0 | − | 35633.6i | 2.30830 | − | 1.15036i | ||||
\(177\) | −25143.3 | −0.802558 | ||||||||
\(178\) | 6483.04 | + | 8923.14i | 0.204616 | + | 0.281629i | ||||
\(179\) | 79.4713 | + | 244.588i | 0.00248030 | + | 0.00763358i | 0.952289 | − | 0.305198i | \(-0.0987226\pi\) |
−0.949809 | + | 0.312831i | \(0.898723\pi\) | |||||||
\(180\) | −10093.0 | + | 31063.2i | −0.311514 | + | 0.958741i | ||||
\(181\) | 41978.1 | + | 30498.9i | 1.28134 | + | 0.930951i | 0.999593 | − | 0.0285361i | \(-0.00908454\pi\) |
0.281752 | + | 0.959487i | \(0.409085\pi\) | |||||||
\(182\) | −29504.1 | + | 40608.9i | −0.890716 | + | 1.22597i | ||||
\(183\) | 9912.52 | + | 3220.77i | 0.295993 | + | 0.0961741i | ||||
\(184\) | −48239.3 | + | 15673.9i | −1.42484 | + | 0.462957i | ||||
\(185\) | −4554.28 | + | 3308.88i | −0.133069 | + | 0.0966801i | ||||
\(186\) | 67915.0i | 1.96309i | ||||||||
\(187\) | −4831.09 | − | 9694.02i | −0.138153 | − | 0.277218i | ||||
\(188\) | 84285.6 | 2.38472 | ||||||||
\(189\) | 3521.44 | + | 4846.85i | 0.0985818 | + | 0.135686i | ||||
\(190\) | −46410.2 | − | 142836.i | −1.28560 | − | 3.95667i | ||||
\(191\) | 9798.08 | − | 30155.4i | 0.268580 | − | 0.826605i | −0.722267 | − | 0.691615i | \(-0.756900\pi\) |
0.990847 | − | 0.134990i | \(-0.0431004\pi\) | |||||||
\(192\) | −22390.9 | − | 16268.0i | −0.607393 | − | 0.441297i | ||||
\(193\) | −27719.4 | + | 38152.5i | −0.744166 | + | 1.02426i | 0.254203 | + | 0.967151i | \(0.418187\pi\) |
−0.998368 | + | 0.0571051i | \(0.981813\pi\) | |||||||
\(194\) | −46310.9 | − | 15047.3i | −1.23050 | − | 0.399812i | ||||
\(195\) | 24037.2 | − | 7810.17i | 0.632143 | − | 0.205396i | ||||
\(196\) | 18364.6 | − | 13342.6i | 0.478044 | − | 0.347320i | ||||
\(197\) | 17794.4i | 0.458512i | 0.973366 | + | 0.229256i | \(0.0736293\pi\) | ||||
−0.973366 | + | 0.229256i | \(0.926371\pi\) | |||||||
\(198\) | −17332.7 | + | 17026.6i | −0.442114 | + | 0.434308i | ||||
\(199\) | −3961.00 | −0.100023 | −0.0500114 | − | 0.998749i | \(-0.515926\pi\) | ||||
−0.0500114 | + | 0.998749i | \(0.515926\pi\) | |||||||
\(200\) | 32813.9 | + | 45164.4i | 0.820347 | + | 1.12911i | ||||
\(201\) | 8008.93 | + | 24648.9i | 0.198236 | + | 0.610107i | ||||
\(202\) | −2934.83 | + | 9032.47i | −0.0719250 | + | 0.221362i | ||||
\(203\) | −23487.9 | − | 17065.0i | −0.569971 | − | 0.414108i | ||||
\(204\) | −10746.8 | + | 14791.7i | −0.258237 | + | 0.355433i | ||||
\(205\) | 17040.1 | + | 5536.66i | 0.405475 | + | 0.131747i | ||||
\(206\) | −77578.2 | + | 25206.7i | −1.82812 | + | 0.593993i | ||||
\(207\) | 6391.44 | − | 4643.65i | 0.149162 | − | 0.108372i | ||||
\(208\) | 104355.i | 2.41205i | ||||||||
\(209\) | 13119.2 | − | 78310.9i | 0.300341 | − | 1.79279i | ||||
\(210\) | 50783.3 | 1.15155 | ||||||||
\(211\) | −985.500 | − | 1356.42i | −0.0221356 | − | 0.0304671i | 0.797806 | − | 0.602915i | \(-0.205994\pi\) |
−0.819941 | + | 0.572448i | \(0.805994\pi\) | |||||||
\(212\) | −26780.1 | − | 82420.6i | −0.595854 | − | 1.83385i | ||||
\(213\) | 8691.06 | − | 26748.3i | 0.191564 | − | 0.589573i | ||||
\(214\) | −79188.8 | − | 57534.0i | −1.72916 | − | 1.25631i | ||||
\(215\) | 5403.60 | − | 7437.41i | 0.116898 | − | 0.160896i | ||||
\(216\) | 23129.7 | + | 7515.28i | 0.495749 | + | 0.161079i | ||||
\(217\) | 71375.4 | − | 23191.3i | 1.51576 | − | 0.492499i | ||||
\(218\) | 28133.6 | − | 20440.3i | 0.591988 | − | 0.430104i | ||||
\(219\) | − | 10525.7i | − | 0.219464i | ||||||
\(220\) | 21609.3 | + | 144769.i | 0.446474 | + | 2.99110i | ||||
\(221\) | 14148.1 | 0.289677 | ||||||||
\(222\) | 4155.02 | + | 5718.90i | 0.0843078 | + | 0.116040i | ||||
\(223\) | −10870.5 | − | 33456.0i | −0.218595 | − | 0.672766i | −0.998879 | − | 0.0473403i | \(-0.984925\pi\) |
0.780284 | − | 0.625425i | \(-0.215075\pi\) | |||||||
\(224\) | −28195.0 | + | 86775.3i | −0.561922 | + | 1.72942i | ||||
\(225\) | −7034.66 | − | 5110.98i | −0.138956 | − | 0.100958i | ||||
\(226\) | −25247.8 | + | 34750.6i | −0.494319 | + | 0.680371i | ||||
\(227\) | 79303.3 | + | 25767.2i | 1.53900 | + | 0.500053i | 0.951101 | − | 0.308879i | \(-0.0999538\pi\) |
0.587903 | + | 0.808932i | \(0.299954\pi\) | |||||||
\(228\) | −127475. | + | 41419.2i | −2.45220 | + | 0.796768i | ||||
\(229\) | 17206.3 | − | 12501.1i | 0.328108 | − | 0.238384i | −0.411519 | − | 0.911401i | \(-0.635002\pi\) |
0.739627 | + | 0.673017i | \(0.235002\pi\) | |||||||
\(230\) | − | 66966.9i | − | 1.26592i | ||||||
\(231\) | 23812.9 | + | 12401.6i | 0.446260 | + | 0.232410i | ||||
\(232\) | −117855. | −2.18964 | ||||||||
\(233\) | −41041.6 | − | 56488.9i | −0.755984 | − | 1.04052i | −0.997538 | − | 0.0701350i | \(-0.977657\pi\) |
0.241554 | − | 0.970387i | \(-0.422343\pi\) | |||||||
\(234\) | −9807.39 | − | 30184.1i | −0.179111 | − | 0.551247i | ||||
\(235\) | −20390.7 | + | 62756.1i | −0.369229 | + | 1.13637i | ||||
\(236\) | 153882. | + | 111802.i | 2.76290 | + | 2.00736i | ||||
\(237\) | −9466.13 | + | 13029.0i | −0.168529 | + | 0.231961i | ||||
\(238\) | 27036.3 | + | 8784.64i | 0.477303 | + | 0.155085i | ||||
\(239\) | −96280.6 | + | 31283.5i | −1.68556 | + | 0.547670i | −0.985976 | − | 0.166885i | \(-0.946629\pi\) |
−0.699579 | + | 0.714555i | \(0.746629\pi\) | |||||||
\(240\) | 85413.9 | − | 62056.8i | 1.48288 | − | 1.07738i | ||||
\(241\) | 73340.5i | 1.26273i | 0.775487 | + | 0.631364i | \(0.217505\pi\) | ||||
−0.775487 | + | 0.631364i | \(0.782495\pi\) | |||||||
\(242\) | −35486.5 | + | 102940.i | −0.605943 | + | 1.75774i | ||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | −46345.2 | − | 63788.7i | −0.778439 | − | 1.07143i | ||||
\(245\) | 5491.63 | + | 16901.5i | 0.0914891 | + | 0.281574i | ||||
\(246\) | 6952.49 | − | 21397.6i | 0.114887 | − | 0.353585i | ||||
\(247\) | 83910.3 | + | 60964.4i | 1.37538 | + | 0.999269i | ||||
\(248\) | 179070. | − | 246468.i | 2.91152 | − | 4.00736i | ||||
\(249\) | 28951.5 | + | 9406.90i | 0.466951 | + | 0.151722i | ||||
\(250\) | 65942.0 | − | 21425.9i | 1.05507 | − | 0.342814i | ||||
\(251\) | 28293.2 | − | 20556.2i | 0.449091 | − | 0.326284i | −0.340146 | − | 0.940373i | \(-0.610476\pi\) |
0.789237 | + | 0.614089i | \(0.210476\pi\) | |||||||
\(252\) | − | 45322.1i | − | 0.713688i | ||||||
\(253\) | 16353.8 | − | 31401.5i | 0.255492 | − | 0.490580i | ||||
\(254\) | −90521.2 | −1.40308 | ||||||||
\(255\) | −8413.47 | − | 11580.2i | −0.129388 | − | 0.178088i | ||||
\(256\) | −13865.6 | − | 42674.0i | −0.211572 | − | 0.651153i | ||||
\(257\) | 1580.93 | − | 4865.60i | 0.0239357 | − | 0.0736666i | −0.938375 | − | 0.345618i | \(-0.887669\pi\) |
0.962311 | + | 0.271952i | \(0.0876692\pi\) | |||||||
\(258\) | −9339.31 | − | 6785.40i | −0.140306 | − | 0.101938i | ||||
\(259\) | 4591.46 | − | 6319.60i | 0.0684464 | − | 0.0942084i | ||||
\(260\) | −181841. | − | 59083.8i | −2.68996 | − | 0.874021i | ||||
\(261\) | 17458.3 | − | 5672.54i | 0.256283 | − | 0.0832715i | ||||
\(262\) | −106680. | + | 77507.5i | −1.55410 | + | 1.12912i | ||||
\(263\) | 79876.9i | 1.15481i | 0.816458 | + | 0.577404i | \(0.195934\pi\) | ||||
−0.816458 | + | 0.577404i | \(0.804066\pi\) | |||||||
\(264\) | 107795. | − | 16090.3i | 1.54665 | − | 0.230864i | ||||
\(265\) | 67846.2 | 0.966127 | ||||||||
\(266\) | 122495. | + | 168600.i | 1.73123 | + | 2.38284i | ||||
\(267\) | 2381.37 | + | 7329.11i | 0.0334045 | + | 0.102808i | ||||
\(268\) | 60587.4 | − | 186469.i | 0.843554 | − | 2.59619i | ||||
\(269\) | −89030.6 | − | 64684.5i | −1.23037 | − | 0.893914i | −0.233450 | − | 0.972369i | \(-0.575002\pi\) |
−0.996918 | + | 0.0784544i | \(0.975002\pi\) | |||||||
\(270\) | −18873.3 | + | 25976.9i | −0.258893 | + | 0.356335i | ||||
\(271\) | −54208.5 | − | 17613.4i | −0.738123 | − | 0.239831i | −0.0842599 | − | 0.996444i | \(-0.526853\pi\) |
−0.653863 | + | 0.756613i | \(0.726853\pi\) | |||||||
\(272\) | 56208.0 | − | 18263.1i | 0.759731 | − | 0.246852i | ||||
\(273\) | −28373.0 | + | 20614.2i | −0.380698 | + | 0.276593i | ||||
\(274\) | − | 112944.i | − | 1.50439i | ||||||
\(275\) | −38432.3 | − | 6438.46i | −0.508196 | − | 0.0851367i | ||||
\(276\) | −59765.3 | −0.784568 | ||||||||
\(277\) | −62705.4 | − | 86306.6i | −0.817233 | − | 1.12482i | −0.990167 | − | 0.139891i | \(-0.955325\pi\) |
0.172934 | − | 0.984933i | \(-0.444675\pi\) | |||||||
\(278\) | 59702.0 | + | 183744.i | 0.772501 | + | 2.37751i | ||||
\(279\) | −14663.3 | + | 45129.1i | −0.188375 | + | 0.579760i | ||||
\(280\) | −184296. | − | 133899.i | −2.35072 | − | 1.70790i | ||||
\(281\) | 9259.35 | − | 12744.4i | 0.117265 | − | 0.161401i | −0.746349 | − | 0.665554i | \(-0.768195\pi\) |
0.863614 | + | 0.504153i | \(0.168195\pi\) | |||||||
\(282\) | 78804.1 | + | 25605.0i | 0.990948 | + | 0.321978i | ||||
\(283\) | −49311.7 | + | 16022.3i | −0.615711 | + | 0.200057i | −0.600235 | − | 0.799824i | \(-0.704926\pi\) |
−0.0154758 | + | 0.999880i | \(0.504926\pi\) | |||||||
\(284\) | −172130. | + | 125060.i | −2.13412 | + | 1.55053i | ||||
\(285\) | − | 104934.i | − | 1.29189i | ||||||
\(286\) | −99672.5 | − | 101464.i | −1.21855 | − | 1.24045i | ||||
\(287\) | −24861.9 | −0.301836 | ||||||||
\(288\) | −33909.1 | − | 46671.9i | −0.408819 | − | 0.562691i | ||||
\(289\) | 23333.4 | + | 71812.7i | 0.279371 | + | 0.859816i | ||||
\(290\) | 48083.6 | − | 147986.i | 0.571743 | − | 1.75964i | ||||
\(291\) | −27524.5 | − | 19997.7i | −0.325038 | − | 0.236154i | ||||
\(292\) | −46803.6 | + | 64419.6i | −0.548925 | + | 0.755531i | ||||
\(293\) | 13682.8 | + | 4445.80i | 0.159382 | + | 0.0517863i | 0.387621 | − | 0.921819i | \(-0.373297\pi\) |
−0.228239 | + | 0.973605i | \(0.573297\pi\) | |||||||
\(294\) | 21223.6 | − | 6895.95i | 0.245541 | − | 0.0797810i | ||||
\(295\) | −120472. | + | 87527.8i | −1.38433 | + | 1.00578i | ||||
\(296\) | − | 31709.8i | − | 0.361917i | ||||||
\(297\) | −15193.6 | + | 7571.85i | −0.172246 | + | 0.0858399i | ||||
\(298\) | 241439. | 2.71879 | ||||||||
\(299\) | 27183.5 | + | 37414.9i | 0.304063 | + | 0.418507i | ||||
\(300\) | 20327.1 | + | 62560.4i | 0.225857 | + | 0.695116i | ||||
\(301\) | −3942.00 | + | 12132.2i | −0.0435094 | + | 0.133908i | ||||
\(302\) | 180183. | + | 130911.i | 1.97560 | + | 1.43536i | ||||
\(303\) | −3900.35 | + | 5368.37i | −0.0424833 | + | 0.0584733i | ||||
\(304\) | 412056. | + | 133885.i | 4.45871 | + | 1.44872i | ||||
\(305\) | 58706.8 | − | 19075.0i | 0.631086 | − | 0.205052i | ||||
\(306\) | −14541.4 | + | 10565.0i | −0.155297 | + | 0.112830i | ||||
\(307\) | 81285.6i | 0.862455i | 0.902243 | + | 0.431228i | \(0.141919\pi\) | ||||
−0.902243 | + | 0.431228i | \(0.858081\pi\) | |||||||
\(308\) | −90594.6 | − | 181786.i | −0.954994 | − | 1.91628i | ||||
\(309\) | −56992.6 | −0.596900 | ||||||||
\(310\) | 236422. | + | 325407.i | 2.46017 | + | 3.38613i | ||||
\(311\) | 24970.5 | + | 76851.3i | 0.258170 | + | 0.794567i | 0.993188 | + | 0.116519i | \(0.0371737\pi\) |
−0.735018 | + | 0.678048i | \(0.762826\pi\) | |||||||
\(312\) | −43993.8 | + | 135399.i | −0.451942 | + | 1.39093i | ||||
\(313\) | −77100.6 | − | 56016.8i | −0.786990 | − | 0.571781i | 0.120079 | − | 0.992764i | \(-0.461685\pi\) |
−0.907069 | + | 0.420983i | \(0.861685\pi\) | |||||||
\(314\) | 22481.9 | − | 30943.7i | 0.228021 | − | 0.313843i | ||||
\(315\) | 33745.2 | + | 10964.5i | 0.340088 | + | 0.110501i | ||||
\(316\) | 115869. | − | 37648.2i | 1.16036 | − | 0.377025i | ||||
\(317\) | 2501.97 | − | 1817.79i | 0.0248980 | − | 0.0180894i | −0.575267 | − | 0.817966i | \(-0.695102\pi\) |
0.600165 | + | 0.799876i | \(0.295102\pi\) | |||||||
\(318\) | − | 85195.9i | − | 0.842489i | ||||||
\(319\) | 58686.1 | − | 57650.0i | 0.576705 | − | 0.566523i | ||||
\(320\) | −163915. | −1.60073 | ||||||||
\(321\) | −40198.5 | − | 55328.4i | −0.390121 | − | 0.536956i | ||||
\(322\) | 28715.2 | + | 88376.4i | 0.276950 | + | 0.852363i | ||||
\(323\) | 18151.7 | − | 55865.3i | 0.173986 | − | 0.535473i | ||||
\(324\) | 23183.3 | + | 16843.6i | 0.220844 | + | 0.160452i | ||||
\(325\) | 29919.2 | − | 41180.3i | 0.283259 | − | 0.389873i | ||||
\(326\) | −199879. | − | 64944.5i | −1.88075 | − | 0.611093i | ||||
\(327\) | 23107.8 | − | 7508.19i | 0.216104 | − | 0.0702166i | ||||
\(328\) | −81649.6 | + | 59321.9i | −0.758938 | + | 0.551401i | ||||
\(329\) | − | 91562.9i | − | 0.845917i | ||||||
\(330\) | −23775.3 | + | 141919.i | −0.218322 | + | 1.30320i | ||||
\(331\) | −188225. | −1.71799 | −0.858996 | − | 0.511982i | \(-0.828912\pi\) | ||||
−0.858996 | + | 0.511982i | \(0.828912\pi\) | |||||||
\(332\) | −135360. | − | 186307.i | −1.22805 | − | 1.69026i | ||||
\(333\) | 1526.24 | + | 4697.27i | 0.0137636 | + | 0.0423601i | ||||
\(334\) | 21589.0 | − | 66444.2i | 0.193526 | − | 0.595613i | ||||
\(335\) | 124181. | + | 90222.5i | 1.10653 | + | 0.803943i | ||||
\(336\) | −86111.1 | + | 118522.i | −0.762747 | + | 1.04983i | ||||
\(337\) | −3247.89 | − | 1055.30i | −0.0285984 | − | 0.00929218i | 0.294683 | − | 0.955595i | \(-0.404786\pi\) |
−0.323281 | + | 0.946303i | \(0.604786\pi\) | |||||||
\(338\) | −25316.9 | + | 8225.96i | −0.221604 | + | 0.0720034i | ||||
\(339\) | −24279.9 | + | 17640.4i | −0.211275 | + | 0.153500i | ||||
\(340\) | 108284.i | 0.936714i | ||||||||
\(341\) | 31394.4 | + | 210323.i | 0.269987 | + | 1.80875i | ||||
\(342\) | −131767. | −1.12656 | ||||||||
\(343\) | −74759.9 | − | 102898.i | −0.635448 | − | 0.874620i | ||||
\(344\) | 16002.1 | + | 49249.5i | 0.135226 | + | 0.416183i | ||||
\(345\) | 14458.6 | − | 44499.1i | 0.121476 | − | 0.373864i | ||||
\(346\) | −136295. | − | 99024.3i | −1.13849 | − | 0.827160i | ||||
\(347\) | 122720. | − | 168910.i | 1.01920 | − | 1.40280i | 0.106431 | − | 0.994320i | \(-0.466058\pi\) |
0.912766 | − | 0.408484i | \(-0.133942\pi\) | |||||||
\(348\) | −132072. | − | 42912.7i | −1.09056 | − | 0.354346i | ||||
\(349\) | 75500.1 | − | 24531.5i | 0.619865 | − | 0.201406i | 0.0177844 | − | 0.999842i | \(-0.494339\pi\) |
0.602080 | + | 0.798436i | \(0.294339\pi\) | |||||||
\(350\) | 82743.2 | − | 60116.5i | 0.675455 | − | 0.490747i | ||||
\(351\) | − | 22174.6i | − | 0.179987i | ||||||
\(352\) | −229302. | − | 119419.i | −1.85064 | − | 0.963805i | ||||
\(353\) | −136810. | −1.09792 | −0.548958 | − | 0.835850i | \(-0.684975\pi\) | ||||
−0.548958 | + | 0.835850i | \(0.684975\pi\) | |||||||
\(354\) | 109910. | + | 151279.i | 0.877066 | + | 1.20718i | ||||
\(355\) | −51472.7 | − | 158417.i | −0.408432 | − | 1.25703i | ||||
\(356\) | 18015.0 | − | 55444.6i | 0.142146 | − | 0.437481i | ||||
\(357\) | 16068.8 | + | 11674.7i | 0.126080 | + | 0.0916028i | ||||
\(358\) | 1124.20 | − | 1547.33i | 0.00877158 | − | 0.0120730i | ||||
\(359\) | 150057. | + | 48756.5i | 1.16431 | + | 0.378306i | 0.826515 | − | 0.562914i | \(-0.190320\pi\) |
0.337792 | + | 0.941221i | \(0.390320\pi\) | |||||||
\(360\) | 136985. | − | 44509.2i | 1.05698 | − | 0.343435i | ||||
\(361\) | 242947. | − | 176512.i | 1.86422 | − | 1.35444i | ||||
\(362\) | − | 385889.i | − | 2.94473i | ||||||
\(363\) | −45806.0 | + | 60741.2i | −0.347624 | + | 0.460968i | ||||
\(364\) | 265312. | 2.00241 | ||||||||
\(365\) | −36641.7 | − | 50432.9i | −0.275036 | − | 0.378555i | ||||
\(366\) | −23952.9 | − | 73719.3i | −0.178811 | − | 0.550325i | ||||
\(367\) | −71021.8 | + | 218582.i | −0.527302 | + | 1.62287i | 0.232417 | + | 0.972616i | \(0.425337\pi\) |
−0.759719 | + | 0.650252i | \(0.774663\pi\) | |||||||
\(368\) | 156292. | + | 113553.i | 1.15410 | + | 0.838500i | ||||
\(369\) | 9239.78 | − | 12717.5i | 0.0678592 | − | 0.0934002i | ||||
\(370\) | 39816.7 | + | 12937.2i | 0.290845 | + | 0.0945013i | ||||
\(371\) | −89536.9 | + | 29092.3i | −0.650510 | + | 0.211364i | ||||
\(372\) | 290413. | − | 210997.i | 2.09860 | − | 1.52472i | ||||
\(373\) | 72069.3i | 0.518004i | 0.965877 | + | 0.259002i | \(0.0833936\pi\) | ||||
−0.965877 | + | 0.259002i | \(0.916606\pi\) | |||||||
\(374\) | −37207.2 | + | 71443.0i | −0.266001 | + | 0.510759i | ||||
\(375\) | 48444.1 | 0.344491 | ||||||||
\(376\) | −218474. | − | 300703.i | −1.54534 | − | 2.12698i | ||||
\(377\) | 33206.6 | + | 102199.i | 0.233637 | + | 0.719060i | ||||
\(378\) | 13768.3 | − | 42374.5i | 0.0963602 | − | 0.296566i | ||||
\(379\) | −150282. | − | 109186.i | −1.04623 | − | 0.760133i | −0.0747411 | − | 0.997203i | \(-0.523813\pi\) |
−0.971493 | + | 0.237070i | \(0.923813\pi\) | |||||||
\(380\) | −466597. | + | 642216.i | −3.23128 | + | 4.44748i | ||||
\(381\) | −60150.8 | − | 19544.2i | −0.414373 | − | 0.134638i | ||||
\(382\) | −224265. | + | 72868.2i | −1.53686 | + | 0.499357i | ||||
\(383\) | 58599.2 | − | 42574.8i | 0.399479 | − | 0.290239i | −0.369850 | − | 0.929092i | \(-0.620591\pi\) |
0.769329 | + | 0.638853i | \(0.220591\pi\) | |||||||
\(384\) | 28193.7i | 0.191201i | ||||||||
\(385\) | 157269. | − | 23475.1i | 1.06101 | − | 0.158375i | ||||
\(386\) | 350722. | 2.35390 | ||||||||
\(387\) | −4740.90 | − | 6525.28i | −0.0316547 | − | 0.0435690i | ||||
\(388\) | 79533.9 | + | 244780.i | 0.528310 | + | 1.62597i | ||||
\(389\) | −53473.4 | + | 164574.i | −0.353378 | + | 1.08758i | 0.603567 | + | 0.797313i | \(0.293746\pi\) |
−0.956944 | + | 0.290272i | \(0.906254\pi\) | |||||||
\(390\) | −152066. | − | 110483.i | −0.999779 | − | 0.726382i | ||||
\(391\) | 15395.2 | − | 21189.6i | 0.100700 | − | 0.138602i | ||||
\(392\) | −95204.3 | − | 30933.7i | −0.619561 | − | 0.201308i | ||||
\(393\) | −87622.5 | + | 28470.3i | −0.567324 | + | 0.184335i | ||||
\(394\) | 107063. | − | 77785.5i | 0.689676 | − | 0.501079i | ||||
\(395\) | 95380.1i | 0.611313i | ||||||||
\(396\) | 126657. | + | 21218.5i | 0.807678 | + | 0.135308i | ||||
\(397\) | 264583. | 1.67873 | 0.839367 | − | 0.543566i | \(-0.182926\pi\) | ||||
0.839367 | + | 0.543566i | \(0.182926\pi\) | |||||||
\(398\) | 17314.9 | + | 23832.0i | 0.109309 | + | 0.150451i | ||||
\(399\) | 44995.3 | + | 138481.i | 0.282632 | + | 0.869853i | ||||
\(400\) | 65706.3 | − | 202223.i | 0.410664 | − | 1.26389i | ||||
\(401\) | −107684. | − | 78237.2i | −0.669674 | − | 0.486547i | 0.200242 | − | 0.979747i | \(-0.435827\pi\) |
−0.869916 | + | 0.493200i | \(0.835827\pi\) | |||||||
\(402\) | 113294. | − | 155936.i | 0.701061 | − | 0.964928i | ||||
\(403\) | −264182. | − | 85837.9i | −1.62665 | − | 0.528529i | ||||
\(404\) | 47741.9 | − | 15512.3i | 0.292507 | − | 0.0950414i | ||||
\(405\) | −18149.8 | + | 13186.6i | −0.110653 | + | 0.0803938i | ||||
\(406\) | 215916.i | 1.30988i | ||||||||
\(407\) | 15511.1 | + | 15789.9i | 0.0936386 | + | 0.0953215i | ||||
\(408\) | 80628.3 | 0.484359 | ||||||||
\(409\) | 1337.05 | + | 1840.29i | 0.00799285 | + | 0.0110012i | 0.812995 | − | 0.582271i | \(-0.197836\pi\) |
−0.805002 | + | 0.593272i | \(0.797836\pi\) | |||||||
\(410\) | −41176.0 | − | 126727.i | −0.244950 | − | 0.753878i | ||||
\(411\) | 24385.3 | − | 75050.4i | 0.144359 | − | 0.444293i | ||||
\(412\) | 348806. | + | 253422.i | 2.05489 | + | 1.49297i | ||||
\(413\) | 121455. | − | 167169.i | 0.712058 | − | 0.980064i | ||||
\(414\) | −55878.4 | − | 18156.0i | −0.326020 | − | 0.105930i | ||||
\(415\) | 171465. | − | 55712.3i | 0.995585 | − | 0.323485i | ||||
\(416\) | 273213. | − | 198501.i | 1.57876 | − | 1.14703i | ||||
\(417\) | 134987.i | 0.776281i | ||||||||
\(418\) | −528518. | + | 263391.i | −3.02487 | + | 1.50747i | ||||
\(419\) | −47549.2 | −0.270841 | −0.135421 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135421 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(420\) | −157773. | − | 217156.i | −0.894404 | − | 1.23104i | ||||
\(421\) | −28298.3 | − | 87093.3i | −0.159660 | − | 0.491383i | 0.838943 | − | 0.544219i | \(-0.183174\pi\) |
−0.998603 | + | 0.0528358i | \(0.983174\pi\) | |||||||
\(422\) | −3853.16 | + | 11858.8i | −0.0216368 | + | 0.0665911i | ||||
\(423\) | 46836.6 | + | 34028.7i | 0.261761 | + | 0.190180i | ||||
\(424\) | −224634. | + | 309182.i | −1.24952 | + | 1.71982i | ||||
\(425\) | −27416.8 | − | 8908.25i | −0.151788 | − | 0.0493191i | ||||
\(426\) | −198927. | + | 64635.3i | −1.09616 | + | 0.356164i | ||||
\(427\) | −69296.2 | + | 50346.6i | −0.380061 | + | 0.276131i | ||||
\(428\) | 517367.i | 2.82430i | ||||||||
\(429\) | −44325.0 | − | 88942.2i | −0.240843 | − | 0.483274i | ||||
\(430\) | −68369.3 | −0.369764 | ||||||||
\(431\) | −677.399 | − | 932.359i | −0.00364661 | − | 0.00501913i | 0.807190 | − | 0.590292i | \(-0.200987\pi\) |
−0.810836 | + | 0.585273i | \(0.800987\pi\) | |||||||
\(432\) | −28624.0 | − | 88095.7i | −0.153378 | − | 0.472049i | ||||
\(433\) | −56561.5 | + | 174078.i | −0.301679 | + | 0.928473i | 0.679217 | + | 0.733938i | \(0.262320\pi\) |
−0.980896 | + | 0.194535i | \(0.937680\pi\) | |||||||
\(434\) | −451541. | − | 328064.i | −2.39727 | − | 1.74172i | ||||
\(435\) | 63902.5 | − | 87954.3i | 0.337707 | − | 0.464813i | ||||
\(436\) | −174810. | − | 56799.3i | −0.919590 | − | 0.298793i | ||||
\(437\) | 182613. | − | 59334.4i | 0.956242 | − | 0.310702i | ||||
\(438\) | −63329.7 | + | 46011.7i | −0.330110 | + | 0.239839i | ||||
\(439\) | 171391.i | 0.889319i | 0.895700 | + | 0.444660i | \(0.146675\pi\) | ||||
−0.895700 | + | 0.444660i | \(0.853325\pi\) | |||||||
\(440\) | 460477. | − | 452346.i | 2.37849 | − | 2.33650i | ||||
\(441\) | 15591.8 | 0.0801714 | ||||||||
\(442\) | −61846.5 | − | 85124.3i | −0.316570 | − | 0.435722i | ||||
\(443\) | −6465.23 | − | 19897.9i | −0.0329440 | − | 0.101391i | 0.933232 | − | 0.359273i | \(-0.116975\pi\) |
−0.966176 | + | 0.257882i | \(0.916975\pi\) | |||||||
\(444\) | 11546.0 | − | 35534.8i | 0.0585685 | − | 0.180255i | ||||
\(445\) | 36923.8 | + | 26826.7i | 0.186460 | + | 0.135471i | ||||
\(446\) | −153774. | + | 211652.i | −0.773060 | + | 1.06403i | ||||
\(447\) | 160435. | + | 52128.5i | 0.802941 | + | 0.260891i | ||||
\(448\) | 216319. | − | 70286.4i | 1.07780 | − | 0.350199i | ||||
\(449\) | −298589. | + | 216938.i | −1.48109 | + | 1.07607i | −0.503885 | + | 0.863771i | \(0.668096\pi\) |
−0.977204 | + | 0.212303i | \(0.931904\pi\) | |||||||
\(450\) | 64667.0i | 0.319343i | ||||||||
\(451\) | 11639.6 | − | 69479.1i | 0.0572251 | − | 0.341587i | ||||
\(452\) | 227038. | 1.11127 | ||||||||
\(453\) | 91466.0 | + | 125892.i | 0.445721 | + | 0.613483i | ||||
\(454\) | −191631. | − | 589778.i | −0.929722 | − | 2.86139i | ||||
\(455\) | −64185.2 | + | 197542.i | −0.310036 | + | 0.954192i | ||||
\(456\) | 478194. | + | 347428.i | 2.29972 | + | 1.67084i | ||||
\(457\) | −18538.9 | + | 25516.6i | −0.0887670 | + | 0.122177i | −0.851091 | − | 0.525018i | \(-0.824058\pi\) |
0.762324 | + | 0.647196i | \(0.224058\pi\) | |||||||
\(458\) | −150430. | − | 48877.6i | −0.717138 | − | 0.233012i | ||||
\(459\) | −11943.7 | + | 3880.76i | −0.0566911 | + | 0.0184201i | ||||
\(460\) | −286359. | + | 208052.i | −1.35330 | + | 0.983232i | ||||
\(461\) | − | 187345.i | − | 0.881538i | −0.897621 | − | 0.440769i | \(-0.854706\pi\) | ||
0.897621 | − | 0.440769i | \(-0.145294\pi\) | |||||||
\(462\) | −29478.1 | − | 197486.i | −0.138107 | − | 0.925233i | ||||
\(463\) | 406644. | 1.89693 | 0.948466 | − | 0.316878i | \(-0.102634\pi\) | ||||
0.948466 | + | 0.316878i | \(0.102634\pi\) | |||||||
\(464\) | 263847. | + | 363155.i | 1.22551 | + | 1.68677i | ||||
\(465\) | 86843.4 | + | 267277.i | 0.401634 | + | 1.23610i | ||||
\(466\) | −160467. | + | 493866.i | −0.738947 | + | 2.27425i | ||||
\(467\) | −184337. | − | 133929.i | −0.845238 | − | 0.614102i | 0.0785907 | − | 0.996907i | \(-0.474958\pi\) |
−0.923829 | + | 0.382805i | \(0.874958\pi\) | |||||||
\(468\) | −98601.3 | + | 135713.i | −0.450185 | + | 0.619626i | ||||
\(469\) | −202569. | − | 65818.6i | −0.920930 | − | 0.299228i | ||||
\(470\) | 466717. | − | 151645.i | 2.11280 | − | 0.686489i | ||||
\(471\) | 21620.1 | − | 15707.9i | 0.0974575 | − | 0.0708070i | ||||
\(472\) | − | 838800.i | − | 3.76508i | ||||||
\(473\) | −32059.1 | − | 16696.2i | −0.143294 | − | 0.0746271i | ||||
\(474\) | 119771. | 0.533082 | ||||||||
\(475\) | −124219. | − | 170973.i | −0.550555 | − | 0.757773i | ||||
\(476\) | −46431.9 | − | 142903.i | −0.204929 | − | 0.630706i | ||||
\(477\) | 18394.4 | − | 56612.2i | 0.0808442 | − | 0.248813i | ||||
\(478\) | 609098. | + | 442536.i | 2.66582 | + | 1.93683i | ||||
\(479\) | 113070. | − | 155627.i | 0.492806 | − | 0.678289i | −0.488097 | − | 0.872790i | \(-0.662309\pi\) |
0.980902 | + | 0.194501i | \(0.0623087\pi\) | |||||||
\(480\) | −324944. | − | 105581.i | −1.41035 | − | 0.458249i | ||||
\(481\) | −27497.5 | + | 8934.46i | −0.118851 | + | 0.0386170i | ||||
\(482\) | 441264. | − | 320597.i | 1.89935 | − | 1.37996i | ||||
\(483\) | 64925.4i | 0.278305i | ||||||||
\(484\) | 550433. | − | 168068.i | 2.34971 | − | 0.717455i | ||||
\(485\) | −201496. | −0.856609 | ||||||||
\(486\) | 16558.7 | + | 22791.0i | 0.0701056 | + | 0.0964921i | ||||
\(487\) | 69428.6 | + | 213679.i | 0.292739 | + | 0.900957i | 0.983972 | + | 0.178325i | \(0.0570679\pi\) |
−0.691233 | + | 0.722632i | \(0.742932\pi\) | |||||||
\(488\) | −107447. | + | 330689.i | −0.451186 | + | 1.38861i | ||||
\(489\) | −118796. | − | 86310.5i | −0.496804 | − | 0.360949i | ||||
\(490\) | 77684.6 | − | 106924.i | 0.323551 | − | 0.445330i | ||||
\(491\) | −28943.2 | − | 9404.21i | −0.120056 | − | 0.0390085i | 0.248373 | − | 0.968664i | \(-0.420104\pi\) |
−0.368429 | + | 0.929656i | \(0.620104\pi\) | |||||||
\(492\) | −113099. | + | 36747.9i | −0.467226 | + | 0.151811i | ||||
\(493\) | 49235.4 | − | 35771.6i | 0.202574 | − | 0.147179i | ||||
\(494\) | − | 771356.i | − | 3.16083i | ||||||
\(495\) | −46439.8 | + | 89171.0i | −0.189531 | + | 0.363926i | ||||
\(496\) | −1.16035e6 | −4.71657 | ||||||||
\(497\) | 135857. | + | 186992.i | 0.550010 | + | 0.757023i | ||||
\(498\) | −69959.0 | − | 215312.i | −0.282088 | − | 0.868178i | ||||
\(499\) | 44849.3 | − | 138032.i | 0.180117 | − | 0.554343i | −0.819713 | − | 0.572774i | \(-0.805867\pi\) |
0.999830 | + | 0.0184313i | \(0.00586721\pi\) | |||||||
\(500\) | −296488. | − | 215411.i | −1.18595 | − | 0.861643i | ||||
\(501\) | 28691.6 | − | 39490.6i | 0.114309 | − | 0.157332i | ||||
\(502\) | −247359. | − | 80371.8i | −0.981567 | − | 0.318931i | ||||
\(503\) | 30280.8 | − | 9838.83i | 0.119683 | − | 0.0388873i | −0.248563 | − | 0.968616i | \(-0.579958\pi\) |
0.368246 | + | 0.929728i | \(0.379958\pi\) | |||||||
\(504\) | −161694. | + | 117478.i | −0.636551 | + | 0.462482i | ||||
\(505\) | 39299.7i | 0.154101i | ||||||||
\(506\) | −260420. | + | 38872.2i | −1.01712 | + | 0.151823i | ||||
\(507\) | −18599.0 | −0.0723557 | ||||||||
\(508\) | 281230. | + | 387080.i | 1.08977 | + | 1.49994i | ||||
\(509\) | −47435.7 | − | 145992.i | −0.183092 | − | 0.563500i | 0.816818 | − | 0.576895i | \(-0.195736\pi\) |
−0.999910 | + | 0.0133953i | \(0.995736\pi\) | |||||||
\(510\) | −32895.5 | + | 101242.i | −0.126472 | + | 0.389242i | ||||
\(511\) | 69981.6 | + | 50844.6i | 0.268005 | + | 0.194717i | ||||
\(512\) | −247171. | + | 340201.i | −0.942882 | + | 1.29777i | ||||
\(513\) | −87558.7 | − | 28449.5i | −0.332709 | − | 0.108104i | ||||
\(514\) | −36185.4 | + | 11757.4i | −0.136964 | + | 0.0445024i | ||||
\(515\) | −273074. | + | 198400.i | −1.02959 | + | 0.748043i | ||||
\(516\) | 61016.8i | 0.229166i | ||||||||
\(517\) | 255881. | + | 42867.1i | 0.957321 | + | 0.160377i | ||||
\(518\) | −58093.7 | −0.216506 | ||||||||
\(519\) | −69187.3 | − | 95228.2i | −0.256857 | − | 0.353534i | ||||
\(520\) | 260553. | + | 801900.i | 0.963584 | + | 2.96561i | ||||
\(521\) | 67447.1 | − | 207581.i | 0.248478 | − | 0.764736i | −0.746567 | − | 0.665310i | \(-0.768299\pi\) |
0.995045 | − | 0.0994259i | \(-0.0317006\pi\) | |||||||
\(522\) | −110446. | − | 80243.7i | −0.405330 | − | 0.294490i | ||||
\(523\) | 243310. | − | 334887.i | 0.889521 | − | 1.22432i | −0.0841701 | − | 0.996451i | \(-0.526824\pi\) |
0.973692 | − | 0.227870i | \(-0.0731761\pi\) | |||||||
\(524\) | 662863. | + | 215377.i | 2.41413 | + | 0.784400i | ||||
\(525\) | 67961.9 | − | 22082.2i | 0.246574 | − | 0.0801167i | ||||
\(526\) | 480592. | − | 349170.i | 1.73702 | − | 1.26202i | ||||
\(527\) | 157317.i | 0.566440i | ||||||||
\(528\) | −290906. | − | 296134.i | −1.04348 | − | 1.06224i | ||||
\(529\) | −194225. | −0.694055 | ||||||||
\(530\) | −296580. | − | 408207.i | −1.05582 | − | 1.45321i | ||||
\(531\) | 40372.6 | + | 124254.i | 0.143185 | + | 0.440679i | ||||
\(532\) | 340389. | − | 1.04761e6i | 1.20269 | − | 3.70149i | ||||
\(533\) | 74447.0 | + | 54088.9i | 0.262055 | + | 0.190394i | ||||
\(534\) | 33686.9 | − | 46366.0i | 0.118135 | − | 0.162599i | ||||
\(535\) | −385213. | − | 125163.i | −1.34584 | − | 0.437290i | ||||
\(536\) | −822306. | + | 267184.i | −2.86223 | + | 0.929994i | ||||
\(537\) | 1081.10 | − | 785.468i | 0.00374903 | − | 0.00272383i | ||||
\(538\) | 818425.i | 2.82758i | ||||||||
\(539\) | 62538.6 | − | 31166.6i | 0.215264 | − | 0.107278i | ||||
\(540\) | 169716. | 0.582015 | ||||||||
\(541\) | 235574. | + | 324239.i | 0.804882 | + | 1.10783i | 0.992093 | + | 0.125506i | \(0.0400553\pi\) |
−0.187211 | + | 0.982320i | \(0.559945\pi\) | |||||||
\(542\) | 130991. | + | 403148.i | 0.445904 | + | 1.37235i | ||||
\(543\) | 83316.2 | − | 256421.i | 0.282573 | − | 0.869669i | ||||
\(544\) | −154732. | − | 112419.i | −0.522856 | − | 0.379877i | ||||
\(545\) | 84581.6 | − | 116417.i | 0.284763 | − | 0.391942i | ||||
\(546\) | 248057. | + | 80598.6i | 0.832082 | + | 0.270360i | ||||
\(547\) | −55348.4 | + | 17983.8i | −0.184982 | + | 0.0601044i | −0.400043 | − | 0.916496i | \(-0.631005\pi\) |
0.215061 | + | 0.976601i | \(0.431005\pi\) | |||||||
\(548\) | −482961. | + | 350892.i | −1.60824 | + | 1.16846i | ||||
\(549\) | − | 54157.6i | − | 0.179686i | ||||||
\(550\) | 129263. | + | 259379.i | 0.427316 | + | 0.857450i | ||||
\(551\) | 446148. | 1.46952 | ||||||||
\(552\) | 154916. | + | 213223.i | 0.508413 | + | 0.699771i | ||||
\(553\) | −40898.7 | − | 125873.i | −0.133740 | − | 0.411608i | ||||
\(554\) | −245169. | + | 754554.i | −0.798816 | + | 2.45850i | ||||
\(555\) | 23664.7 | + | 17193.4i | 0.0768273 | + | 0.0558183i | ||||
\(556\) | 600230. | − | 826146.i | 1.94164 | − | 2.67243i | ||||
\(557\) | 84762.1 | + | 27540.9i | 0.273207 | + | 0.0887703i | 0.442416 | − | 0.896810i | \(-0.354121\pi\) |
−0.169209 | + | 0.985580i | \(0.554121\pi\) | |||||||
\(558\) | 335625. | − | 109051.i | 1.07792 | − | 0.350236i | ||||
\(559\) | 38198.5 | − | 27752.8i | 0.122243 | − | 0.0888144i | ||||
\(560\) | 867651.i | 2.76674i | ||||||||
\(561\) | −40149.0 | + | 39440.1i | −0.127570 | + | 0.125318i | ||||
\(562\) | −117155. | −0.370925 | ||||||||
\(563\) | −273826. | − | 376890.i | −0.863890 | − | 1.18904i | −0.980628 | − | 0.195880i | \(-0.937244\pi\) |
0.116737 | − | 0.993163i | \(-0.462756\pi\) | |||||||
\(564\) | −135337. | − | 416526.i | −0.425461 | − | 1.30943i | ||||
\(565\) | −54925.8 | + | 169044.i | −0.172060 | + | 0.529546i | ||||
\(566\) | 311959. | + | 226652.i | 0.973790 | + | 0.707500i | ||||
\(567\) | 18297.9 | − | 25185.0i | 0.0569162 | − | 0.0783385i | ||||
\(568\) | 892343. | + | 289940.i | 2.76589 | + | 0.898693i | ||||
\(569\) | 123667. | − | 40181.9i | 0.381970 | − | 0.124110i | −0.111737 | − | 0.993738i | \(-0.535641\pi\) |
0.493707 | + | 0.869628i | \(0.335641\pi\) | |||||||
\(570\) | −631350. | + | 458703.i | −1.94321 | + | 1.41183i | ||||
\(571\) | − | 600320.i | − | 1.84124i | −0.390457 | − | 0.920621i | \(-0.627683\pi\) | ||
0.390457 | − | 0.920621i | \(-0.372317\pi\) | |||||||
\(572\) | −124211. | + | 741439.i | −0.379637 | + | 2.26612i | ||||
\(573\) | −164756. | −0.501801 | ||||||||
\(574\) | 108680. | + | 149586.i | 0.329858 | + | 0.454011i | ||||
\(575\) | −29119.3 | − | 89620.0i | −0.0880735 | − | 0.271062i | ||||
\(576\) | −44440.5 | + | 136774.i | −0.133947 | + | 0.412247i | ||||
\(577\) | −457370. | − | 332299.i | −1.37378 | − | 0.998108i | −0.997431 | − | 0.0716284i | \(-0.977180\pi\) |
−0.376346 | − | 0.926479i | \(-0.622820\pi\) | |||||||
\(578\) | 330074. | − | 454307.i | 0.987996 | − | 1.35986i | ||||
\(579\) | 233052. | + | 75723.3i | 0.695179 | + | 0.225877i | ||||
\(580\) | −782193. | + | 254150.i | −2.32519 | + | 0.755499i | ||||
\(581\) | −202393. | + | 147047.i | −0.599575 | + | 0.435617i | ||||
\(582\) | 253022.i | 0.746987i | ||||||||
\(583\) | −39382.6 | − | 263840.i | −0.115869 | − | 0.776252i | ||||
\(584\) | 351146. | 1.02958 | ||||||||
\(585\) | −77193.2 | − | 106247.i | −0.225563 | − | 0.310460i | ||||
\(586\) | −33063.4 | − | 101759.i | −0.0962836 | − | 0.296330i | ||||
\(587\) | 122795. | − | 377925.i | 0.356374 | − | 1.09681i | −0.598835 | − | 0.800873i | \(-0.704369\pi\) |
0.955209 | − | 0.295934i | \(-0.0956307\pi\) | |||||||
\(588\) | −95425.0 | − | 69330.3i | −0.275999 | − | 0.200525i | ||||
\(589\) | −677880. | + | 933021.i | −1.95399 | + | 2.68943i | ||||
\(590\) | 1.05325e6 | + | 342221.i | 3.02571 | + | 0.983112i | ||||
\(591\) | 87936.9 | − | 28572.4i | 0.251765 | − | 0.0818036i | ||||
\(592\) | −97709.4 | + | 70990.0i | −0.278800 | + | 0.202560i | ||||
\(593\) | 351638.i | 0.999970i | 0.866034 | + | 0.499985i | \(0.166661\pi\) | ||||
−0.866034 | + | 0.499985i | \(0.833339\pi\) | |||||||
\(594\) | 111974. | + | 58315.4i | 0.317354 | + | 0.165276i | ||||
\(595\) | 117633. | 0.332274 | ||||||||
\(596\) | −750100. | − | 1.03242e6i | −2.11167 | − | 2.90647i | ||||
\(597\) | 6360.18 | + | 19574.6i | 0.0178452 | + | 0.0549218i | ||||
\(598\) | 106284. | − | 327108.i | 0.297211 | − | 0.914721i | ||||
\(599\) | 17371.8 | + | 12621.3i | 0.0484162 | + | 0.0351764i | 0.611730 | − | 0.791067i | \(-0.290474\pi\) |
−0.563314 | + | 0.826243i | \(0.690474\pi\) | |||||||
\(600\) | 170506. | − | 234681.i | 0.473627 | − | 0.651892i | ||||
\(601\) | −13343.8 | − | 4335.67i | −0.0369429 | − | 0.0120035i | 0.290487 | − | 0.956879i | \(-0.406183\pi\) |
−0.327430 | + | 0.944875i | \(0.606183\pi\) | |||||||
\(602\) | 90227.2 | − | 29316.6i | 0.248968 | − | 0.0808948i | ||||
\(603\) | 108951. | − | 79157.6i | 0.299638 | − | 0.217700i | ||||
\(604\) | − | 1.17720e6i | − | 3.22682i | ||||||
\(605\) | −8025.28 | + | 450493.i | −0.0219255 | + | 1.23077i | ||||
\(606\) | 49349.4 | 0.134381 | ||||||||
\(607\) | 141102. | + | 194211.i | 0.382963 | + | 0.527104i | 0.956367 | − | 0.292170i | \(-0.0943772\pi\) |
−0.573403 | + | 0.819273i | \(0.694377\pi\) | |||||||
\(608\) | −433275. | − | 1.33348e6i | −1.17208 | − | 3.60728i | ||||
\(609\) | −46617.8 | + | 143475.i | −0.125695 | + | 0.386848i | ||||
\(610\) | −371396. | − | 269835.i | −0.998107 | − | 0.725167i | ||||
\(611\) | −199201. | + | 274177.i | −0.533593 | + | 0.734428i | ||||
\(612\) | 90354.3 | + | 29357.9i | 0.241238 | + | 0.0783830i | ||||
\(613\) | −242629. | + | 78834.9i | −0.645686 | + | 0.209796i | −0.613511 | − | 0.789686i | \(-0.710243\pi\) |
−0.0321752 | + | 0.999482i | \(0.510243\pi\) | |||||||
\(614\) | 489067. | − | 355328.i | 1.29727 | − | 0.942524i | ||||
\(615\) | − | 93099.4i | − | 0.246148i | ||||||
\(616\) | −413727. | + | 794414.i | −1.09032 | + | 2.09356i | ||||
\(617\) | −715781. | −1.88022 | −0.940112 | − | 0.340865i | \(-0.889280\pi\) | ||||
−0.940112 | + | 0.340865i | \(0.889280\pi\) | |||||||
\(618\) | 249135. | + | 342904.i | 0.652315 | + | 0.897834i | ||||
\(619\) | 67647.5 | + | 208198.i | 0.176551 | + | 0.543368i | 0.999701 | − | 0.0244558i | \(-0.00778531\pi\) |
−0.823150 | + | 0.567824i | \(0.807785\pi\) | |||||||
\(620\) | 656969. | − | 2.02194e6i | 1.70908 | − | 5.26000i | ||||
\(621\) | −33210.9 | − | 24129.1i | −0.0861186 | − | 0.0625689i | ||||
\(622\) | 353233. | − | 486183.i | 0.913020 | − | 1.25666i | ||||
\(623\) | −60231.7 | − | 19570.5i | −0.155185 | − | 0.0504226i | ||||
\(624\) | 515705. | − | 167563.i | 1.32444 | − | 0.430337i | ||||
\(625\) | 394954. | − | 286951.i | 1.01108 | − | 0.734594i | ||||
\(626\) | 708757.i | 1.80862i | ||||||||
\(627\) | −408065. | + | 60910.8i | −1.03799 | + | 0.154938i | ||||
\(628\) | −202166. | −0.512611 | ||||||||
\(629\) | 9624.61 | + | 13247.1i | 0.0243266 | + | 0.0334827i | ||||
\(630\) | −81542.8 | − | 250963.i | −0.205449 | − | 0.632307i | ||||
\(631\) | −189769. | + | 584050.i | −0.476614 | + | 1.46687i | 0.367154 | + | 0.930160i | \(0.380332\pi\) |
−0.843768 | + | 0.536708i | \(0.819668\pi\) | |||||||
\(632\) | −434657. | − | 315797.i | −1.08821 | − | 0.790630i | ||||
\(633\) | −5120.81 | + | 7048.19i | −0.0127800 | + | 0.0175902i | ||||
\(634\) | −21874.0 | − | 7107.30i | −0.0544189 | − | 0.0176818i | ||||
\(635\) | −356242. | + | 115750.i | −0.883483 | + | 0.287061i | ||||
\(636\) | −364308. | + | 264685.i | −0.900647 | + | 0.654359i | ||||
\(637\) | 91273.2i | 0.224939i | ||||||||
\(638\) | −603397. | − | 101086.i | −1.48239 | − | 0.248341i | ||||
\(639\) | −146141. | −0.357907 | ||||||||
\(640\) | 98146.4 | + | 135087.i | 0.239615 | + | 0.329802i | ||||
\(641\) | 70528.6 | + | 217065.i | 0.171652 | + | 0.528291i | 0.999465 | − | 0.0327139i | \(-0.0104150\pi\) |
−0.827813 | + | 0.561005i | \(0.810415\pi\) | |||||||
\(642\) | −157170. | + | 483720.i | −0.381329 | + | 1.17361i | ||||
\(643\) | 468717. | + | 340543.i | 1.13368 | + | 0.823664i | 0.986226 | − | 0.165405i | \(-0.0528933\pi\) |
0.147451 | + | 0.989069i | \(0.452893\pi\) | |||||||
\(644\) | 288697. | − | 397357.i | 0.696097 | − | 0.958096i | ||||
\(645\) | −45431.0 | − | 14761.4i | −0.109203 | − | 0.0354821i | ||||
\(646\) | −415470. | + | 134994.i | −0.995576 | + | 0.323482i | ||||
\(647\) | 494134. | − | 359009.i | 1.18042 | − | 0.857625i | 0.188200 | − | 0.982131i | \(-0.439735\pi\) |
0.992219 | + | 0.124506i | \(0.0397347\pi\) | |||||||
\(648\) | − | 126370.i | − | 0.300950i | ||||||
\(649\) | 410307. | + | 417681.i | 0.974136 | + | 0.991644i | ||||
\(650\) | −378555. | −0.895988 | ||||||||
\(651\) | −229215. | − | 315487.i | −0.540855 | − | 0.744423i | ||||
\(652\) | 343269. | + | 1.05647e6i | 0.807495 | + | 2.48521i | ||||
\(653\) | 205996. | − | 633991.i | 0.483095 | − | 1.48681i | −0.351626 | − | 0.936141i | \(-0.614371\pi\) |
0.834721 | − | 0.550673i | \(-0.185629\pi\) | |||||||
\(654\) | −146187. | − | 106211.i | −0.341784 | − | 0.248321i | ||||
\(655\) | −320725. | + | 441440.i | −0.747567 | + | 1.02894i | ||||
\(656\) | 365585. | + | 118786.i | 0.849533 | + | 0.276030i | ||||
\(657\) | −52016.4 | + | 16901.2i | −0.120506 | + | 0.0391549i | ||||
\(658\) | −550902. | + | 400254.i | −1.27240 | + | 0.924450i | ||||
\(659\) | − | 261408.i | − | 0.601933i | −0.953635 | − | 0.300967i | \(-0.902691\pi\) | ||
0.953635 | − | 0.300967i | \(-0.0973093\pi\) | |||||||
\(660\) | 680728. | − | 339246.i | 1.56274 | − | 0.778801i | ||||
\(661\) | −117901. | −0.269846 | −0.134923 | − | 0.990856i | \(-0.543079\pi\) | ||||
−0.134923 | + | 0.990856i | \(0.543079\pi\) | |||||||
\(662\) | 822798. | + | 1.13248e6i | 1.87749 | + | 2.58414i | ||||
\(663\) | −22717.6 | − | 69917.7i | −0.0516816 | − | 0.159060i | ||||
\(664\) | −313821. | + | 965841.i | −0.711780 | + | 2.19063i | ||||
\(665\) | 697665. | + | 506883.i | 1.57762 | + | 1.14621i | ||||
\(666\) | 21590.1 | − | 29716.3i | 0.0486751 | − | 0.0669955i | ||||
\(667\) | 189197. | + | 61473.9i | 0.425268 | + | 0.138178i | ||||
\(668\) | −351196. | + | 114111.i | −0.787041 | + | 0.255725i | ||||
\(669\) | −147879. | + | 107440.i | −0.330411 | + | 0.240058i | ||||
\(670\) | − | 1.14155e6i | − | 2.54299i | ||||||
\(671\) | −108256. | − | 217226.i | −0.240440 | − | 0.482466i | ||||
\(672\) | 474102. | 1.04986 | ||||||||
\(673\) | −404924. | − | 557330.i | −0.894012 | − | 1.23050i | −0.972339 | − | 0.233574i | \(-0.924958\pi\) |
0.0783272 | − | 0.996928i | \(-0.475042\pi\) | |||||||
\(674\) | 7848.28 | + | 24154.5i | 0.0172765 | + | 0.0531715i | ||||
\(675\) | −13962.1 | + | 42970.8i | −0.0306438 | + | 0.0943118i | ||||
\(676\) | 113829. | + | 82701.9i | 0.249093 | + | 0.180977i | ||||
\(677\) | 363597. | − | 500448.i | 0.793310 | − | 1.09190i | −0.200378 | − | 0.979719i | \(-0.564217\pi\) |
0.993688 | − | 0.112179i | \(-0.0357830\pi\) | |||||||
\(678\) | 212272. | + | 68971.5i | 0.461779 | + | 0.150041i | ||||
\(679\) | 265915. | − | 86400.9i | 0.576770 | − | 0.187404i | ||||
\(680\) | 386322. | − | 280680.i | 0.835472 | − | 0.607006i | ||||
\(681\) | − | 433278.i | − | 0.934271i | ||||||
\(682\) | 1.12820e6 | − | 1.10828e6i | 2.42560 | − | 2.38277i | ||||
\(683\) | 488052. | 1.04622 | 0.523112 | − | 0.852264i | \(-0.324771\pi\) | ||||
0.523112 | + | 0.852264i | \(0.324771\pi\) | |||||||
\(684\) | 409373. | + | 563454.i | 0.874999 | + | 1.20433i | ||||
\(685\) | −144422. | − | 444485.i | −0.307788 | − | 0.947275i | ||||
\(686\) | −292300. | + | 899608.i | −0.621128 | + | 1.91164i | ||||
\(687\) | −89406.6 | − | 64957.7i | −0.189433 | − | 0.137631i | ||||
\(688\) | 115931. | − | 159565.i | 0.244919 | − | 0.337102i | ||||
\(689\) | 331403. | + | 107679.i | 0.698100 | + | 0.226827i | ||||
\(690\) | −330940. | + | 107529.i | −0.695105 | + | 0.225853i | ||||
\(691\) | 229190. | − | 166516.i | 0.479999 | − | 0.348739i | −0.321327 | − | 0.946968i | \(-0.604129\pi\) |
0.801325 | + | 0.598229i | \(0.204129\pi\) | |||||||
\(692\) | 890463.i | 1.85953i | ||||||||
\(693\) | 23050.5 | − | 137592.i | 0.0479970 | − | 0.286502i | ||||
\(694\) | −1.55273e6 | −3.22386 | ||||||||
\(695\) | 469909. | + | 646775.i | 0.972847 | + | 1.33901i | ||||
\(696\) | 189240. | + | 582421.i | 0.390656 | + | 1.20232i | ||||
\(697\) | 16104.6 | − | 49564.9i | 0.0331501 | − | 0.102025i | ||||
\(698\) | −477635. | − | 347022.i | −0.980359 | − | 0.712273i | ||||
\(699\) | −213258. | + | 293525.i | −0.436467 | + | 0.600746i | ||||
\(700\) | −514131. | − | 167051.i | −1.04925 | − | 0.340921i | ||||
\(701\) | −723076. | + | 234942.i | −1.47146 | + | 0.478106i | −0.931548 | − | 0.363618i | \(-0.881542\pi\) |
−0.539909 | + | 0.841723i | \(0.681542\pi\) | |||||||
\(702\) | −133417. | + | 96933.0i | −0.270730 | + | 0.196697i | ||||
\(703\) | 120039.i | 0.242892i | ||||||||
\(704\) | 95147.6 | + | 637431.i | 0.191979 | + | 1.28614i | ||||
\(705\) | 342872. | 0.689848 | ||||||||
\(706\) | 598046. | + | 823139.i | 1.19984 | + | 1.65144i | ||||
\(707\) | −16851.6 | − | 51863.9i | −0.0337134 | − | 0.103759i | ||||
\(708\) | 305418. | − | 939981.i | 0.609297 | − | 1.87522i | ||||
\(709\) | 245643. | + | 178470.i | 0.488665 | + | 0.355036i | 0.804671 | − | 0.593721i | \(-0.202342\pi\) |
−0.316006 | + | 0.948757i | \(0.602342\pi\) | |||||||
\(710\) | −728133. | + | 1.00219e6i | −1.44442 | + | 1.98807i | ||||
\(711\) | 79586.9 | + | 25859.4i | 0.157435 | + | 0.0511539i | ||||
\(712\) | −244504. | + | 79444.3i | −0.482310 | + | 0.156712i | ||||
\(713\) | −416027. | + | 302261.i | −0.818356 | + | 0.594570i | ||||
\(714\) | − | 147715.i | − | 0.289752i | ||||||
\(715\) | −522000. | − | 271855.i | −1.02108 | − | 0.531772i | ||||
\(716\) | −10109.2 | −0.0197193 | ||||||||
\(717\) | 309195. | + | 425571.i | 0.601443 | + | 0.827816i | ||||
\(718\) | −362602. | − | 1.11597e6i | −0.703365 | − | 2.16474i | ||||
\(719\) | −43324.2 | + | 133338.i | −0.0838055 | + | 0.257927i | −0.984175 | − | 0.177199i | \(-0.943296\pi\) |
0.900369 | + | 0.435126i | \(0.143296\pi\) | |||||||
\(720\) | −443824. | − | 322457.i | −0.856141 | − | 0.622023i | ||||
\(721\) | 275303. | − | 378922.i | 0.529591 | − | 0.728919i | ||||
\(722\) | −2.12402e6 | − | 690135.i | −4.07459 | − | 1.32391i | ||||
\(723\) | 362437. | − | 117763.i | 0.693355 | − | 0.225285i | ||||
\(724\) | −1.65011e6 | + | 1.19888e6i | −3.14801 | + | 2.28716i | ||||
\(725\) | − | 218954.i | − | 0.416559i | ||||||
\(726\) | 565693. | + | 10077.5i | 1.07327 | + | 0.0191197i | ||||
\(727\) | −69575.5 | −0.131640 | −0.0658199 | − | 0.997832i | \(-0.520966\pi\) | ||||
−0.0658199 | + | 0.997832i | \(0.520966\pi\) | |||||||
\(728\) | −687705. | − | 946545.i | −1.29760 | − | 1.78599i | ||||
\(729\) | 6082.38 | + | 18719.6i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −143264. | + | 440920.i | −0.268838 | + | 0.827398i | ||||
\(731\) | −21633.4 | − | 15717.6i | −0.0404846 | − | 0.0294138i | ||||
\(732\) | −240817. | + | 331456.i | −0.449432 | + | 0.618590i | ||||
\(733\) | 8909.16 | + | 2894.76i | 0.0165817 | + | 0.00538772i | 0.317296 | − | 0.948327i | \(-0.397225\pi\) |
−0.300714 | + | 0.953714i | \(0.597225\pi\) | |||||||
\(734\) | 1.62560e6 | − | 528188.i | 3.01731 | − | 0.980384i | ||||
\(735\) | 74706.5 | − | 54277.5i | 0.138288 | − | 0.100472i | ||||
\(736\) | − | 625188.i | − | 1.15413i | ||||||
\(737\) | 278773. | − | 535283.i | 0.513235 | − | 0.985482i | ||||
\(738\) | −116907. | −0.214648 | ||||||||
\(739\) | 30204.8 | + | 41573.3i | 0.0553078 | + | 0.0761247i | 0.835775 | − | 0.549072i | \(-0.185019\pi\) |
−0.780467 | + | 0.625197i | \(0.785019\pi\) | |||||||
\(740\) | −68380.8 | − | 210454.i | −0.124874 | − | 0.384322i | ||||
\(741\) | 166541. | − | 512561.i | 0.303309 | − | 0.933490i | ||||
\(742\) | 566435. | + | 411539.i | 1.02883 | + | 0.747487i | ||||
\(743\) | 53639.0 | − | 73827.8i | 0.0971635 | − | 0.133734i | −0.757667 | − | 0.652641i | \(-0.773661\pi\) |
0.854831 | + | 0.518907i | \(0.173661\pi\) | |||||||
\(744\) | −1.50554e6 | − | 489179.i | −2.71986 | − | 0.883735i | ||||
\(745\) | 950174. | − | 308730.i | 1.71195 | − | 0.556246i | ||||
\(746\) | 433616. | − | 315040.i | 0.779162 | − | 0.566094i | ||||
\(747\) | − | 158178.i | − | 0.283468i | ||||||
\(748\) | 421094. | − | 62855.6i | 0.752620 | − | 0.112342i | ||||
\(749\) | 562037. | 1.00185 | ||||||||
\(750\) | −211766. | − | 291471.i | −0.376473 | − | 0.518171i | ||||
\(751\) | −240883. | − | 741361.i | −0.427096 | − | 1.31447i | −0.900973 | − | 0.433876i | \(-0.857146\pi\) |
0.473876 | − | 0.880592i | \(-0.342854\pi\) | |||||||
\(752\) | −437470. | + | 1.34640e6i | −0.773594 | + | 2.38088i | ||||
\(753\) | −147016. | − | 106813.i | −0.259283 | − | 0.188380i | ||||
\(754\) | 469740. | − | 646542.i | 0.826256 | − | 1.13724i | ||||
\(755\) | 876499. | + | 284792.i | 1.53765 | + | 0.499613i | ||||
\(756\) | −223974. | + | 72773.6i | −0.391881 | + | 0.127330i | ||||
\(757\) | −187749. | + | 136407.i | −0.327631 | + | 0.238038i | −0.739425 | − | 0.673239i | \(-0.764902\pi\) |
0.411794 | + | 0.911277i | \(0.364902\pi\) | |||||||
\(758\) | 1.38149e6i | 2.40441i | ||||||||
\(759\) | −181440. | − | 30396.2i | −0.314956 | − | 0.0527638i | ||||
\(760\) | 3.50067e6 | 6.06071 | ||||||||
\(761\) | 483226. | + | 665103.i | 0.834412 | + | 1.14847i | 0.987086 | + | 0.160193i | \(0.0512118\pi\) |
−0.152673 | + | 0.988277i | \(0.548788\pi\) | |||||||
\(762\) | 145350. | + | 447341.i | 0.250325 | + | 0.770422i | ||||
\(763\) | −61703.4 | + | 189904.i | −0.105989 | + | 0.326200i | ||||
\(764\) | 1.00834e6 | + | 732600.i | 1.72751 | + | 1.25511i | ||||
\(765\) | −43717.7 | + | 60172.2i | −0.0747024 | + | 0.102819i | ||||
\(766\) | −512316. | − | 166461.i | −0.873132 | − | 0.283698i | ||||
\(767\) | −727374. | + | 236338.i | −1.23642 | + | 0.401738i | ||||
\(768\) | −188624. | + | 137043.i | −0.319796 | + | 0.232346i | ||||
\(769\) | 944226.i | 1.59670i | 0.602194 | + | 0.798350i | \(0.294293\pi\) | ||||
−0.602194 | + | 0.798350i | \(0.705707\pi\) | |||||||
\(770\) | −828718. | − | 843613.i | −1.39774 | − | 1.42286i | ||||
\(771\) | −26583.5 | −0.0447202 | ||||||||
\(772\) | −1.08962e6 | − | 1.49973e6i | −1.82827 | − | 2.51639i | ||||
\(773\) | −283782. | − | 873390.i | −0.474925 | − | 1.46167i | −0.846058 | − | 0.533091i | \(-0.821031\pi\) |
0.371133 | − | 0.928580i | \(-0.378969\pi\) | |||||||
\(774\) | −18536.2 | + | 57048.6i | −0.0309414 | + | 0.0952277i | ||||
\(775\) | 457895. | + | 332680.i | 0.762364 | + | 0.553890i | ||||
\(776\) | 667138. | − | 918237.i | 1.10788 | − | 1.52487i | ||||
\(777\) | −38602.9 | − | 12542.8i | −0.0639408 | − | 0.0207756i | ||||
\(778\) | 1.22394e6 | − | 397681.i | 2.02209 | − | 0.657016i | ||||
\(779\) | 309089. | − | 224567.i | 0.509341 | − | 0.370058i | ||||
\(780\) | 993501.i | 1.63297i | ||||||||
\(781\) | −586170. | + | 292122.i | −0.960996 | + | 0.478920i | ||||
\(782\) | −194788. | −0.318529 | ||||||||
\(783\) | −56065.5 | − | 77167.5i | −0.0914476 | − | 0.125867i | ||||
\(784\) | 117820. | + | 362612.i | 0.191684 | + | 0.589943i | ||||
\(785\) | 48908.7 | − | 150525.i | 0.0793682 | − | 0.244270i | ||||
\(786\) | 554325. | + | 402741.i | 0.897262 | + | 0.651899i | ||||
\(787\) | −534468. | + | 735631.i | −0.862923 | + | 1.18771i | 0.117942 | + | 0.993020i | \(0.462370\pi\) |
−0.980865 | + | 0.194691i | \(0.937630\pi\) | |||||||
\(788\) | −665241. | − | 216150.i | −1.07134 | − | 0.348099i | ||||
\(789\) | 394739. | − | 128258.i | 0.634097 | − | 0.206031i | ||||
\(790\) | 573869. | − | 416940.i | 0.919514 | − | 0.668066i | ||||
\(791\) | − | 246640.i | − | 0.394195i | ||||||
\(792\) | −252602. | − | 506870.i | −0.402705 | − | 0.808065i | ||||
\(793\) | 317034. | 0.504150 | ||||||||
\(794\) | −1.15659e6 | − | 1.59191e6i | −1.83458 | − | 2.52509i | ||||
\(795\) | −108941. | − | 335285.i | −0.172368 | − | 0.530493i | ||||
\(796\) | 48114.7 | − | 148082.i | 0.0759366 | − | 0.233709i | ||||
\(797\) | −667167. | − | 484726.i | −1.05031 | − | 0.763096i | −0.0780400 | − | 0.996950i | \(-0.524866\pi\) |
−0.972272 | + | 0.233854i | \(0.924866\pi\) | |||||||
\(798\) | 636504. | − | 876072.i | 0.999529 | − | 1.37573i | ||||
\(799\) | 182540. | + | 59310.9i | 0.285933 | + | 0.0929054i | ||||
\(800\) | −654428. | + | 212636.i | −1.02254 | + | 0.332244i | ||||
\(801\) | 32395.5 | − | 23536.7i | 0.0504916 | − | 0.0366843i | ||||
\(802\) | 989901.i | 1.53902i | ||||||||
\(803\) | −174854. | + | 171766.i | −0.271171 | + | 0.266383i | ||||
\(804\) | −1.01878e6 | −1.57605 | ||||||||
\(805\) | 226015. | + | 311083.i | 0.348776 | + | 0.480048i | ||||
\(806\) | 638376. | + | 1.96472e6i | 0.982667 | + | 3.02434i | ||||
\(807\) | −176704. | + | 543839.i | −0.271331 | + | 0.835070i | ||||
\(808\) | −179093. | − | 130119.i | −0.274319 | − | 0.199304i | ||||
\(809\) | −607670. | + | 836385.i | −0.928475 | + | 1.27794i | 0.0319759 | + | 0.999489i | \(0.489820\pi\) |
−0.960451 | + | 0.278448i | \(0.910180\pi\) | |||||||
\(810\) | 158678. | + | 51557.7i | 0.241851 | + | 0.0785820i | ||||
\(811\) | −206959. | + | 67245.2i | −0.314661 | + | 0.102240i | −0.462090 | − | 0.886833i | \(-0.652900\pi\) |
0.147429 | + | 0.989073i | \(0.452900\pi\) | |||||||
\(812\) | 923283. | − | 670804.i | 1.40031 | − | 1.01738i | ||||
\(813\) | 296171.i | 0.448086i | ||||||||
\(814\) | 27197.8 | − | 162348.i | 0.0410473 | − | 0.245019i | ||||
\(815\) | −869659. | −1.30928 | ||||||||
\(816\) | −180506. | − | 248445.i | −0.271089 | − | 0.373122i | ||||
\(817\) | −60577.0 | − | 186437.i | −0.0907535 | − | 0.279311i | ||||
\(818\) | 5227.68 | − | 16089.1i | 0.00781272 | − | 0.0240451i | ||||
\(819\) | 147431. | + | 107115.i | 0.219796 | + | 0.159691i | ||||
\(820\) | −413975. | + | 569787.i | −0.615667 | + | 0.847393i | ||||
\(821\) | −299091. | − | 97180.6i | −0.443728 | − | 0.144176i | 0.0786269 | − | 0.996904i | \(-0.474946\pi\) |
−0.522355 | + | 0.852728i | \(0.674946\pi\) | |||||||
\(822\) | −558149. | + | 181354.i | −0.826050 | + | 0.268400i | ||||
\(823\) | 273376. | − | 198619.i | 0.403609 | − | 0.293239i | −0.367400 | − | 0.930063i | \(-0.619752\pi\) |
0.771009 | + | 0.636824i | \(0.219752\pi\) | |||||||
\(824\) | − | 1.90131e6i | − | 2.80027i | ||||||
\(825\) | 29892.9 | + | 200264.i | 0.0439198 | + | 0.294236i | ||||
\(826\) | −1.53672e6 | −2.25234 | ||||||||
\(827\) | −365551. | − | 503138.i | −0.534487 | − | 0.735659i | 0.453319 | − | 0.891349i | \(-0.350240\pi\) |
−0.987806 | + | 0.155690i | \(0.950240\pi\) | |||||||
\(828\) | 95965.1 | + | 295350.i | 0.139976 | + | 0.430801i | ||||
\(829\) | 206669. | − | 636062.i | 0.300723 | − | 0.925530i | −0.680516 | − | 0.732734i | \(-0.738244\pi\) |
0.981239 | − | 0.192797i | \(-0.0617558\pi\) | |||||||
\(830\) | −1.08473e6 | − | 788105.i | −1.57459 | − | 1.14401i | ||||
\(831\) | −325827. | + | 448462.i | −0.471830 | + | 0.649418i | ||||
\(832\) | −800663. | − | 260151.i | −1.15665 | − | 0.375819i | ||||
\(833\) | 49161.8 | − | 15973.6i | 0.0708497 | − | 0.0230205i | ||||
\(834\) | 812168. | − | 590075.i | 1.16765 | − | 0.848349i | ||||
\(835\) | − | 289095.i | − | 0.414636i | ||||||
\(836\) | 2.76829e6 | + | 1.44171e6i | 3.96094 | + | 2.06284i | ||||
\(837\) | 246565. | 0.351950 | ||||||||
\(838\) | 207854. | + | 286087.i | 0.295986 | + | 0.407389i | ||||
\(839\) | −106181. | − | 326793.i | −0.150843 | − | 0.464247i | 0.846873 | − | 0.531795i | \(-0.178482\pi\) |
−0.997716 | + | 0.0675483i | \(0.978482\pi\) | |||||||
\(840\) | −365783. | + | 1.12576e6i | −0.518400 | + | 1.59547i | ||||
\(841\) | −198247. | − | 144035.i | −0.280294 | − | 0.203645i | ||||
\(842\) | −400308. | + | 550977.i | −0.564638 | + | 0.777157i | ||||
\(843\) | −77848.5 | − | 25294.5i | −0.109546 | − | 0.0355935i | ||||
\(844\) | 62680.7 | − | 20366.2i | 0.0879932 | − | 0.0285907i | ||||
\(845\) | −89115.0 | + | 64745.8i | −0.124807 | + | 0.0906773i | ||||
\(846\) | − | 430551.i | − | 0.601567i | ||||||
\(847\) | −182579. | − | 597958.i | −0.254498 | − | 0.833497i | ||||
\(848\) | 1.45560e6 | 2.02419 | ||||||||
\(849\) | 158359. | + | 217963.i | 0.219699 | + | 0.302390i | ||||
\(850\) | 66250.6 | + | 203898.i | 0.0916963 | + | 0.282212i | ||||
\(851\) | −16540.0 | + | 50904.9i | −0.0228389 | + | 0.0702911i | ||||
\(852\) | 894412. | + | 649829.i | 1.23214 | + | 0.895199i | ||||
\(853\) | −129864. | + | 178742.i | −0.178480 | + | 0.245657i | −0.888879 | − | 0.458143i | \(-0.848515\pi\) |
0.710398 | + | 0.703800i | \(0.248515\pi\) | |||||||
\(854\) | 605836. | + | 196848.i | 0.830691 | + | 0.269908i | ||||
\(855\) | −518565. | + | 168492.i | −0.709368 | + | 0.230488i | ||||
\(856\) | 1.84580e6 | − | 1.34105e6i | 2.51905 | − | 1.83019i | ||||
\(857\) | − | 88561.8i | − | 0.120583i | −0.998181 | − | 0.0602913i | \(-0.980797\pi\) | ||
0.998181 | − | 0.0602913i | \(-0.0192030\pi\) | |||||||
\(858\) | −341374. | + | 655485.i | −0.463720 | + | 0.890407i | ||||
\(859\) | 188831. | 0.255909 | 0.127955 | − | 0.991780i | \(-0.459159\pi\) | ||||
0.127955 | + | 0.991780i | \(0.459159\pi\) | |||||||
\(860\) | 212409. | + | 292356.i | 0.287194 | + | 0.395289i | ||||
\(861\) | 39920.8 | + | 122864.i | 0.0538509 | + | 0.165736i | ||||
\(862\) | −2648.53 | + | 8151.34i | −0.00356443 | + | 0.0109702i | ||||
\(863\) | −367870. | − | 267273.i | −0.493938 | − | 0.358867i | 0.312759 | − | 0.949833i | \(-0.398747\pi\) |
−0.806697 | + | 0.590966i | \(0.798747\pi\) | |||||||
\(864\) | −176197. | + | 242514.i | −0.236032 | + | 0.324870i | ||||
\(865\) | −663007. | − | 215424.i | −0.886107 | − | 0.287914i | ||||
\(866\) | 1.29462e6 | − | 420647.i | 1.72626 | − | 0.560896i | ||||
\(867\) | 317420. | − | 230619.i | 0.422276 | − | 0.306801i | ||||
\(868\) | 2.95007e6i | 3.91555i | ||||||||
\(869\) | 370913. | − | 55365.2i | 0.491171 | − | 0.0733158i | ||||
\(870\) | −808531. | −1.06821 | ||||||||
\(871\) | 463382. | + | 637791.i | 0.610805 | + | 0.840701i | ||||
\(872\) | 250479. | + | 770894.i | 0.329411 | + | 1.01382i | ||||
\(873\) | −54629.4 | + | 168132.i | −0.0716799 | + | 0.220608i | ||||
\(874\) | −1.15526e6 | − | 839345.i | −1.51236 | − | 1.09880i | ||||
\(875\) | −234010. | + | 322086.i | −0.305645 | + | 0.420684i | ||||
\(876\) | 393503. | + | 127857.i | 0.512791 | + | 0.166616i | ||||
\(877\) | −1.42540e6 | + | 463140.i | −1.85326 | + | 0.602162i | −0.857050 | + | 0.515232i | \(0.827706\pi\) |
−0.996214 | + | 0.0869298i | \(0.972294\pi\) | |||||||
\(878\) | 1.03120e6 | − | 749208.i | 1.33768 | − | 0.971882i | ||||
\(879\) | − | 74756.7i | − | 0.0967547i | ||||||
\(880\) | −2.42473e6 | − | 406209.i | −3.13111 | − | 0.524547i | ||||
\(881\) | −999336. | −1.28754 | −0.643768 | − | 0.765220i | \(-0.722630\pi\) | ||||
−0.643768 | + | 0.765220i | \(0.722630\pi\) | |||||||
\(882\) | −68157.3 | − | 93810.5i | −0.0876143 | − | 0.120591i | ||||
\(883\) | 313137. | + | 963736.i | 0.401618 | + | 1.23605i | 0.923687 | + | 0.383149i | \(0.125160\pi\) |
−0.522069 | + | 0.852903i | \(0.674840\pi\) | |||||||
\(884\) | −171859. | + | 528926.i | −0.219921 | + | 0.676847i | ||||
\(885\) | 625989. | + | 454808.i | 0.799246 | + | 0.580686i | ||||
\(886\) | −91457.1 | + | 125880.i | −0.116506 | + | 0.160357i | ||||
\(887\) | −280958. | − | 91288.8i | −0.357104 | − | 0.116030i | 0.124970 | − | 0.992160i | \(-0.460116\pi\) |
−0.482074 | + | 0.876130i | \(0.660116\pi\) | |||||||
\(888\) | −156704. | + | 50916.3i | −0.198726 | + | 0.0645701i | ||||
\(889\) | 420501. | − | 305512.i | 0.532063 | − | 0.386566i | ||||
\(890\) | − | 339427.i | − | 0.428515i | ||||||
\(891\) | 61815.2 | + | 62926.2i | 0.0778646 | + | 0.0792640i | ||||
\(892\) | 1.38279e6 | 1.73791 | ||||||||
\(893\) | 827046. | + | 1.13833e6i | 1.03711 | + | 1.42747i | ||||
\(894\) | −387679. | − | 1.19315e6i | −0.485062 | − | 1.49287i | ||||
\(895\) | 2445.66 | − | 7526.98i | 0.00305317 | − | 0.00939668i | ||||
\(896\) | −187449. | − | 136190.i | −0.233489 | − | 0.169640i | ||||
\(897\) | 141250. | − | 194414.i | 0.175551 | − | 0.241625i | ||||
\(898\) | 2.61048e6 | + | 848195.i | 3.23718 | + | 1.05182i | ||||
\(899\) | −1.13638e6 | + | 369233.i | −1.40606 | + | 0.456858i | ||||
\(900\) | 276524. | − | 200906.i | 0.341388 | − | 0.248033i | ||||
\(901\) | − | 197346.i | − | 0.243096i | ||||||
\(902\) | −468912. | + | 233686.i | −0.576340 | + | 0.287223i | ||||
\(903\) | 66285.1 | 0.0812906 | ||||||||
\(904\) | −588497. | − | 809996.i | −0.720124 | − | 0.991165i | ||||
\(905\) | −493440. | − | 1.51865e6i | −0.602472 | − | 1.85422i | ||||
\(906\) | 357619. | − | 1.10064e6i | 0.435676 | − | 1.34087i | ||||
\(907\) | 704353. | + | 511742.i | 0.856201 | + | 0.622067i | 0.926849 | − | 0.375435i | \(-0.122507\pi\) |
−0.0706476 | + | 0.997501i | \(0.522507\pi\) | |||||||
\(908\) | −1.92661e6 | + | 2.65175e6i | −2.33680 | + | 3.21633i | ||||
\(909\) | 32792.4 | + | 10654.9i | 0.0396868 | + | 0.0128950i | ||||
\(910\) | 1.46912e6 | − | 477345.i | 1.77408 | − | 0.576433i | ||||
\(911\) | −821849. | + | 597108.i | −0.990274 | + | 0.719476i | −0.959981 | − | 0.280065i | \(-0.909644\pi\) |
−0.0302930 | + | 0.999541i | \(0.509644\pi\) | |||||||
\(912\) | − | 2.25129e6i | − | 2.70671i | ||||||
\(913\) | −316183. | − | 634450.i | −0.379312 | − | 0.761125i | ||||
\(914\) | 234565. | 0.280783 | ||||||||
\(915\) | −188531. | − | 259491.i | −0.225186 | − | 0.309941i | ||||
\(916\) | 258346. | + | 795108.i | 0.307901 | + | 0.947622i | ||||
\(917\) | 233973. | − | 720095.i | 0.278245 | − | 0.856350i | ||||
\(918\) | 75559.5 | + | 54897.2i | 0.0896610 | + | 0.0651426i | ||||
\(919\) | 233287. | − | 321092.i | 0.276223 | − | 0.380188i | −0.648255 | − | 0.761423i | \(-0.724501\pi\) |
0.924478 | + | 0.381235i | \(0.124501\pi\) | |||||||
\(920\) | 1.48452e6 | + | 482351.i | 1.75393 | + | 0.569885i | ||||
\(921\) | 401700. | − | 130520.i | 0.473568 | − | 0.153872i | ||||
\(922\) | −1.12719e6 | + | 818953.i | −1.32598 | + | 0.963378i | ||||
\(923\) | − | 855498.i | − | 1.00419i | ||||||
\(924\) | −752890. | + | 739598.i | −0.881836 | + | 0.866266i | ||||
\(925\) | 58911.1 | 0.0688516 | ||||||||
\(926\) | −1.77758e6 | − | 2.44663e6i | −2.07304 | − | 2.85330i | ||||
\(927\) | 91512.9 | + | 281648.i | 0.106493 | + | 0.327753i | ||||
\(928\) | 448898. | − | 1.38156e6i | 0.521256 | − | 1.60426i | ||||
\(929\) | 583560. | + | 423981.i | 0.676168 | + | 0.491264i | 0.872084 | − | 0.489356i | \(-0.162768\pi\) |
−0.195917 | + | 0.980621i | \(0.562768\pi\) | |||||||
\(930\) | 1.22849e6 | − | 1.69087e6i | 1.42038 | − | 1.95499i | ||||
\(931\) | 360401. | + | 117102.i | 0.415803 | + | 0.135102i | ||||
\(932\) | 2.61037e6 | − | 848160.i | 3.00518 | − | 0.976441i | ||||
\(933\) | 339691. | − | 246800.i | 0.390231 | − | 0.283519i | ||||
\(934\) | 1.69454e6i | 1.94249i | ||||||||
\(935\) | −55072.6 | + | 328738.i | −0.0629959 | + | 0.376034i | ||||
\(936\) | 739761. | 0.844383 | ||||||||
\(937\) | −503823. | − | 693453.i | −0.573850 | − | 0.789837i | 0.419154 | − | 0.907915i | \(-0.362327\pi\) |
−0.993004 | + | 0.118078i | \(0.962327\pi\) | |||||||
\(938\) | 489492. | + | 1.50650e6i | 0.556340 | + | 1.71224i | ||||
\(939\) | −153026. | + | 470965.i | −0.173553 | + | 0.534142i | ||||
\(940\) | −2.09844e6 | − | 1.52461e6i | −2.37488 | − | 1.72545i | ||||
\(941\) | −5816.43 | + | 8005.63i | −0.00656867 | + | 0.00904099i | −0.812289 | − | 0.583256i | \(-0.801779\pi\) |
0.805720 | + | 0.592297i | \(0.201779\pi\) | |||||||
\(942\) | −189018. | − | 61415.6i | −0.213010 | − | 0.0692113i | ||||
\(943\) | 162018. | − | 52642.7i | 0.182196 | − | 0.0591991i | ||||
\(944\) | −2.58465e6 | + | 1.87786e6i | −2.90040 | + | 2.10726i | ||||
\(945\) | − | 184369.i | − | 0.206454i | ||||||
\(946\) | 39686.3 | + | 265874.i | 0.0443464 | + | 0.297093i | ||||
\(947\) | 150146. | 0.167423 | 0.0837114 | − | 0.996490i | \(-0.473323\pi\) | ||||
0.0837114 | + | 0.996490i | \(0.473323\pi\) | |||||||
\(948\) | −372102. | − | 512155.i | −0.414043 | − | 0.569881i | ||||
\(949\) | −98938.0 | − | 304500.i | −0.109858 | − | 0.338107i | ||||
\(950\) | −485678. | + | 1.49476e6i | −0.538147 | + | 1.65625i | ||||
\(951\) | −13000.6 | − | 9445.51i | −0.0143749 | − | 0.0104439i | ||||
\(952\) | −389476. | + | 536067.i | −0.429741 | + | 0.591487i | ||||
\(953\) | 672400. | + | 218476.i | 0.740358 | + | 0.240557i | 0.654827 | − | 0.755779i | \(-0.272741\pi\) |
0.0855309 | + | 0.996336i | \(0.472741\pi\) | |||||||
\(954\) | −421024. | + | 136799.i | −0.462605 | + | 0.150309i | ||||
\(955\) | −789409. | + | 573540.i | −0.865557 | + | 0.628864i | ||||
\(956\) | − | 3.97944e6i | − | 4.35418i | ||||||
\(957\) | −379129. | − | 197449.i | −0.413964 | − | 0.215591i | ||||
\(958\) | −1.43062e6 | −1.55881 | ||||||||
\(959\) | 381188. | + | 524660.i | 0.414478 | + | 0.570481i | ||||
\(960\) | 263198. | + | 810041.i | 0.285589 | + | 0.878951i | ||||
\(961\) | 669071. | − | 2.05919e6i | 0.724478 | − | 2.22972i | ||||
\(962\) | 173957. | + | 126387.i | 0.187971 | + | 0.136569i | ||||
\(963\) | −208877. | + | 287495.i | −0.225236 | + | 0.310011i | ||||
\(964\) | −2.74183e6 | − | 890873.i | −2.95043 | − | 0.958654i | ||||
\(965\) | 1.38025e6 | − | 448471.i | 1.48219 | − | 0.481592i | ||||
\(966\) | 390634. | − | 283812.i | 0.418616 | − | 0.304142i | ||||
\(967\) | − | 1.59915e6i | − | 1.71016i | −0.518493 | − | 0.855082i | \(-0.673507\pi\) | ||
0.518493 | − | 0.855082i | \(-0.326493\pi\) | |||||||
\(968\) | −2.02637e6 | − | 1.52812e6i | −2.16256 | − | 1.63082i | ||||
\(969\) | −305223. | −0.325065 | ||||||||
\(970\) | 880810. | + | 1.21233e6i | 0.936135 | + | 1.28848i | ||||
\(971\) | 221471. | + | 681618.i | 0.234898 | + | 0.722940i | 0.997135 | + | 0.0756429i | \(0.0241009\pi\) |
−0.762237 | + | 0.647298i | \(0.775899\pi\) | |||||||
\(972\) | 46013.1 | − | 141614.i | 0.0487023 | − | 0.149890i | ||||
\(973\) | −897476. | − | 652054.i | −0.947975 | − | 0.688744i | ||||
\(974\) | 982136. | − | 1.35179e6i | 1.03527 | − | 1.42493i | ||||
\(975\) | −251548. | − | 81732.8i | −0.264613 | − | 0.0859779i | ||||
\(976\) | 1.25952e6 | − | 409243.i | 1.32223 | − | 0.429617i | ||||
\(977\) | 95869.6 | − | 69653.3i | 0.100437 | − | 0.0729714i | −0.536434 | − | 0.843943i | \(-0.680229\pi\) |
0.636870 | + | 0.770971i | \(0.280229\pi\) | |||||||
\(978\) | 1.09205e6i | 1.14173i | ||||||||
\(979\) | 82890.3 | − | 159161.i | 0.0864845 | − | 0.166062i | ||||
\(980\) | −698568. | −0.727372 | ||||||||
\(981\) | −74208.5 | − | 102139.i | −0.0771108 | − | 0.106134i | ||||
\(982\) | 69939.0 | + | 215250.i | 0.0725265 | + | 0.223214i | ||||
\(983\) | −439511. | + | 1.35268e6i | −0.454845 | + | 1.39987i | 0.416473 | + | 0.909148i | \(0.363266\pi\) |
−0.871317 | + | 0.490720i | \(0.836734\pi\) | |||||||
\(984\) | 424264. | + | 308246.i | 0.438173 | + | 0.318351i | ||||
\(985\) | 321875. | − | 443023.i | 0.331753 | − | 0.456619i | ||||
\(986\) | −430451. | − | 139862.i | −0.442761 | − | 0.143862i | ||||
\(987\) | −452489. | + | 147022.i | −0.464487 | + | 0.150921i | ||||
\(988\) | −3.29841e6 | + | 2.39644e6i | −3.37902 | + | 2.45500i | ||||
\(989\) | − | 87408.8i | − | 0.0893640i | ||||||
\(990\) | 739516. | − | 110386.i | 0.754531 | − | 0.112627i | ||||
\(991\) | 1.18582e6 | 1.20746 | 0.603729 | − | 0.797190i | \(-0.293681\pi\) | ||||
0.603729 | + | 0.797190i | \(0.293681\pi\) | |||||||
\(992\) | 2.20719e6 | + | 3.03793e6i | 2.24293 | + | 3.08713i | ||||
\(993\) | 302233. | + | 930177.i | 0.306509 | + | 0.943337i | ||||
\(994\) | 531183. | − | 1.63481e6i | 0.537615 | − | 1.65461i | ||||
\(995\) | 98616.4 | + | 71649.0i | 0.0996100 | + | 0.0723709i | ||||
\(996\) | −703352. | + | 968081.i | −0.709013 | + | 0.975872i | ||||
\(997\) | 219810. | + | 71420.5i | 0.221134 | + | 0.0718510i | 0.417489 | − | 0.908682i | \(-0.362910\pi\) |
−0.196354 | + | 0.980533i | \(0.562910\pi\) | |||||||
\(998\) | −1.02654e6 | + | 333544.i | −1.03066 | + | 0.334882i | ||||
\(999\) | 20762.5 | − | 15084.8i | 0.0208041 | − | 0.0151150i |
(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 | 33.5.g.a.19.1 | yes | 32 | |
3.2 | odd | 2 | 99.5.k.c.19.8 | 32 | |||
11.2 | odd | 10 | 363.5.c.e.241.2 | 32 | |||
11.7 | odd | 10 | inner | 33.5.g.a.7.1 | ✓ | 32 | |
11.9 | even | 5 | 363.5.c.e.241.31 | 32 | |||
33.29 | even | 10 | 99.5.k.c.73.8 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.g.a.7.1 | ✓ | 32 | 11.7 | odd | 10 | inner | |
33.5.g.a.19.1 | yes | 32 | 1.1 | even | 1 | trivial | |
99.5.k.c.19.8 | 32 | 3.2 | odd | 2 | |||
99.5.k.c.73.8 | 32 | 33.29 | even | 10 | |||
363.5.c.e.241.2 | 32 | 11.2 | odd | 10 | |||
363.5.c.e.241.31 | 32 | 11.9 | even | 5 |