Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,6,Mod(10,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.10");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.93420133308\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 10.1 | ||
Character | \(\chi\) | \(=\) | 37.10 |
Dual form | 37.6.c.a.26.1 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.29373 | + | 9.16901i | −0.935808 | + | 1.62087i | −0.162622 | + | 0.986688i | \(0.551995\pi\) |
−0.773186 | + | 0.634179i | \(0.781338\pi\) | |||||||
\(3\) | −7.75625 | − | 13.4342i | −0.497564 | − | 0.861806i | 0.502432 | − | 0.864617i | \(-0.332439\pi\) |
−0.999996 | + | 0.00281069i | \(0.999105\pi\) | |||||||
\(4\) | −40.0472 | − | 69.3637i | −1.25147 | − | 2.16762i | ||||
\(5\) | 14.2918 | + | 24.7542i | 0.255660 | + | 0.442816i | 0.965075 | − | 0.261975i | \(-0.0843739\pi\) |
−0.709415 | + | 0.704791i | \(0.751041\pi\) | |||||||
\(6\) | 164.238 | 1.86250 | ||||||||
\(7\) | 10.7449 | + | 18.6107i | 0.0828812 | + | 0.143554i | 0.904486 | − | 0.426503i | \(-0.140254\pi\) |
−0.821605 | + | 0.570057i | \(0.806921\pi\) | |||||||
\(8\) | 509.197 | 2.81294 | ||||||||
\(9\) | 1.18106 | − | 2.04566i | 0.00486034 | − | 0.00841836i | ||||
\(10\) | −302.628 | −0.956995 | ||||||||
\(11\) | −76.4480 | −0.190495 | −0.0952477 | − | 0.995454i | \(-0.530364\pi\) | ||||
−0.0952477 | + | 0.995454i | \(0.530364\pi\) | |||||||
\(12\) | −621.232 | + | 1076.01i | −1.24538 | + | 2.15706i | ||||
\(13\) | 377.201 | + | 653.332i | 0.619035 | + | 1.07220i | 0.989662 | + | 0.143418i | \(0.0458092\pi\) |
−0.370628 | + | 0.928782i | \(0.620857\pi\) | |||||||
\(14\) | −227.522 | −0.310244 | ||||||||
\(15\) | 221.702 | − | 383.999i | 0.254414 | − | 0.440659i | ||||
\(16\) | −1414.04 | + | 2449.19i | −1.38090 | + | 2.39179i | ||||
\(17\) | 1162.24 | − | 2013.06i | 0.975381 | − | 1.68941i | 0.296709 | − | 0.954968i | \(-0.404111\pi\) |
0.678672 | − | 0.734442i | \(-0.262556\pi\) | |||||||
\(18\) | 12.5045 | + | 21.6584i | 0.00909670 | + | 0.0157559i | ||||
\(19\) | 974.165 | + | 1687.30i | 0.619082 | + | 1.07228i | 0.989654 | + | 0.143478i | \(0.0458286\pi\) |
−0.370571 | + | 0.928804i | \(0.620838\pi\) | |||||||
\(20\) | 1144.69 | − | 1982.67i | 0.639904 | − | 1.10835i | ||||
\(21\) | 166.680 | − | 288.698i | 0.0824774 | − | 0.142855i | ||||
\(22\) | 404.695 | − | 700.952i | 0.178267 | − | 0.308768i | ||||
\(23\) | 3500.15 | 1.37964 | 0.689822 | − | 0.723979i | \(-0.257689\pi\) | ||||
0.689822 | + | 0.723979i | \(0.257689\pi\) | |||||||
\(24\) | −3949.46 | − | 6840.67i | −1.39962 | − | 2.42421i | ||||
\(25\) | 1153.99 | − | 1998.76i | 0.369276 | − | 0.639605i | ||||
\(26\) | −7987.21 | −2.31719 | ||||||||
\(27\) | −3806.18 | −1.00480 | ||||||||
\(28\) | 860.603 | − | 1490.61i | 0.207447 | − | 0.359309i | ||||
\(29\) | 5347.24 | 1.18069 | 0.590343 | − | 0.807152i | \(-0.298992\pi\) | ||||
0.590343 | + | 0.807152i | \(0.298992\pi\) | |||||||
\(30\) | 2347.26 | + | 4065.58i | 0.476166 | + | 0.824744i | ||||
\(31\) | −547.123 | −0.102254 | −0.0511270 | − | 0.998692i | \(-0.516281\pi\) | ||||
−0.0511270 | + | 0.998692i | \(0.516281\pi\) | |||||||
\(32\) | −6823.97 | − | 11819.5i | −1.17805 | − | 2.04043i | ||||
\(33\) | 592.950 | + | 1027.02i | 0.0947836 | + | 0.164170i | ||||
\(34\) | 12305.2 | + | 21313.2i | 1.82554 | + | 3.16193i | ||||
\(35\) | −307.127 | + | 531.960i | −0.0423788 | + | 0.0734022i | ||||
\(36\) | −189.193 | −0.0243304 | ||||||||
\(37\) | −8095.55 | − | 1950.92i | −0.972169 | − | 0.234280i | ||||
\(38\) | −20627.9 | −2.31737 | ||||||||
\(39\) | 5851.34 | − | 10134.8i | 0.616018 | − | 1.06698i | ||||
\(40\) | 7277.35 | + | 12604.7i | 0.719157 | + | 1.24562i | ||||
\(41\) | −3364.04 | − | 5826.70i | −0.312537 | − | 0.541331i | 0.666374 | − | 0.745618i | \(-0.267846\pi\) |
−0.978911 | + | 0.204287i | \(0.934512\pi\) | |||||||
\(42\) | 1764.72 | + | 3056.58i | 0.154366 | + | 0.267370i | ||||
\(43\) | 4181.80 | 0.344899 | 0.172450 | − | 0.985018i | \(-0.444832\pi\) | ||||
0.172450 | + | 0.985018i | \(0.444832\pi\) | |||||||
\(44\) | 3061.53 | + | 5302.72i | 0.238400 | + | 0.412921i | ||||
\(45\) | 67.5182 | 0.00497038 | ||||||||
\(46\) | −18528.8 | + | 32092.9i | −1.29108 | + | 2.23622i | ||||
\(47\) | −2603.06 | −0.171885 | −0.0859427 | − | 0.996300i | \(-0.527390\pi\) | ||||
−0.0859427 | + | 0.996300i | \(0.527390\pi\) | |||||||
\(48\) | 43870.7 | 2.74835 | ||||||||
\(49\) | 8172.60 | − | 14155.4i | 0.486261 | − | 0.842229i | ||||
\(50\) | 12217.8 | + | 21161.8i | 0.691143 | + | 1.19709i | ||||
\(51\) | −36058.6 | −1.94126 | ||||||||
\(52\) | 30211.7 | − | 52328.2i | 1.54941 | − | 2.68366i | ||||
\(53\) | 10068.1 | − | 17438.5i | 0.492334 | − | 0.852747i | −0.507627 | − | 0.861577i | \(-0.669477\pi\) |
0.999961 | + | 0.00882980i | \(0.00281065\pi\) | |||||||
\(54\) | 20148.9 | − | 34898.9i | 0.940301 | − | 1.62865i | ||||
\(55\) | −1092.58 | − | 1892.41i | −0.0487020 | − | 0.0843544i | ||||
\(56\) | 5471.25 | + | 9476.49i | 0.233140 | + | 0.403810i | ||||
\(57\) | 15111.7 | − | 26174.3i | 0.616066 | − | 1.06706i | ||||
\(58\) | −28306.8 | + | 49028.9i | −1.10490 | + | 1.91374i | ||||
\(59\) | −22085.0 | + | 38252.3i | −0.825976 | + | 1.43063i | 0.0751957 | + | 0.997169i | \(0.476042\pi\) |
−0.901171 | + | 0.433463i | \(0.857291\pi\) | |||||||
\(60\) | −35514.2 | −1.27357 | ||||||||
\(61\) | 12156.5 | + | 21055.7i | 0.418296 | + | 0.724510i | 0.995768 | − | 0.0919005i | \(-0.0292942\pi\) |
−0.577472 | + | 0.816410i | \(0.695961\pi\) | |||||||
\(62\) | 2896.32 | − | 5016.58i | 0.0956902 | − | 0.165740i | ||||
\(63\) | 50.7615 | 0.00161132 | ||||||||
\(64\) | 53998.2 | 1.64790 | ||||||||
\(65\) | −10781.8 | + | 18674.6i | −0.316525 | + | 0.548237i | ||||
\(66\) | −12555.7 | −0.354797 | ||||||||
\(67\) | 16756.9 | + | 29023.8i | 0.456045 | + | 0.789893i | 0.998748 | − | 0.0500322i | \(-0.0159324\pi\) |
−0.542703 | + | 0.839925i | \(0.682599\pi\) | |||||||
\(68\) | −186178. | −4.88266 | ||||||||
\(69\) | −27148.0 | − | 47021.8i | −0.686461 | − | 1.18898i | ||||
\(70\) | −3251.70 | − | 5632.11i | −0.0793168 | − | 0.137381i | ||||
\(71\) | 19911.2 | + | 34487.2i | 0.468761 | + | 0.811917i | 0.999362 | − | 0.0357040i | \(-0.0113674\pi\) |
−0.530602 | + | 0.847621i | \(0.678034\pi\) | |||||||
\(72\) | 601.394 | − | 1041.64i | 0.0136719 | − | 0.0236804i | ||||
\(73\) | −10784.0 | −0.236850 | −0.118425 | − | 0.992963i | \(-0.537785\pi\) | ||||
−0.118425 | + | 0.992963i | \(0.537785\pi\) | |||||||
\(74\) | 60743.6 | − | 63900.5i | 1.28950 | − | 1.35652i | ||||
\(75\) | −35802.5 | −0.734954 | ||||||||
\(76\) | 78025.1 | − | 135143.i | 1.54953 | − | 2.68387i | ||||
\(77\) | −821.423 | − | 1422.75i | −0.0157885 | − | 0.0273464i | ||||
\(78\) | 61950.8 | + | 107302.i | 1.15295 | + | 1.99697i | ||||
\(79\) | 8215.11 | + | 14229.0i | 0.148097 | + | 0.256511i | 0.930524 | − | 0.366231i | \(-0.119352\pi\) |
−0.782427 | + | 0.622742i | \(0.786019\pi\) | |||||||
\(80\) | −80837.0 | −1.41216 | ||||||||
\(81\) | 29234.7 | + | 50636.0i | 0.495092 | + | 0.857525i | ||||
\(82\) | 71233.4 | 1.16990 | ||||||||
\(83\) | 56127.2 | − | 97215.2i | 0.894289 | − | 1.54895i | 0.0596080 | − | 0.998222i | \(-0.481015\pi\) |
0.834681 | − | 0.550733i | \(-0.185652\pi\) | |||||||
\(84\) | −26700.2 | −0.412873 | ||||||||
\(85\) | 66442.2 | 0.997463 | ||||||||
\(86\) | −22137.3 | + | 38343.0i | −0.322760 | + | 0.559036i | ||||
\(87\) | −41474.5 | − | 71836.0i | −0.587467 | − | 1.01752i | ||||
\(88\) | −38927.1 | −0.535852 | ||||||||
\(89\) | −581.269 | + | 1006.79i | −0.00777862 | + | 0.0134730i | −0.869889 | − | 0.493248i | \(-0.835809\pi\) |
0.862110 | + | 0.506721i | \(0.169143\pi\) | |||||||
\(90\) | −357.423 | + | 619.075i | −0.00465132 | + | 0.00805633i | ||||
\(91\) | −8105.96 | + | 14039.9i | −0.102613 | + | 0.177730i | ||||
\(92\) | −140171. | − | 242783.i | −1.72659 | − | 2.99054i | ||||
\(93\) | 4243.62 | + | 7350.17i | 0.0508779 | + | 0.0881232i | ||||
\(94\) | 13779.9 | − | 23867.5i | 0.160852 | − | 0.278603i | ||||
\(95\) | −27845.2 | + | 48229.3i | −0.316549 | + | 0.548279i | ||||
\(96\) | −105857. | + | 183349.i | −1.17231 | + | 2.03049i | ||||
\(97\) | −15860.3 | −0.171152 | −0.0855758 | − | 0.996332i | \(-0.527273\pi\) | ||||
−0.0855758 | + | 0.996332i | \(0.527273\pi\) | |||||||
\(98\) | 86527.0 | + | 149869.i | 0.910095 | + | 1.57633i | ||||
\(99\) | −90.2899 | + | 156.387i | −0.000925873 | + | 0.00160366i | ||||
\(100\) | −184856. | −1.84856 | ||||||||
\(101\) | 172602. | 1.68362 | 0.841809 | − | 0.539776i | \(-0.181491\pi\) | ||||
0.841809 | + | 0.539776i | \(0.181491\pi\) | |||||||
\(102\) | 190884. | − | 330621.i | 1.81664 | − | 3.14652i | ||||
\(103\) | −34437.4 | −0.319843 | −0.159922 | − | 0.987130i | \(-0.551124\pi\) | ||||
−0.159922 | + | 0.987130i | \(0.551124\pi\) | |||||||
\(104\) | 192070. | + | 332675.i | 1.74131 | + | 3.01603i | ||||
\(105\) | 9528.63 | 0.0843446 | ||||||||
\(106\) | 106596. | + | 184630.i | 0.921460 | + | 1.59602i | ||||
\(107\) | −88604.9 | − | 153468.i | −0.748167 | − | 1.29586i | −0.948701 | − | 0.316176i | \(-0.897601\pi\) |
0.200534 | − | 0.979687i | \(-0.435732\pi\) | |||||||
\(108\) | 152427. | + | 264011.i | 1.25748 | + | 2.17802i | ||||
\(109\) | −53253.4 | + | 92237.6i | −0.429320 | + | 0.743604i | −0.996813 | − | 0.0797741i | \(-0.974580\pi\) |
0.567493 | + | 0.823378i | \(0.307913\pi\) | |||||||
\(110\) | 23135.3 | 0.182303 | ||||||||
\(111\) | 36582.0 | + | 123889.i | 0.281813 | + | 0.954390i | ||||
\(112\) | −60774.8 | −0.457803 | ||||||||
\(113\) | −16286.5 | + | 28209.0i | −0.119986 | + | 0.207822i | −0.919762 | − | 0.392477i | \(-0.871618\pi\) |
0.799776 | + | 0.600299i | \(0.204952\pi\) | |||||||
\(114\) | 159995. | + | 277119.i | 1.15304 | + | 1.99712i | ||||
\(115\) | 50023.5 | + | 86643.2i | 0.352719 | + | 0.610928i | ||||
\(116\) | −214142. | − | 370904.i | −1.47760 | − | 2.55928i | ||||
\(117\) | 1782.00 | 0.0120349 | ||||||||
\(118\) | −233824. | − | 404995.i | −1.54591 | − | 2.67759i | ||||
\(119\) | 49952.5 | 0.323363 | ||||||||
\(120\) | 112890. | − | 195531.i | 0.715653 | − | 1.23955i | ||||
\(121\) | −155207. | −0.963712 | ||||||||
\(122\) | −257413. | −1.56578 | ||||||||
\(123\) | −52184.8 | + | 90386.7i | −0.311015 | + | 0.538693i | ||||
\(124\) | 21910.7 | + | 37950.5i | 0.127968 | + | 0.221648i | ||||
\(125\) | 155294. | 0.888956 | ||||||||
\(126\) | −268.718 | + | 465.433i | −0.00150789 | + | 0.00261174i | ||||
\(127\) | −104434. | + | 180885.i | −0.574558 | + | 0.995163i | 0.421532 | + | 0.906814i | \(0.361493\pi\) |
−0.996090 | + | 0.0883495i | \(0.971841\pi\) | |||||||
\(128\) | −67485.3 | + | 116888.i | −0.364069 | + | 0.630587i | ||||
\(129\) | −32435.1 | − | 56179.3i | −0.171609 | − | 0.297236i | ||||
\(130\) | −114152. | − | 197717.i | −0.592413 | − | 1.02609i | ||||
\(131\) | −87591.1 | + | 151712.i | −0.445946 | + | 0.772400i | −0.998118 | − | 0.0613298i | \(-0.980466\pi\) |
0.552172 | + | 0.833730i | \(0.313799\pi\) | |||||||
\(132\) | 47491.9 | − | 82258.5i | 0.237238 | − | 0.410909i | ||||
\(133\) | −20934.5 | + | 36259.7i | −0.102621 | + | 0.177744i | ||||
\(134\) | −354827. | −1.70708 | ||||||||
\(135\) | −54397.3 | − | 94218.9i | −0.256887 | − | 0.444942i | ||||
\(136\) | 591810. | − | 1.02505e6i | 2.74369 | − | 4.75221i | ||||
\(137\) | −53015.1 | −0.241323 | −0.120661 | − | 0.992694i | \(-0.538502\pi\) | ||||
−0.120661 | + | 0.992694i | \(0.538502\pi\) | |||||||
\(138\) | 574857. | 2.56958 | ||||||||
\(139\) | 104217. | − | 180509.i | 0.457510 | − | 0.792431i | −0.541319 | − | 0.840818i | \(-0.682075\pi\) |
0.998829 | + | 0.0483868i | \(0.0154080\pi\) | |||||||
\(140\) | 49198.3 | 0.212144 | ||||||||
\(141\) | 20190.0 | + | 34970.1i | 0.0855240 | + | 0.148132i | ||||
\(142\) | −421618. | −1.75468 | ||||||||
\(143\) | −28836.3 | − | 49945.9i | −0.117923 | − | 0.204249i | ||||
\(144\) | 3340.15 | + | 5785.31i | 0.0134233 | + | 0.0232498i | ||||
\(145\) | 76421.8 | + | 132366.i | 0.301854 | + | 0.522827i | ||||
\(146\) | 57087.7 | − | 98878.7i | 0.221646 | − | 0.383902i | ||||
\(147\) | −253555. | −0.967785 | ||||||||
\(148\) | 188881. | + | 639666.i | 0.708816 | + | 2.40049i | ||||
\(149\) | 265717. | 0.980515 | 0.490257 | − | 0.871578i | \(-0.336903\pi\) | ||||
0.490257 | + | 0.871578i | \(0.336903\pi\) | |||||||
\(150\) | 189529. | − | 328273.i | 0.687776 | − | 1.19126i | ||||
\(151\) | −152436. | − | 264027.i | −0.544058 | − | 0.942336i | −0.998666 | − | 0.0516441i | \(-0.983554\pi\) |
0.454608 | − | 0.890692i | \(-0.349779\pi\) | |||||||
\(152\) | 496042. | + | 859169.i | 1.74144 | + | 3.01627i | ||||
\(153\) | −2745.36 | − | 4755.11i | −0.00948137 | − | 0.0164222i | ||||
\(154\) | 17393.6 | 0.0590999 | ||||||||
\(155\) | −7819.38 | − | 13543.6i | −0.0261423 | − | 0.0452797i | ||||
\(156\) | −937318. | −3.08372 | ||||||||
\(157\) | 55274.5 | − | 95738.3i | 0.178968 | − | 0.309982i | −0.762559 | − | 0.646918i | \(-0.776057\pi\) |
0.941527 | + | 0.336936i | \(0.109391\pi\) | |||||||
\(158\) | −173954. | −0.554361 | ||||||||
\(159\) | −312364. | −0.979870 | ||||||||
\(160\) | 195054. | − | 337843.i | 0.602358 | − | 1.04331i | ||||
\(161\) | 37608.6 | + | 65140.0i | 0.114346 | + | 0.198054i | ||||
\(162\) | −619043. | −1.85325 | ||||||||
\(163\) | −55011.9 | + | 95283.4i | −0.162176 | + | 0.280898i | −0.935649 | − | 0.352932i | \(-0.885185\pi\) |
0.773473 | + | 0.633830i | \(0.218518\pi\) | |||||||
\(164\) | −269441. | + | 466685.i | −0.782265 | + | 1.35492i | ||||
\(165\) | −16948.7 | + | 29356.0i | −0.0484647 | + | 0.0839434i | ||||
\(166\) | 594245. | + | 1.02926e6i | 1.67377 | + | 2.89905i | ||||
\(167\) | −170680. | − | 295627.i | −0.473579 | − | 0.820263i | 0.525963 | − | 0.850507i | \(-0.323705\pi\) |
−0.999543 | + | 0.0302439i | \(0.990372\pi\) | |||||||
\(168\) | 84872.8 | − | 147004.i | 0.232004 | − | 0.401843i | ||||
\(169\) | −98915.2 | + | 171326.i | −0.266407 | + | 0.461431i | ||||
\(170\) | −351727. | + | 609210.i | −0.933435 | + | 1.61676i | ||||
\(171\) | 4602.20 | 0.0120358 | ||||||||
\(172\) | −167469. | − | 290065.i | −0.431632 | − | 0.747609i | ||||
\(173\) | −132933. | + | 230247.i | −0.337690 | + | 0.584895i | −0.983998 | − | 0.178181i | \(-0.942979\pi\) |
0.646308 | + | 0.763076i | \(0.276312\pi\) | |||||||
\(174\) | 878220. | 2.19903 | ||||||||
\(175\) | 49597.8 | 0.122424 | ||||||||
\(176\) | 108101. | − | 187236.i | 0.263055 | − | 0.455625i | ||||
\(177\) | 685187. | 1.64390 | ||||||||
\(178\) | −6154.17 | − | 10659.3i | −0.0145586 | − | 0.0252162i | ||||
\(179\) | −276376. | −0.644715 | −0.322358 | − | 0.946618i | \(-0.604475\pi\) | ||||
−0.322358 | + | 0.946618i | \(0.604475\pi\) | |||||||
\(180\) | −2703.91 | − | 4683.32i | −0.00622030 | − | 0.0107739i | ||||
\(181\) | −89464.1 | − | 154956.i | −0.202979 | − | 0.351571i | 0.746508 | − | 0.665377i | \(-0.231729\pi\) |
−0.949487 | + | 0.313806i | \(0.898396\pi\) | |||||||
\(182\) | −85821.5 | − | 148647.i | −0.192051 | − | 0.332643i | ||||
\(183\) | 188578. | − | 326626.i | 0.416258 | − | 0.720980i | ||||
\(184\) | 1.78226e6 | 3.88086 | ||||||||
\(185\) | −67406.8 | − | 228281.i | −0.144802 | − | 0.490388i | ||||
\(186\) | −89858.4 | −0.190448 | ||||||||
\(187\) | −88851.1 | + | 153895.i | −0.185806 | + | 0.321825i | ||||
\(188\) | 104245. | + | 180558.i | 0.215110 | + | 0.372582i | ||||
\(189\) | −40896.9 | − | 70835.5i | −0.0832791 | − | 0.144244i | ||||
\(190\) | −294810. | − | 510626.i | −0.592458 | − | 1.02617i | ||||
\(191\) | 720024. | 1.42812 | 0.714058 | − | 0.700086i | \(-0.246855\pi\) | ||||
0.714058 | + | 0.700086i | \(0.246855\pi\) | |||||||
\(192\) | −418824. | − | 725425.i | −0.819933 | − | 1.42017i | ||||
\(193\) | 119592. | 0.231104 | 0.115552 | − | 0.993301i | \(-0.463136\pi\) | ||||
0.115552 | + | 0.993301i | \(0.463136\pi\) | |||||||
\(194\) | 83960.0 | − | 145423.i | 0.160165 | − | 0.277414i | ||||
\(195\) | 334505. | 0.629965 | ||||||||
\(196\) | −1.30916e6 | −2.43417 | ||||||||
\(197\) | 313235. | − | 542538.i | 0.575048 | − | 0.996013i | −0.420988 | − | 0.907066i | \(-0.638317\pi\) |
0.996036 | − | 0.0889465i | \(-0.0283500\pi\) | |||||||
\(198\) | −955.941 | − | 1655.74i | −0.00173288 | − | 0.00300143i | ||||
\(199\) | −421571. | −0.754637 | −0.377319 | − | 0.926083i | \(-0.623154\pi\) | ||||
−0.377319 | + | 0.926083i | \(0.623154\pi\) | |||||||
\(200\) | 587607. | − | 1.01776e6i | 1.03875 | − | 1.79917i | ||||
\(201\) | 259942. | − | 450233.i | 0.453823 | − | 0.786044i | ||||
\(202\) | −913711. | + | 1.58259e6i | −1.57554 | + | 2.72892i | ||||
\(203\) | 57455.4 | + | 99515.6i | 0.0978567 | + | 0.169493i | ||||
\(204\) | 1.44404e6 | + | 2.50116e6i | 2.42943 | + | 4.20790i | ||||
\(205\) | 96156.7 | − | 166548.i | 0.159807 | − | 0.276793i | ||||
\(206\) | 182302. | − | 315757.i | 0.299312 | − | 0.518423i | ||||
\(207\) | 4133.90 | − | 7160.12i | 0.00670554 | − | 0.0116143i | ||||
\(208\) | −2.13351e6 | −3.41930 | ||||||||
\(209\) | −74472.9 | − | 128991.i | −0.117932 | − | 0.204265i | ||||
\(210\) | −50442.0 | + | 87368.1i | −0.0789304 | + | 0.136711i | ||||
\(211\) | −725830. | −1.12235 | −0.561176 | − | 0.827697i | \(-0.689651\pi\) | ||||
−0.561176 | + | 0.827697i | \(0.689651\pi\) | |||||||
\(212\) | −1.61280e6 | −2.46457 | ||||||||
\(213\) | 308872. | − | 534983.i | 0.466477 | − | 0.807961i | ||||
\(214\) | 1.87620e6 | 2.80056 | ||||||||
\(215\) | 59765.6 | + | 103517.i | 0.0881769 | + | 0.152727i | ||||
\(216\) | −1.93810e6 | −2.82645 | ||||||||
\(217\) | −5878.76 | − | 10182.3i | −0.00847494 | − | 0.0146790i | ||||
\(218\) | −563818. | − | 976562.i | −0.803523 | − | 1.39174i | ||||
\(219\) | 83643.5 | + | 144875.i | 0.117848 | + | 0.204119i | ||||
\(220\) | −87509.6 | + | 151571.i | −0.121899 | + | 0.211135i | ||||
\(221\) | 1.75360e6 | 2.41518 | ||||||||
\(222\) | −1.32960e6 | − | 320415.i | −1.81066 | − | 0.436345i | ||||
\(223\) | 253141. | 0.340879 | 0.170440 | − | 0.985368i | \(-0.445481\pi\) | ||||
0.170440 | + | 0.985368i | \(0.445481\pi\) | |||||||
\(224\) | 146645. | − | 253997.i | 0.195275 | − | 0.338227i | ||||
\(225\) | −2725.87 | − | 4721.34i | −0.00358962 | − | 0.00621740i | ||||
\(226\) | −172432. | − | 298661.i | −0.224568 | − | 0.388963i | ||||
\(227\) | −49217.5 | − | 85247.2i | −0.0633950 | − | 0.109803i | 0.832586 | − | 0.553896i | \(-0.186859\pi\) |
−0.895981 | + | 0.444093i | \(0.853526\pi\) | |||||||
\(228\) | −2.42073e6 | −3.08396 | ||||||||
\(229\) | 675529. | + | 1.17005e6i | 0.851246 | + | 1.47440i | 0.880084 | + | 0.474818i | \(0.157486\pi\) |
−0.0288381 | + | 0.999584i | \(0.509181\pi\) | |||||||
\(230\) | −1.05924e6 | −1.32031 | ||||||||
\(231\) | −12742.3 | + | 22070.4i | −0.0157116 | + | 0.0272132i | ||||
\(232\) | 2.72280e6 | 3.32120 | ||||||||
\(233\) | −1.07960e6 | −1.30279 | −0.651395 | − | 0.758738i | \(-0.725816\pi\) | ||||
−0.651395 | + | 0.758738i | \(0.725816\pi\) | |||||||
\(234\) | −9433.40 | + | 16339.1i | −0.0112623 | + | 0.0195069i | ||||
\(235\) | −37202.4 | − | 64436.5i | −0.0439442 | − | 0.0761136i | ||||
\(236\) | 3.53777e6 | 4.13475 | ||||||||
\(237\) | 127437. | − | 220727.i | 0.147375 | − | 0.255262i | ||||
\(238\) | −264435. | + | 458015.i | −0.302606 | + | 0.524128i | ||||
\(239\) | 179456. | − | 310827.i | 0.203218 | − | 0.351984i | −0.746345 | − | 0.665559i | \(-0.768193\pi\) |
0.949564 | + | 0.313575i | \(0.101527\pi\) | |||||||
\(240\) | 626992. | + | 1.08598e6i | 0.702642 | + | 1.21701i | ||||
\(241\) | 700831. | + | 1.21387e6i | 0.777268 | + | 1.34627i | 0.933511 | + | 0.358549i | \(0.116728\pi\) |
−0.156243 | + | 0.987719i | \(0.549938\pi\) | |||||||
\(242\) | 821622. | − | 1.42309e6i | 0.901849 | − | 1.56205i | ||||
\(243\) | −8947.41 | + | 15497.4i | −0.00972034 | + | 0.0168361i | ||||
\(244\) | 973666. | − | 1.68644e6i | 1.04697 | − | 1.81341i | ||||
\(245\) | 467205. | 0.497270 | ||||||||
\(246\) | −552504. | − | 956965.i | −0.582100 | − | 1.00823i | ||||
\(247\) | −734912. | + | 1.27291e6i | −0.766466 | + | 1.32756i | ||||
\(248\) | −278593. | −0.287635 | ||||||||
\(249\) | −1.74135e6 | −1.77986 | ||||||||
\(250\) | −822086. | + | 1.42389e6i | −0.831893 | + | 1.44088i | ||||
\(251\) | −1.42358e6 | −1.42625 | −0.713127 | − | 0.701035i | \(-0.752722\pi\) | ||||
−0.713127 | + | 0.701035i | \(0.752722\pi\) | |||||||
\(252\) | −2032.85 | − | 3521.01i | −0.00201653 | − | 0.00349273i | ||||
\(253\) | −267579. | −0.262816 | ||||||||
\(254\) | −1.10569e6 | − | 1.91512e6i | −1.07535 | − | 1.86256i | ||||
\(255\) | −515343. | − | 892600.i | −0.496302 | − | 0.859620i | ||||
\(256\) | 149474. | + | 258897.i | 0.142550 | + | 0.246903i | ||||
\(257\) | 576067. | − | 997777.i | 0.544052 | − | 0.942325i | −0.454614 | − | 0.890688i | \(-0.650223\pi\) |
0.998666 | − | 0.0516367i | \(-0.0164438\pi\) | |||||||
\(258\) | 686811. | 0.642374 | ||||||||
\(259\) | −50677.7 | − | 171626.i | −0.0469426 | − | 0.158977i | ||||
\(260\) | 1.72712e6 | 1.58449 | ||||||||
\(261\) | 6315.43 | − | 10938.6i | 0.00573854 | − | 0.00993945i | ||||
\(262\) | −927368. | − | 1.60625e6i | −0.834639 | − | 1.44564i | ||||
\(263\) | 304165. | + | 526828.i | 0.271156 | + | 0.469656i | 0.969158 | − | 0.246440i | \(-0.0792607\pi\) |
−0.698002 | + | 0.716096i | \(0.745927\pi\) | |||||||
\(264\) | 301928. | + | 522955.i | 0.266621 | + | 0.461801i | ||||
\(265\) | 575568. | 0.503480 | ||||||||
\(266\) | −221644. | − | 383898.i | −0.192066 | − | 0.332668i | ||||
\(267\) | 18033.9 | 0.0154814 | ||||||||
\(268\) | 1.34214e6 | − | 2.32465e6i | 1.14146 | − | 1.97706i | ||||
\(269\) | −1.07935e6 | −0.909452 | −0.454726 | − | 0.890631i | \(-0.650263\pi\) | ||||
−0.454726 | + | 0.890631i | \(0.650263\pi\) | |||||||
\(270\) | 1.15186e6 | 0.961589 | ||||||||
\(271\) | −557279. | + | 965236.i | −0.460945 | + | 0.798381i | −0.999008 | − | 0.0445239i | \(-0.985823\pi\) |
0.538063 | + | 0.842905i | \(0.319156\pi\) | |||||||
\(272\) | 3.28692e6 | + | 5.69311e6i | 2.69381 | + | 4.66581i | ||||
\(273\) | 251487. | 0.204225 | ||||||||
\(274\) | 280648. | − | 486096.i | 0.225832 | − | 0.391152i | ||||
\(275\) | −88220.0 | + | 152802.i | −0.0703454 | + | 0.121842i | ||||
\(276\) | −2.17440e6 | + | 3.76618e6i | −1.71818 | + | 2.97597i | ||||
\(277\) | 347185. | + | 601342.i | 0.271870 | + | 0.470893i | 0.969341 | − | 0.245721i | \(-0.0790246\pi\) |
−0.697471 | + | 0.716613i | \(0.745691\pi\) | |||||||
\(278\) | 1.10339e6 | + | 1.91113e6i | 0.856284 | + | 1.48313i | ||||
\(279\) | −646.187 | + | 1119.23i | −0.000496990 | + | 0.000860812i | ||||
\(280\) | −156388. | + | 270873.i | −0.119209 | + | 0.206476i | ||||
\(281\) | −1.05421e6 | + | 1.82594e6i | −0.796452 | + | 1.37949i | 0.125461 | + | 0.992098i | \(0.459959\pi\) |
−0.921913 | + | 0.387396i | \(0.873374\pi\) | |||||||
\(282\) | −427521. | −0.320136 | ||||||||
\(283\) | 90560.8 | + | 156856.i | 0.0672163 | + | 0.116422i | 0.897675 | − | 0.440658i | \(-0.145255\pi\) |
−0.830459 | + | 0.557080i | \(0.811922\pi\) | |||||||
\(284\) | 1.59477e6 | − | 2.76223e6i | 1.17328 | − | 2.03219i | ||||
\(285\) | 863897. | 0.630014 | ||||||||
\(286\) | 610606. | 0.441414 | ||||||||
\(287\) | 72292.4 | − | 125214.i | 0.0518069 | − | 0.0897322i | ||||
\(288\) | −32238.2 | −0.0229028 | ||||||||
\(289\) | −1.99168e6 | − | 3.44970e6i | −1.40274 | − | 2.42961i | ||||
\(290\) | −1.61823e6 | −1.12991 | ||||||||
\(291\) | 123016. | + | 213070.i | 0.0851589 | + | 0.147500i | ||||
\(292\) | 431869. | + | 748019.i | 0.296412 | + | 0.513400i | ||||
\(293\) | −597994. | − | 1.03576e6i | −0.406938 | − | 0.704837i | 0.587607 | − | 0.809146i | \(-0.300070\pi\) |
−0.994545 | + | 0.104309i | \(0.966737\pi\) | |||||||
\(294\) | 1.34225e6 | − | 2.32485e6i | 0.905661 | − | 1.56865i | ||||
\(295\) | −1.26254e6 | −0.844676 | ||||||||
\(296\) | −4.12223e6 | − | 993402.i | −2.73466 | − | 0.659015i | ||||
\(297\) | 290975. | 0.191410 | ||||||||
\(298\) | −1.40664e6 | + | 2.43637e6i | −0.917574 | + | 1.58928i | ||||
\(299\) | 1.32026e6 | + | 2.28676e6i | 0.854047 | + | 1.47925i | ||||
\(300\) | 1.43379e6 | + | 2.48339e6i | 0.919775 | + | 1.59310i | ||||
\(301\) | 44932.9 | + | 77826.0i | 0.0285857 | + | 0.0495118i | ||||
\(302\) | 3.22782e6 | 2.03654 | ||||||||
\(303\) | −1.33875e6 | − | 2.31878e6i | −0.837707 | − | 1.45095i | ||||
\(304\) | −5.51004e6 | −3.41956 | ||||||||
\(305\) | −347477. | + | 601848.i | −0.213883 | + | 0.370456i | ||||
\(306\) | 58132.9 | 0.0354910 | ||||||||
\(307\) | −2.06735e6 | −1.25190 | −0.625948 | − | 0.779865i | \(-0.715288\pi\) | ||||
−0.625948 | + | 0.779865i | \(0.715288\pi\) | |||||||
\(308\) | −65791.4 | + | 113954.i | −0.0395177 | + | 0.0684467i | ||||
\(309\) | 267105. | + | 462639.i | 0.159142 | + | 0.275643i | ||||
\(310\) | 165575. | 0.0978566 | ||||||||
\(311\) | −1.25468e6 | + | 2.17316e6i | −0.735582 | + | 1.27407i | 0.218886 | + | 0.975751i | \(0.429758\pi\) |
−0.954468 | + | 0.298315i | \(0.903575\pi\) | |||||||
\(312\) | 2.97948e6 | − | 5.16062e6i | 1.73282 | − | 3.00134i | ||||
\(313\) | 955598. | − | 1.65514e6i | 0.551334 | − | 0.954938i | −0.446845 | − | 0.894611i | \(-0.647452\pi\) |
0.998179 | − | 0.0603265i | \(-0.0192142\pi\) | |||||||
\(314\) | 585217. | + | 1.01363e6i | 0.334960 | + | 0.580168i | ||||
\(315\) | 725.474 | + | 1256.56i | 0.000411951 | + | 0.000713520i | ||||
\(316\) | 657984. | − | 1.13966e6i | 0.370679 | − | 0.642035i | ||||
\(317\) | 239594. | − | 414989.i | 0.133915 | − | 0.231947i | −0.791268 | − | 0.611470i | \(-0.790579\pi\) |
0.925182 | + | 0.379523i | \(0.123912\pi\) | |||||||
\(318\) | 1.65357e6 | − | 2.86407e6i | 0.916970 | − | 1.58824i | ||||
\(319\) | −408786. | −0.224915 | ||||||||
\(320\) | 771734. | + | 1.33668e6i | 0.421301 | + | 0.729715i | ||||
\(321\) | −1.37448e6 | + | 2.38068e6i | −0.744521 | + | 1.28955i | ||||
\(322\) | −796359. | −0.428025 | ||||||||
\(323\) | 4.52886e6 | 2.41536 | ||||||||
\(324\) | 2.34153e6 | − | 4.05566e6i | 1.23919 | − | 2.14634i | ||||
\(325\) | 1.74114e6 | 0.914378 | ||||||||
\(326\) | −582436. | − | 1.00881e6i | −0.303532 | − | 0.525733i | ||||
\(327\) | 1.65219e6 | 0.854457 | ||||||||
\(328\) | −1.71296e6 | − | 2.96694e6i | −0.879150 | − | 1.52273i | ||||
\(329\) | −27969.5 | − | 48444.6i | −0.0142461 | − | 0.0246749i | ||||
\(330\) | −179443. | − | 310805.i | −0.0907074 | − | 0.157110i | ||||
\(331\) | 495787. | − | 858727.i | 0.248728 | − | 0.430810i | −0.714445 | − | 0.699691i | \(-0.753321\pi\) |
0.963173 | + | 0.268882i | \(0.0866541\pi\) | |||||||
\(332\) | −8.99094e6 | −4.47672 | ||||||||
\(333\) | −13552.3 | + | 14256.6i | −0.00669733 | + | 0.00704539i | ||||
\(334\) | 3.61415e6 | 1.77272 | ||||||||
\(335\) | −478974. | + | 829608.i | −0.233185 | + | 0.403888i | ||||
\(336\) | 471384. | + | 816462.i | 0.227786 | + | 0.394537i | ||||
\(337\) | 978872. | + | 1.69546e6i | 0.469517 | + | 0.813227i | 0.999393 | − | 0.0348482i | \(-0.0110948\pi\) |
−0.529876 | + | 0.848075i | \(0.677761\pi\) | |||||||
\(338\) | −1.04726e6 | − | 1.81391e6i | −0.498613 | − | 0.863622i | ||||
\(339\) | 505288. | 0.238803 | ||||||||
\(340\) | −2.66082e6 | − | 4.60868e6i | −1.24830 | − | 2.16212i | ||||
\(341\) | 41826.4 | 0.0194789 | ||||||||
\(342\) | −24362.8 | + | 42197.6i | −0.0112632 | + | 0.0195085i | ||||
\(343\) | 712432. | 0.326970 | ||||||||
\(344\) | 2.12936e6 | 0.970182 | ||||||||
\(345\) | 775990. | − | 1.34405e6i | 0.351001 | − | 0.607952i | ||||
\(346\) | −1.40742e6 | − | 2.43773e6i | −0.632025 | − | 1.09470i | ||||
\(347\) | 2.55966e6 | 1.14119 | 0.570596 | − | 0.821231i | \(-0.306712\pi\) | ||||
0.570596 | + | 0.821231i | \(0.306712\pi\) | |||||||
\(348\) | −3.32188e6 | + | 5.75366e6i | −1.47040 | + | 2.54681i | ||||
\(349\) | −1.42203e6 | + | 2.46302e6i | −0.624948 | + | 1.08244i | 0.363602 | + | 0.931554i | \(0.381547\pi\) |
−0.988551 | + | 0.150888i | \(0.951787\pi\) | |||||||
\(350\) | −262557. | + | 454762.i | −0.114565 | + | 0.198433i | ||||
\(351\) | −1.43570e6 | − | 2.48670e6i | −0.622007 | − | 1.07735i | ||||
\(352\) | 521678. | + | 903574.i | 0.224412 | + | 0.388693i | ||||
\(353\) | −184527. | + | 319610.i | −0.0788175 | + | 0.136516i | −0.902740 | − | 0.430187i | \(-0.858448\pi\) |
0.823923 | + | 0.566702i | \(0.191781\pi\) | |||||||
\(354\) | −3.62720e6 | + | 6.28249e6i | −1.53838 | + | 2.66455i | ||||
\(355\) | −569134. | + | 985769.i | −0.239687 | + | 0.415149i | ||||
\(356\) | 93112.8 | 0.0389390 | ||||||||
\(357\) | −387445. | − | 671074.i | −0.160894 | − | 0.278676i | ||||
\(358\) | 1.46306e6 | − | 2.53410e6i | 0.603330 | − | 1.04500i | ||||
\(359\) | −413282. | −0.169243 | −0.0846214 | − | 0.996413i | \(-0.526968\pi\) | ||||
−0.0846214 | + | 0.996413i | \(0.526968\pi\) | |||||||
\(360\) | 34380.1 | 0.0139814 | ||||||||
\(361\) | −659944. | + | 1.14306e6i | −0.266525 | + | 0.461636i | ||||
\(362\) | 1.89439e6 | 0.759799 | ||||||||
\(363\) | 1.20382e6 | + | 2.08508e6i | 0.479508 | + | 0.830532i | ||||
\(364\) | 1.29848e6 | 0.513668 | ||||||||
\(365\) | −154123. | − | 266949.i | −0.0605530 | − | 0.104881i | ||||
\(366\) | 1.99656e6 | + | 3.45814e6i | 0.779075 | + | 1.34940i | ||||
\(367\) | 1.41431e6 | + | 2.44965e6i | 0.548124 | + | 0.949378i | 0.998403 | + | 0.0564906i | \(0.0179911\pi\) |
−0.450279 | + | 0.892888i | \(0.648676\pi\) | |||||||
\(368\) | −4.94936e6 | + | 8.57254e6i | −1.90515 | + | 3.29982i | ||||
\(369\) | −15892.6 | −0.00607616 | ||||||||
\(370\) | 2.44994e6 | + | 590403.i | 0.930361 | + | 0.224205i | ||||
\(371\) | 432723. | 0.163221 | ||||||||
\(372\) | 339890. | − | 588707.i | 0.127345 | − | 0.220568i | ||||
\(373\) | −1.76435e6 | − | 3.05595e6i | −0.656619 | − | 1.13730i | −0.981485 | − | 0.191537i | \(-0.938653\pi\) |
0.324866 | − | 0.945760i | \(-0.394681\pi\) | |||||||
\(374\) | −940707. | − | 1.62935e6i | −0.347757 | − | 0.602332i | ||||
\(375\) | −1.20450e6 | − | 2.08626e6i | −0.442313 | − | 0.766108i | ||||
\(376\) | −1.32547e6 | −0.483504 | ||||||||
\(377\) | 2.01699e6 | + | 3.49352e6i | 0.730886 | + | 1.26593i | ||||
\(378\) | 865989. | 0.311733 | ||||||||
\(379\) | 2.34548e6 | − | 4.06248e6i | 0.838751 | − | 1.45276i | −0.0521889 | − | 0.998637i | \(-0.516620\pi\) |
0.890940 | − | 0.454122i | \(-0.150047\pi\) | |||||||
\(380\) | 4.46048e6 | 1.58461 | ||||||||
\(381\) | 3.24007e6 | 1.14352 | ||||||||
\(382\) | −3.81161e6 | + | 6.60191e6i | −1.33644 | + | 2.31479i | ||||
\(383\) | −904670. | − | 1.56693e6i | −0.315133 | − | 0.545826i | 0.664333 | − | 0.747437i | \(-0.268716\pi\) |
−0.979466 | + | 0.201611i | \(0.935382\pi\) | |||||||
\(384\) | 2.09373e6 | 0.724591 | ||||||||
\(385\) | 23479.3 | − | 40667.3i | 0.00807296 | − | 0.0139828i | ||||
\(386\) | −633086. | + | 1.09654e6i | −0.216269 | + | 0.374589i | ||||
\(387\) | 4938.97 | − | 8554.55i | 0.00167633 | − | 0.00290349i | ||||
\(388\) | 635159. | + | 1.10013e6i | 0.214192 | + | 0.370991i | ||||
\(389\) | −1.16201e6 | − | 2.01266e6i | −0.389347 | − | 0.674368i | 0.603015 | − | 0.797730i | \(-0.293966\pi\) |
−0.992362 | + | 0.123362i | \(0.960632\pi\) | |||||||
\(390\) | −1.77078e6 | + | 3.06708e6i | −0.589526 | + | 1.02109i | ||||
\(391\) | 4.06802e6 | − | 7.04602e6i | 1.34568 | − | 2.33078i | ||||
\(392\) | 4.16146e6 | − | 7.20786e6i | 1.36783 | − | 2.36914i | ||||
\(393\) | 2.71752e6 | 0.887546 | ||||||||
\(394\) | 3.31636e6 | + | 5.74410e6i | 1.07627 | + | 1.86415i | ||||
\(395\) | −234818. | + | 406717.i | −0.0757249 | + | 0.131159i | ||||
\(396\) | 14463.4 | 0.00463482 | ||||||||
\(397\) | −2.06164e6 | −0.656503 | −0.328251 | − | 0.944590i | \(-0.606459\pi\) | ||||
−0.328251 | + | 0.944590i | \(0.606459\pi\) | |||||||
\(398\) | 2.23168e6 | − | 3.86539e6i | 0.706196 | − | 1.22317i | ||||
\(399\) | 649494. | 0.204241 | ||||||||
\(400\) | 3.26357e6 | + | 5.65268e6i | 1.01987 | + | 1.76646i | ||||
\(401\) | −4.19444e6 | −1.30261 | −0.651303 | − | 0.758818i | \(-0.725777\pi\) | ||||
−0.651303 | + | 0.758818i | \(0.725777\pi\) | |||||||
\(402\) | 2.75213e6 | + | 4.76682e6i | 0.849382 | + | 1.47117i | ||||
\(403\) | −206375. | − | 357453.i | −0.0632988 | − | 0.109637i | ||||
\(404\) | −6.91224e6 | − | 1.19723e7i | −2.10700 | − | 3.64944i | ||||
\(405\) | −835635. | + | 1.44736e6i | −0.253151 | + | 0.438470i | ||||
\(406\) | −1.21661e6 | −0.366300 | ||||||||
\(407\) | 618888. | + | 149144.i | 0.185194 | + | 0.0446292i | ||||
\(408\) | −1.83609e7 | −5.46065 | ||||||||
\(409\) | 591244. | − | 1.02407e6i | 0.174767 | − | 0.302705i | −0.765314 | − | 0.643657i | \(-0.777416\pi\) |
0.940081 | + | 0.340952i | \(0.110750\pi\) | |||||||
\(410\) | 1.01806e6 | + | 1.76332e6i | 0.299097 | + | 0.518051i | ||||
\(411\) | 411199. | + | 712217.i | 0.120074 | + | 0.207973i | ||||
\(412\) | 1.37912e6 | + | 2.38870e6i | 0.400275 | + | 0.693297i | ||||
\(413\) | −949201. | −0.273831 | ||||||||
\(414\) | 43767.5 | + | 75807.5i | 0.0125502 | + | 0.0217376i | ||||
\(415\) | 3.20864e6 | 0.914536 | ||||||||
\(416\) | 5.14802e6 | − | 8.91663e6i | 1.45850 | − | 2.52620i | ||||
\(417\) | −3.23333e6 | −0.910562 | ||||||||
\(418\) | 1.57696e6 | 0.441448 | ||||||||
\(419\) | −959408. | + | 1.66174e6i | −0.266974 | + | 0.462412i | −0.968079 | − | 0.250646i | \(-0.919357\pi\) |
0.701105 | + | 0.713058i | \(0.252690\pi\) | |||||||
\(420\) | −381595. | − | 660942.i | −0.105555 | − | 0.182827i | ||||
\(421\) | −6.70176e6 | −1.84282 | −0.921412 | − | 0.388588i | \(-0.872963\pi\) | ||||
−0.921412 | + | 0.388588i | \(0.872963\pi\) | |||||||
\(422\) | 3.84235e6 | − | 6.65515e6i | 1.05031 | − | 1.81918i | ||||
\(423\) | −3074.38 | + | 5324.98i | −0.000835422 | + | 0.00144699i | ||||
\(424\) | 5.12667e6 | − | 8.87965e6i | 1.38491 | − | 2.39873i | ||||
\(425\) | −2.68243e6 | − | 4.64610e6i | −0.720370 | − | 1.24772i | ||||
\(426\) | 3.27017e6 | + | 5.66411e6i | 0.873065 | + | 1.51219i | ||||
\(427\) | −261240. | + | 452480.i | −0.0693377 | + | 0.120096i | ||||
\(428\) | −7.09675e6 | + | 1.22919e7i | −1.87262 | + | 3.24348i | ||||
\(429\) | −447323. | + | 774786.i | −0.117349 | + | 0.203254i | ||||
\(430\) | −1.26553e6 | −0.330067 | ||||||||
\(431\) | −940654. | − | 1.62926e6i | −0.243914 | − | 0.422472i | 0.717912 | − | 0.696134i | \(-0.245098\pi\) |
−0.961826 | + | 0.273663i | \(0.911765\pi\) | |||||||
\(432\) | 5.38210e6 | − | 9.32207e6i | 1.38753 | − | 2.40327i | ||||
\(433\) | −4.92491e6 | −1.26235 | −0.631173 | − | 0.775642i | \(-0.717426\pi\) | ||||
−0.631173 | + | 0.775642i | \(0.717426\pi\) | |||||||
\(434\) | 124482. | 0.0317237 | ||||||||
\(435\) | 1.18549e6 | − | 2.05334e6i | 0.300384 | − | 0.520280i | ||||
\(436\) | 8.53059e6 | 2.14913 | ||||||||
\(437\) | 3.40972e6 | + | 5.90581e6i | 0.854112 | + | 1.47937i | ||||
\(438\) | −1.77115e6 | −0.441132 | ||||||||
\(439\) | −282238. | − | 488850.i | −0.0698962 | − | 0.121064i | 0.828959 | − | 0.559309i | \(-0.188933\pi\) |
−0.898855 | + | 0.438245i | \(0.855600\pi\) | |||||||
\(440\) | −556339. | − | 963608.i | −0.136996 | − | 0.237284i | ||||
\(441\) | −19304.7 | − | 33436.7i | −0.00472680 | − | 0.00818705i | ||||
\(442\) | −9.28307e6 | + | 1.60788e7i | −2.26014 | + | 3.91468i | ||||
\(443\) | 5.64681e6 | 1.36708 | 0.683540 | − | 0.729913i | \(-0.260439\pi\) | ||||
0.683540 | + | 0.729913i | \(0.260439\pi\) | |||||||
\(444\) | 7.12841e6 | − | 7.49888e6i | 1.71607 | − | 1.80526i | ||||
\(445\) | −33229.6 | −0.00795473 | ||||||||
\(446\) | −1.34006e6 | + | 2.32106e6i | −0.318998 | + | 0.552520i | ||||
\(447\) | −2.06097e6 | − | 3.56971e6i | −0.487869 | − | 0.845014i | ||||
\(448\) | 580204. | + | 1.00494e6i | 0.136580 | + | 0.236563i | ||||
\(449\) | 937316. | + | 1.62348e6i | 0.219417 | + | 0.380041i | 0.954630 | − | 0.297795i | \(-0.0962512\pi\) |
−0.735213 | + | 0.677836i | \(0.762918\pi\) | |||||||
\(450\) | 57720.0 | 0.0134368 | ||||||||
\(451\) | 257174. | + | 445439.i | 0.0595369 | + | 0.103121i | ||||
\(452\) | 2.60891e6 | 0.600637 | ||||||||
\(453\) | −2.36466e6 | + | 4.09572e6i | −0.541407 | + | 0.937745i | ||||
\(454\) | 1.04218e6 | 0.237302 | ||||||||
\(455\) | −463396. | −0.104936 | ||||||||
\(456\) | 7.69485e6 | − | 1.33279e7i | 1.73296 | − | 3.00157i | ||||
\(457\) | 149098. | + | 258245.i | 0.0333950 | + | 0.0578418i | 0.882240 | − | 0.470800i | \(-0.156035\pi\) |
−0.848845 | + | 0.528642i | \(0.822701\pi\) | |||||||
\(458\) | −1.43043e7 | −3.18641 | ||||||||
\(459\) | −4.42370e6 | + | 7.66208e6i | −0.980064 | + | 1.69752i | ||||
\(460\) | 4.00660e6 | − | 6.93963e6i | 0.882839 | − | 1.52912i | ||||
\(461\) | 1.01828e6 | − | 1.76371e6i | 0.223158 | − | 0.386522i | −0.732607 | − | 0.680652i | \(-0.761697\pi\) |
0.955765 | + | 0.294130i | \(0.0950299\pi\) | |||||||
\(462\) | −134909. | − | 233669.i | −0.0294060 | − | 0.0509327i | ||||
\(463\) | −2.64283e6 | − | 4.57751e6i | −0.572950 | − | 0.992378i | −0.996261 | − | 0.0863937i | \(-0.972466\pi\) |
0.423311 | − | 0.905984i | \(-0.360868\pi\) | |||||||
\(464\) | −7.56122e6 | + | 1.30964e7i | −1.63041 | + | 2.82395i | ||||
\(465\) | −121298. | + | 210095.i | −0.0260149 | + | 0.0450591i | ||||
\(466\) | 5.71513e6 | − | 9.89890e6i | 1.21916 | − | 2.11165i | ||||
\(467\) | 2.55705e6 | 0.542558 | 0.271279 | − | 0.962501i | \(-0.412553\pi\) | ||||
0.271279 | + | 0.962501i | \(0.412553\pi\) | |||||||
\(468\) | −71363.9 | − | 123606.i | −0.0150613 | − | 0.0260870i | ||||
\(469\) | −360102. | + | 623715.i | −0.0755950 | + | 0.130934i | ||||
\(470\) | 787759. | 0.164493 | ||||||||
\(471\) | −1.71489e6 | −0.356193 | ||||||||
\(472\) | −1.12456e7 | + | 1.94780e7i | −2.32342 | + | 4.02428i | ||||
\(473\) | −319690. | −0.0657017 | ||||||||
\(474\) | 1.34923e6 | + | 2.33694e6i | 0.275830 | + | 0.477752i | ||||
\(475\) | 4.49669e6 | 0.914449 | ||||||||
\(476\) | −2.00046e6 | − | 3.46489e6i | −0.404680 | − | 0.700927i | ||||
\(477\) | −23782.2 | − | 41192.0i | −0.00478582 | − | 0.00828929i | ||||
\(478\) | 1.89998e6 | + | 3.29086e6i | 0.380347 | + | 0.658780i | ||||
\(479\) | −1.28242e6 | + | 2.22122e6i | −0.255383 | + | 0.442336i | −0.964999 | − | 0.262252i | \(-0.915535\pi\) |
0.709617 | + | 0.704588i | \(0.248868\pi\) | |||||||
\(480\) | −6.05155e6 | −1.19885 | ||||||||
\(481\) | −1.77905e6 | − | 6.02497e6i | −0.350612 | − | 1.18739i | ||||
\(482\) | −1.48400e7 | −2.90949 | ||||||||
\(483\) | 583404. | − | 1.01049e6i | 0.113789 | − | 0.197089i | ||||
\(484\) | 6.21559e6 | + | 1.07657e7i | 1.20606 | + | 2.08896i | ||||
\(485\) | −226672. | − | 392608.i | −0.0437566 | − | 0.0757887i | ||||
\(486\) | −94730.3 | − | 164078.i | −0.0181928 | − | 0.0315108i | ||||
\(487\) | 3.95740e6 | 0.756115 | 0.378058 | − | 0.925782i | \(-0.376592\pi\) | ||||
0.378058 | + | 0.925782i | \(0.376592\pi\) | |||||||
\(488\) | 6.19005e6 | + | 1.07215e7i | 1.17664 | + | 2.03800i | ||||
\(489\) | 1.70674e6 | 0.322772 | ||||||||
\(490\) | −2.47326e6 | + | 4.28381e6i | −0.465350 | + | 0.806009i | ||||
\(491\) | −320564. | −0.0600083 | −0.0300042 | − | 0.999550i | \(-0.509552\pi\) | ||||
−0.0300042 | + | 0.999550i | \(0.509552\pi\) | |||||||
\(492\) | 8.35941e6 | 1.55691 | ||||||||
\(493\) | 6.21479e6 | − | 1.07643e7i | 1.15162 | − | 1.99466i | ||||
\(494\) | −7.78086e6 | − | 1.34768e7i | −1.43453 | − | 2.48468i | ||||
\(495\) | −5161.63 | −0.000946835 | ||||||||
\(496\) | 773655. | − | 1.34001e6i | 0.141203 | − | 0.244570i | ||||
\(497\) | −427886. | + | 741120.i | −0.0777028 | + | 0.134585i | ||||
\(498\) | 9.21822e6 | − | 1.59664e7i | 1.66561 | − | 2.88492i | ||||
\(499\) | 122595. | + | 212341.i | 0.0220406 | + | 0.0381754i | 0.876835 | − | 0.480791i | \(-0.159650\pi\) |
−0.854795 | + | 0.518966i | \(0.826317\pi\) | |||||||
\(500\) | −6.21910e6 | − | 1.07718e7i | −1.11251 | − | 1.92692i | ||||
\(501\) | −2.64768e6 | + | 4.58592e6i | −0.471272 | + | 0.816267i | ||||
\(502\) | 7.53603e6 | − | 1.30528e7i | 1.33470 | − | 2.31177i | ||||
\(503\) | −2.82627e6 | + | 4.89524e6i | −0.498073 | + | 0.862688i | −0.999998 | − | 0.00222327i | \(-0.999292\pi\) |
0.501924 | + | 0.864912i | \(0.332626\pi\) | |||||||
\(504\) | 25847.6 | 0.00453256 | ||||||||
\(505\) | 2.46680e6 | + | 4.27263e6i | 0.430434 | + | 0.745533i | ||||
\(506\) | 1.41649e6 | − | 2.45344e6i | 0.245945 | − | 0.425989i | ||||
\(507\) | 3.06885e6 | 0.530219 | ||||||||
\(508\) | 1.67292e7 | 2.87618 | ||||||||
\(509\) | −1.47273e6 | + | 2.55084e6i | −0.251958 | + | 0.436403i | −0.964065 | − | 0.265667i | \(-0.914408\pi\) |
0.712107 | + | 0.702071i | \(0.247741\pi\) | |||||||
\(510\) | 1.09123e7 | 1.85777 | ||||||||
\(511\) | −115873. | − | 200697.i | −0.0196304 | − | 0.0340008i | ||||
\(512\) | −7.48416e6 | −1.26174 | ||||||||
\(513\) | −3.70785e6 | − | 6.42218e6i | −0.622054 | − | 1.07743i | ||||
\(514\) | 6.09909e6 | + | 1.05639e7i | 1.01826 | + | 1.76367i | ||||
\(515\) | −492173. | − | 852469.i | −0.0817711 | − | 0.141632i | ||||
\(516\) | −2.59787e6 | + | 4.49964e6i | −0.429529 | + | 0.743967i | ||||
\(517\) | 198998. | 0.0327434 | ||||||||
\(518\) | 1.84191e6 | + | 443876.i | 0.301609 | + | 0.0726838i | ||||
\(519\) | 4.12425e6 | 0.672088 | ||||||||
\(520\) | −5.49006e6 | + | 9.50906e6i | −0.890366 | + | 1.54216i | ||||
\(521\) | 4.06862e6 | + | 7.04705e6i | 0.656678 | + | 1.13740i | 0.981470 | + | 0.191614i | \(0.0613723\pi\) |
−0.324792 | + | 0.945785i | \(0.605294\pi\) | |||||||
\(522\) | 66864.4 | + | 115812.i | 0.0107403 | + | 0.0186028i | ||||
\(523\) | 3.24409e6 | + | 5.61893e6i | 0.518607 | + | 0.898254i | 0.999766 | + | 0.0216208i | \(0.00688265\pi\) |
−0.481159 | + | 0.876633i | \(0.659784\pi\) | |||||||
\(524\) | 1.40311e7 | 2.23236 | ||||||||
\(525\) | −384693. | − | 666307.i | −0.0609138 | − | 0.105506i | ||||
\(526\) | −6.44066e6 | −1.01500 | ||||||||
\(527\) | −635889. | + | 1.10139e6i | −0.0997367 | + | 0.172749i | ||||
\(528\) | −3.35383e6 | −0.523547 | ||||||||
\(529\) | 5.81469e6 | 0.903415 | ||||||||
\(530\) | −3.04690e6 | + | 5.27739e6i | −0.471161 | + | 0.816074i | ||||
\(531\) | 52167.6 | + | 90356.9i | 0.00802905 | + | 0.0139067i | ||||
\(532\) | 3.35347e6 | 0.513708 | ||||||||
\(533\) | 2.53784e6 | − | 4.39567e6i | 0.386943 | − | 0.670205i | ||||
\(534\) | −95466.6 | + | 165353.i | −0.0144877 | + | 0.0250934i | ||||
\(535\) | 2.53265e6 | − | 4.38668e6i | 0.382552 | − | 0.662600i | ||||
\(536\) | 8.53258e6 | + | 1.47789e7i | 1.28283 | + | 2.22192i | ||||
\(537\) | 2.14364e6 | + | 3.71290e6i | 0.320787 | + | 0.555619i | ||||
\(538\) | 5.71376e6 | − | 9.89653e6i | 0.851073 | − | 1.47410i | ||||
\(539\) | −624779. | + | 1.08215e6i | −0.0926305 | + | 0.160441i | ||||
\(540\) | −4.35691e6 | + | 7.54640e6i | −0.642976 | + | 1.11367i | ||||
\(541\) | −1.22611e7 | −1.80110 | −0.900550 | − | 0.434753i | \(-0.856836\pi\) | ||||
−0.900550 | + | 0.434753i | \(0.856836\pi\) | |||||||
\(542\) | −5.90017e6 | − | 1.02194e7i | −0.862713 | − | 1.49426i | ||||
\(543\) | −1.38781e6 | + | 2.40376e6i | −0.201991 | + | 0.349858i | ||||
\(544\) | −3.17244e7 | −4.59617 | ||||||||
\(545\) | −3.04435e6 | −0.439040 | ||||||||
\(546\) | −1.33131e6 | + | 2.30589e6i | −0.191116 | + | 0.331022i | ||||
\(547\) | −4.98338e6 | −0.712124 | −0.356062 | − | 0.934462i | \(-0.615881\pi\) | ||||
−0.356062 | + | 0.934462i | \(0.615881\pi\) | |||||||
\(548\) | 2.12311e6 | + | 3.67733e6i | 0.302009 | + | 0.523095i | ||||
\(549\) | 57430.4 | 0.00813225 | ||||||||
\(550\) | −934026. | − | 1.61778e6i | −0.131660 | − | 0.228041i | ||||
\(551\) | 5.20909e6 | + | 9.02241e6i | 0.730942 | + | 1.26603i | ||||
\(552\) | −1.38237e7 | − | 2.39433e7i | −1.93097 | − | 3.34455i | ||||
\(553\) | −176541. | + | 305777.i | −0.0245489 | + | 0.0425199i | ||||
\(554\) | −7.35161e6 | −1.01767 | ||||||||
\(555\) | −2.54395e6 | + | 2.67616e6i | −0.350571 | + | 0.368791i | ||||
\(556\) | −1.66944e7 | −2.29025 | ||||||||
\(557\) | −3.93877e6 | + | 6.82215e6i | −0.537926 | + | 0.931715i | 0.461089 | + | 0.887354i | \(0.347459\pi\) |
−0.999016 | + | 0.0443617i | \(0.985875\pi\) | |||||||
\(558\) | −6841.48 | − | 11849.8i | −0.000930175 | − | 0.00161111i | ||||
\(559\) | 1.57738e6 | + | 2.73210e6i | 0.213505 | + | 0.369801i | ||||
\(560\) | −868582. | − | 1.50443e6i | −0.117042 | − | 0.202722i | ||||
\(561\) | 2.75661e6 | 0.369801 | ||||||||
\(562\) | −1.11614e7 | − | 1.93320e7i | −1.49065 | − | 2.58189i | ||||
\(563\) | 9.07153e6 | 1.20617 | 0.603087 | − | 0.797676i | \(-0.293937\pi\) | ||||
0.603087 | + | 0.797676i | \(0.293937\pi\) | |||||||
\(564\) | 1.61710e6 | − | 2.80090e6i | 0.214062 | − | 0.370766i | ||||
\(565\) | −931053. | −0.122702 | ||||||||
\(566\) | −1.91762e6 | −0.251606 | ||||||||
\(567\) | −628246. | + | 1.08815e6i | −0.0820677 | + | 0.142145i | ||||
\(568\) | 1.01387e7 | + | 1.75608e7i | 1.31860 | + | 2.28388i | ||||
\(569\) | 353751. | 0.0458054 | 0.0229027 | − | 0.999738i | \(-0.492709\pi\) | ||||
0.0229027 | + | 0.999738i | \(0.492709\pi\) | |||||||
\(570\) | −4.57324e6 | + | 7.92108e6i | −0.589572 | + | 1.02117i | ||||
\(571\) | −3.37774e6 | + | 5.85043e6i | −0.433547 | + | 0.750926i | −0.997176 | − | 0.0751023i | \(-0.976072\pi\) |
0.563628 | + | 0.826028i | \(0.309405\pi\) | |||||||
\(572\) | −2.30962e6 | + | 4.00038e6i | −0.295156 | + | 0.511225i | ||||
\(573\) | −5.58469e6 | − | 9.67297e6i | −0.710579 | − | 1.23076i | ||||
\(574\) | 765393. | + | 1.32570e6i | 0.0969627 | + | 0.167944i | ||||
\(575\) | 4.03913e6 | − | 6.99597e6i | 0.509469 | − | 0.882426i | ||||
\(576\) | 63775.4 | − | 110462.i | 0.00800934 | − | 0.0138726i | ||||
\(577\) | 3.01054e6 | − | 5.21441e6i | 0.376448 | − | 0.652027i | −0.614095 | − | 0.789232i | \(-0.710479\pi\) |
0.990543 | + | 0.137205i | \(0.0438120\pi\) | |||||||
\(578\) | 4.21738e7 | 5.25077 | ||||||||
\(579\) | −927583. | − | 1.60662e6i | −0.114989 | − | 0.199167i | ||||
\(580\) | 6.12095e6 | − | 1.06018e7i | 0.755525 | − | 1.30861i | ||||
\(581\) | 2.41232e6 | 0.296479 | ||||||||
\(582\) | −2.60486e6 | −0.318770 | ||||||||
\(583\) | −769689. | + | 1.33314e6i | −0.0937873 | + | 0.162444i | ||||
\(584\) | −5.49119e6 | −0.666245 | ||||||||
\(585\) | 25468.0 | + | 44111.8i | 0.00307684 | + | 0.00532924i | ||||
\(586\) | 1.26625e7 | 1.52326 | ||||||||
\(587\) | 3.49288e6 | + | 6.04985e6i | 0.418397 | + | 0.724685i | 0.995778 | − | 0.0917895i | \(-0.0292587\pi\) |
−0.577381 | + | 0.816475i | \(0.695925\pi\) | |||||||
\(588\) | 1.01542e7 | + | 1.75875e7i | 1.21116 | + | 2.09779i | ||||
\(589\) | −532988. | − | 923162.i | −0.0633037 | − | 0.109645i | ||||
\(590\) | 6.68354e6 | − | 1.15762e7i | 0.790454 | − | 1.36911i | ||||
\(591\) | −9.71811e6 | −1.14449 | ||||||||
\(592\) | 1.62256e7 | − | 1.70689e7i | 1.90282 | − | 2.00171i | ||||
\(593\) | 1.07245e7 | 1.25239 | 0.626196 | − | 0.779666i | \(-0.284611\pi\) | ||||
0.626196 | + | 0.779666i | \(0.284611\pi\) | |||||||
\(594\) | −1.54034e6 | + | 2.66795e6i | −0.179123 | + | 0.310250i | ||||
\(595\) | 713913. | + | 1.23653e6i | 0.0826709 | + | 0.143190i | ||||
\(596\) | −1.06412e7 | − | 1.84311e7i | −1.22709 | − | 2.12538i | ||||
\(597\) | 3.26981e6 | + | 5.66348e6i | 0.375480 | + | 0.650351i | ||||
\(598\) | −2.79564e7 | −3.19690 | ||||||||
\(599\) | −7.60627e6 | − | 1.31745e7i | −0.866173 | − | 1.50026i | −0.865877 | − | 0.500257i | \(-0.833239\pi\) |
−0.000296251 | − | 1.00000i | \(-0.500094\pi\) | |||||||
\(600\) | −1.82305e7 | −2.06738 | ||||||||
\(601\) | 3.39170e6 | − | 5.87459e6i | 0.383028 | − | 0.663425i | −0.608465 | − | 0.793581i | \(-0.708214\pi\) |
0.991494 | + | 0.130156i | \(0.0415478\pi\) | |||||||
\(602\) | −951450. | −0.107003 | ||||||||
\(603\) | 79164.0 | 0.00886614 | ||||||||
\(604\) | −1.22093e7 | + | 2.11471e7i | −1.36175 | + | 2.35862i | ||||
\(605\) | −2.21819e6 | − | 3.84201e6i | −0.246382 | − | 0.426747i | ||||
\(606\) | 2.83479e7 | 3.13573 | ||||||||
\(607\) | −1.49874e6 | + | 2.59590e6i | −0.165103 | + | 0.285967i | −0.936692 | − | 0.350155i | \(-0.886129\pi\) |
0.771589 | + | 0.636122i | \(0.219462\pi\) | |||||||
\(608\) | 1.32953e7 | − | 2.30282e7i | 1.45861 | − | 2.52639i | ||||
\(609\) | 891277. | − | 1.54374e6i | 0.0973799 | − | 0.168667i | ||||
\(610\) | −3.67890e6 | − | 6.37204e6i | −0.400307 | − | 0.693352i | ||||
\(611\) | −981877. | − | 1.70066e6i | −0.106403 | − | 0.184295i | ||||
\(612\) | −219888. | + | 380857.i | −0.0237314 | + | 0.0411040i | ||||
\(613\) | 5.95491e6 | − | 1.03142e7i | 0.640064 | − | 1.10862i | −0.345354 | − | 0.938473i | \(-0.612241\pi\) |
0.985418 | − | 0.170151i | \(-0.0544257\pi\) | |||||||
\(614\) | 1.09440e7 | − | 1.89556e7i | 1.17153 | − | 2.02916i | ||||
\(615\) | −2.98326e6 | −0.318056 | ||||||||
\(616\) | −418266. | − | 724458.i | −0.0444121 | − | 0.0769240i | ||||
\(617\) | −2.90618e6 | + | 5.03364e6i | −0.307333 | + | 0.532316i | −0.977778 | − | 0.209643i | \(-0.932770\pi\) |
0.670445 | + | 0.741959i | \(0.266103\pi\) | |||||||
\(618\) | −5.65593e6 | −0.595707 | ||||||||
\(619\) | −1.28133e7 | −1.34410 | −0.672052 | − | 0.740504i | \(-0.734587\pi\) | ||||
−0.672052 | + | 0.740504i | \(0.734587\pi\) | |||||||
\(620\) | −626288. | + | 1.08476e6i | −0.0654328 | + | 0.113333i | ||||
\(621\) | −1.33222e7 | −1.38627 | ||||||||
\(622\) | −1.32838e7 | − | 2.30083e7i | −1.37673 | − | 2.38456i | ||||
\(623\) | −24982.6 | −0.00257880 | ||||||||
\(624\) | 1.65481e7 | + | 2.86621e7i | 1.70132 | + | 2.94677i | ||||
\(625\) | −1.38677e6 | − | 2.40196e6i | −0.142005 | − | 0.245961i | ||||
\(626\) | 1.01174e7 | + | 1.75238e7i | 1.03189 | + | 1.78728i | ||||
\(627\) | −1.15526e6 | + | 2.00097e6i | −0.117358 | + | 0.203269i | ||||
\(628\) | −8.85436e6 | −0.895897 | ||||||||
\(629\) | −1.33363e7 | + | 1.40294e7i | −1.34403 | + | 1.41388i | ||||
\(630\) | −15361.9 | −0.00154203 | ||||||||
\(631\) | −2.67993e6 | + | 4.64178e6i | −0.267948 | + | 0.464100i | −0.968332 | − | 0.249667i | \(-0.919679\pi\) |
0.700384 | + | 0.713767i | \(0.253012\pi\) | |||||||
\(632\) | 4.18311e6 | + | 7.24536e6i | 0.416588 | + | 0.721552i | ||||
\(633\) | 5.62972e6 | + | 9.75097e6i | 0.558442 | + | 0.967250i | ||||
\(634\) | 2.53669e6 | + | 4.39368e6i | 0.250637 | + | 0.434115i | ||||
\(635\) | −5.97022e6 | −0.587566 | ||||||||
\(636\) | 1.25093e7 | + | 2.16667e7i | 1.22628 | + | 2.12398i | ||||
\(637\) | 1.23309e7 | 1.20405 | ||||||||
\(638\) | 2.16400e6 | − | 3.74816e6i | 0.210478 | − | 0.364558i | ||||
\(639\) | 94065.5 | 0.00911335 | ||||||||
\(640\) | −3.85795e6 | −0.372312 | ||||||||
\(641\) | 1.89308e6 | − | 3.27891e6i | 0.181980 | − | 0.315198i | −0.760575 | − | 0.649250i | \(-0.775083\pi\) |
0.942555 | + | 0.334052i | \(0.108416\pi\) | |||||||
\(642\) | −1.45523e7 | − | 2.52053e7i | −1.39346 | − | 2.41354i | ||||
\(643\) | 5.89964e6 | 0.562727 | 0.281364 | − | 0.959601i | \(-0.409213\pi\) | ||||
0.281364 | + | 0.959601i | \(0.409213\pi\) | |||||||
\(644\) | 3.01224e6 | − | 5.21735e6i | 0.286203 | − | 0.495718i | ||||
\(645\) | 927114. | − | 1.60581e6i | 0.0877473 | − | 0.151983i | ||||
\(646\) | −2.39746e7 | + | 4.15252e7i | −2.26032 | + | 3.91498i | ||||
\(647\) | −4.68157e6 | − | 8.10871e6i | −0.439674 | − | 0.761537i | 0.557990 | − | 0.829847i | \(-0.311573\pi\) |
−0.997664 | + | 0.0683102i | \(0.978239\pi\) | |||||||
\(648\) | 1.48862e7 | + | 2.57837e7i | 1.39267 | + | 2.41217i | ||||
\(649\) | 1.68835e6 | − | 2.92431e6i | 0.157345 | − | 0.272529i | ||||
\(650\) | −9.21714e6 | + | 1.59646e7i | −0.855683 | + | 1.48209i | ||||
\(651\) | −91194.3 | + | 157953.i | −0.00843365 | + | 0.0146075i | ||||
\(652\) | 8.81228e6 | 0.811838 | ||||||||
\(653\) | 747407. | + | 1.29455e6i | 0.0685921 | + | 0.118805i | 0.898282 | − | 0.439420i | \(-0.144816\pi\) |
−0.829690 | + | 0.558225i | \(0.811483\pi\) | |||||||
\(654\) | −8.74624e6 | + | 1.51489e7i | −0.799608 | + | 1.38496i | ||||
\(655\) | −5.00735e6 | −0.456042 | ||||||||
\(656\) | 1.90276e7 | 1.72633 | ||||||||
\(657\) | −12736.6 | + | 22060.4i | −0.00115117 | + | 0.00199389i | ||||
\(658\) | 592252. | 0.0533263 | ||||||||
\(659\) | 5.66570e6 | + | 9.81328e6i | 0.508206 | + | 0.880239i | 0.999955 | + | 0.00950180i | \(0.00302456\pi\) |
−0.491749 | + | 0.870737i | \(0.663642\pi\) | |||||||
\(660\) | 2.71499e6 | 0.242609 | ||||||||
\(661\) | 3.65486e6 | + | 6.33040e6i | 0.325362 | + | 0.563544i | 0.981586 | − | 0.191023i | \(-0.0611804\pi\) |
−0.656223 | + | 0.754567i | \(0.727847\pi\) | |||||||
\(662\) | 5.24912e6 | + | 9.09174e6i | 0.465524 | + | 0.806310i | ||||
\(663\) | −1.36013e7 | − | 2.35582e7i | −1.20171 | − | 2.08141i | ||||
\(664\) | 2.85798e7 | − | 4.95017e7i | 2.51558 | − | 4.35712i | ||||
\(665\) | −1.19677e6 | −0.104944 | ||||||||
\(666\) | −58976.8 | − | 199732.i | −0.00515223 | − | 0.0174486i | ||||
\(667\) | 1.87161e7 | 1.62893 | ||||||||
\(668\) | −1.36705e7 | + | 2.36781e7i | −1.18534 | + | 2.05308i | ||||
\(669\) | −1.96343e6 | − | 3.40076e6i | −0.169609 | − | 0.293772i | ||||
\(670\) | −5.07112e6 | − | 8.78344e6i | −0.436432 | − | 0.755923i | ||||
\(671\) | −929339. | − | 1.60966e6i | −0.0796834 | − | 0.138016i | ||||
\(672\) | −4.54967e6 | −0.388648 | ||||||||
\(673\) | −3.82120e6 | − | 6.61852e6i | −0.325209 | − | 0.563279i | 0.656346 | − | 0.754460i | \(-0.272101\pi\) |
−0.981555 | + | 0.191182i | \(0.938768\pi\) | |||||||
\(674\) | −2.07275e7 | −1.75751 | ||||||||
\(675\) | −4.39229e6 | + | 7.60766e6i | −0.371049 | + | 0.642676i | ||||
\(676\) | 1.58451e7 | 1.33361 | ||||||||
\(677\) | −8.48703e6 | −0.711679 | −0.355840 | − | 0.934547i | \(-0.615805\pi\) | ||||
−0.355840 | + | 0.934547i | \(0.615805\pi\) | |||||||
\(678\) | −2.67486e6 | + | 4.63299e6i | −0.223474 | + | 0.387068i | ||||
\(679\) | −170416. | − | 295170.i | −0.0141853 | − | 0.0245696i | ||||
\(680\) | 3.38322e7 | 2.80581 | ||||||||
\(681\) | −763487. | + | 1.32240e6i | −0.0630861 | + | 0.109268i | ||||
\(682\) | −221418. | + | 383507.i | −0.0182285 | + | 0.0315728i | ||||
\(683\) | −6.73670e6 | + | 1.16683e7i | −0.552580 | + | 0.957097i | 0.445507 | + | 0.895278i | \(0.353023\pi\) |
−0.998087 | + | 0.0618183i | \(0.980310\pi\) | |||||||
\(684\) | −184305. | − | 319226.i | −0.0150625 | − | 0.0260890i | ||||
\(685\) | −757683. | − | 1.31235e6i | −0.0616966 | − | 0.106862i | ||||
\(686\) | −3.77142e6 | + | 6.53229e6i | −0.305981 | + | 0.529975i | ||||
\(687\) | 1.04791e7 | − | 1.81504e7i | 0.847099 | − | 1.46722i | ||||
\(688\) | −5.91324e6 | + | 1.02420e7i | −0.476272 | + | 0.824927i | ||||
\(689\) | 1.51909e7 | 1.21909 | ||||||||
\(690\) | 8.21576e6 | + | 1.42301e7i | 0.656939 | + | 1.13785i | ||||
\(691\) | −6.96227e6 | + | 1.20590e7i | −0.554697 | + | 0.960763i | 0.443230 | + | 0.896408i | \(0.353832\pi\) |
−0.997927 | + | 0.0643554i | \(0.979501\pi\) | |||||||
\(692\) | 2.12944e7 | 1.69044 | ||||||||
\(693\) | −3880.61 | −0.000306950 | ||||||||
\(694\) | −1.35501e7 | + | 2.34695e7i | −1.06794 | + | 1.84972i | ||||
\(695\) | 5.95779e6 | 0.467868 | ||||||||
\(696\) | −2.11187e7 | − | 3.65787e7i | −1.65251 | − | 2.86223i | ||||
\(697\) | −1.56393e7 | −1.21937 | ||||||||
\(698\) | −1.50557e7 | − | 2.60772e7i | −1.16966 | − | 2.02592i | ||||
\(699\) | 8.37368e6 | + | 1.45036e7i | 0.648222 | + | 1.12275i | ||||
\(700\) | −1.98625e6 | − | 3.44029e6i | −0.153211 | − | 0.265368i | ||||
\(701\) | −7.36436e6 | + | 1.27554e7i | −0.566031 | + | 0.980394i | 0.430922 | + | 0.902389i | \(0.358188\pi\) |
−0.996953 | + | 0.0780047i | \(0.975145\pi\) | |||||||
\(702\) | 3.04008e7 | 2.32832 | ||||||||
\(703\) | −4.59461e6 | − | 1.55602e7i | −0.350639 | − | 1.18748i | ||||
\(704\) | −4.12806e6 | −0.313916 | ||||||||
\(705\) | −577103. | + | 999572.i | −0.0437301 | + | 0.0757428i | ||||
\(706\) | −1.95367e6 | − | 3.38385e6i | −0.147516 | − | 0.255505i | ||||
\(707\) | 1.85459e6 | + | 3.21224e6i | 0.139540 | + | 0.241691i | ||||
\(708\) | −2.74398e7 | − | 4.75271e7i | −2.05730 | − | 3.56335i | ||||
\(709\) | 1.44039e7 | 1.07613 | 0.538065 | − | 0.842904i | \(-0.319156\pi\) | ||||
0.538065 | + | 0.842904i | \(0.319156\pi\) | |||||||
\(710\) | −6.02569e6 | − | 1.04368e7i | −0.448601 | − | 0.777000i | ||||
\(711\) | 38810.3 | 0.00287921 | ||||||||
\(712\) | −295981. | + | 512654.i | −0.0218808 | + | 0.0378987i | ||||
\(713\) | −1.91501e6 | −0.141074 | ||||||||
\(714\) | 8.20411e6 | 0.602263 | ||||||||
\(715\) | 824246. | − | 1.42764e6i | 0.0602965 | − | 0.104437i | ||||
\(716\) | 1.10681e7 | + | 1.91705e7i | 0.806844 | + | 1.39750i | ||||
\(717\) | −5.56762e6 | −0.404456 | ||||||||
\(718\) | 2.18780e6 | − | 3.78939e6i | 0.158379 | − | 0.274320i | ||||
\(719\) | 8.97005e6 | − | 1.55366e7i | 0.647102 | − | 1.12081i | −0.336710 | − | 0.941609i | \(-0.609314\pi\) |
0.983812 | − | 0.179205i | \(-0.0573526\pi\) | |||||||
\(720\) | −95473.6 | + | 165365.i | −0.00686360 | + | 0.0118881i | ||||
\(721\) | −370025. | − | 640902.i | −0.0265090 | − | 0.0459149i | ||||
\(722\) | −6.98713e6 | − | 1.21021e7i | −0.498834 | − | 0.864005i | ||||
\(723\) | 1.08716e7 | − | 1.88302e7i | 0.773481 | − | 1.33971i | ||||
\(724\) | −7.16556e6 | + | 1.24111e7i | −0.508047 | + | 0.879963i | ||||
\(725\) | 6.17065e6 | − | 1.06879e7i | 0.435999 | − | 0.755173i | ||||
\(726\) | −2.54908e7 | −1.79491 | ||||||||
\(727\) | −441525. | − | 764744.i | −0.0309827 | − | 0.0536636i | 0.850118 | − | 0.526592i | \(-0.176530\pi\) |
−0.881101 | + | 0.472928i | \(0.843197\pi\) | |||||||
\(728\) | −4.12753e6 | + | 7.14909e6i | −0.288643 | + | 0.499945i | ||||
\(729\) | 1.44857e7 | 1.00953 | ||||||||
\(730\) | 3.26355e6 | 0.226664 | ||||||||
\(731\) | 4.86027e6 | − | 8.41823e6i | 0.336408 | − | 0.582676i | ||||
\(732\) | −3.02080e7 | −2.08374 | ||||||||
\(733\) | 3.31214e6 | + | 5.73680e6i | 0.227693 | + | 0.394375i | 0.957124 | − | 0.289679i | \(-0.0935486\pi\) |
−0.729431 | + | 0.684054i | \(0.760215\pi\) | |||||||
\(734\) | −2.99479e7 | −2.05176 | ||||||||
\(735\) | −3.62376e6 | − | 6.27654e6i | −0.247424 | − | 0.428551i | ||||
\(736\) | −2.38849e7 | − | 4.13698e7i | −1.62528 | − | 2.81507i | ||||
\(737\) | −1.28103e6 | − | 2.21881e6i | −0.0868744 | − | 0.150471i | ||||
\(738\) | 84131.2 | − | 145719.i | 0.00568612 | − | 0.00984865i | ||||
\(739\) | 9.80466e6 | 0.660422 | 0.330211 | − | 0.943907i | \(-0.392880\pi\) | ||||
0.330211 | + | 0.943907i | \(0.392880\pi\) | |||||||
\(740\) | −1.31350e7 | + | 1.38176e7i | −0.881758 | + | 0.927583i | ||||
\(741\) | 2.28007e7 | 1.52546 | ||||||||
\(742\) | −2.29072e6 | + | 3.96764e6i | −0.152743 | + | 0.264559i | ||||
\(743\) | 2.45829e6 | + | 4.25788e6i | 0.163365 | + | 0.282957i | 0.936074 | − | 0.351804i | \(-0.114432\pi\) |
−0.772708 | + | 0.634761i | \(0.781098\pi\) | |||||||
\(744\) | 2.16084e6 | + | 3.74269e6i | 0.143117 | + | 0.247885i | ||||
\(745\) | 3.79759e6 | + | 6.57761e6i | 0.250678 | + | 0.434188i | ||||
\(746\) | 3.73600e7 | 2.45788 | ||||||||
\(747\) | −132580. | − | 229635.i | −0.00869311 | − | 0.0150569i | ||||
\(748\) | 1.42329e7 | 0.930123 | ||||||||
\(749\) | 1.90410e6 | − | 3.29799e6i | 0.124018 | − | 0.214805i | ||||
\(750\) | 2.55052e7 | 1.65568 | ||||||||
\(751\) | −4.91589e6 | −0.318055 | −0.159027 | − | 0.987274i | \(-0.550836\pi\) | ||||
−0.159027 | + | 0.987274i | \(0.550836\pi\) | |||||||
\(752\) | 3.68083e6 | − | 6.37539e6i | 0.237357 | − | 0.411114i | ||||
\(753\) | 1.10416e7 | + | 1.91247e7i | 0.709652 | + | 1.22915i | ||||
\(754\) | −4.27095e7 | −2.73588 | ||||||||
\(755\) | 4.35718e6 | − | 7.54685e6i | 0.278188 | − | 0.481835i | ||||
\(756\) | −3.27561e6 | + | 5.67352e6i | −0.208443 | + | 0.361034i | ||||
\(757\) | 1.08114e6 | − | 1.87258e6i | 0.0685710 | − | 0.118768i | −0.829702 | − | 0.558207i | \(-0.811489\pi\) |
0.898272 | + | 0.439439i | \(0.144823\pi\) | |||||||
\(758\) | 2.48326e7 | + | 4.30114e7i | 1.56982 | + | 2.71901i | ||||
\(759\) | 2.07541e6 | + | 3.59472e6i | 0.130768 | + | 0.226496i | ||||
\(760\) | −1.41787e7 | + | 2.45582e7i | −0.890434 | + | 1.54228i | ||||
\(761\) | 1.09080e7 | − | 1.88932e7i | 0.682785 | − | 1.18262i | −0.291343 | − | 0.956619i | \(-0.594102\pi\) |
0.974128 | − | 0.225999i | \(-0.0725646\pi\) | |||||||
\(762\) | −1.71521e7 | + | 2.97083e7i | −1.07011 | + | 1.85349i | ||||
\(763\) | −2.28880e6 | −0.142330 | ||||||||
\(764\) | −2.88349e7 | − | 4.99436e7i | −1.78725 | − | 3.09561i | ||||
\(765\) | 78472.5 | − | 135918.i | 0.00484802 | − | 0.00839701i | ||||
\(766\) | 1.91563e7 | 1.17961 | ||||||||
\(767\) | −3.33220e7 | −2.04523 | ||||||||
\(768\) | 2.31872e6 | − | 4.01614e6i | 0.141855 | − | 0.245700i | ||||
\(769\) | 1.35196e7 | 0.824416 | 0.412208 | − | 0.911090i | \(-0.364758\pi\) | ||||
0.412208 | + | 0.911090i | \(0.364758\pi\) | |||||||
\(770\) | 248586. | + | 430564.i | 0.0151095 | + | 0.0261704i | ||||
\(771\) | −1.78725e7 | −1.08280 | ||||||||
\(772\) | −4.78931e6 | − | 8.29532e6i | −0.289221 | − | 0.500945i | ||||
\(773\) | 2.33662e6 | + | 4.04715e6i | 0.140650 | + | 0.243613i | 0.927742 | − | 0.373223i | \(-0.121747\pi\) |
−0.787091 | + | 0.616836i | \(0.788414\pi\) | |||||||
\(774\) | 52291.2 | + | 90571.0i | 0.00313744 | + | 0.00543421i | ||||
\(775\) | −631373. | + | 1.09357e6i | −0.0377600 | + | 0.0654022i | ||||
\(776\) | −8.07600e6 | −0.481440 | ||||||||
\(777\) | −1.91259e6 | + | 2.01199e6i | −0.113650 | + | 0.119556i | ||||
\(778\) | 2.46055e7 | 1.45742 | ||||||||
\(779\) | 6.55427e6 | − | 1.13523e7i | 0.386973 | − | 0.670256i | ||||
\(780\) | −1.33960e7 | − | 2.32025e7i | −0.788385 | − | 1.36552i | ||||
\(781\) | −1.52217e6 | − | 2.63648e6i | −0.0892967 | − | 0.154666i | ||||
\(782\) | 4.30700e7 | + | 7.45994e7i | 2.51859 | + | 4.36233i | ||||
\(783\) | −2.03526e7 | −1.18635 | ||||||||
\(784\) | 2.31128e7 | + | 4.00325e7i | 1.34296 | + | 2.32607i | ||||
\(785\) | 3.15990e6 | 0.183020 | ||||||||
\(786\) | −1.43858e7 | + | 2.49169e7i | −0.830573 | + | 1.43859i | ||||
\(787\) | −1.44587e7 | −0.832133 | −0.416066 | − | 0.909334i | \(-0.636592\pi\) | ||||
−0.416066 | + | 0.909334i | \(0.636592\pi\) | |||||||
\(788\) | −5.01766e7 | −2.87863 | ||||||||
\(789\) | 4.71835e6 | − | 8.17243e6i | 0.269835 | − | 0.467368i | ||||
\(790\) | −2.48613e6 | − | 4.30610e6i | −0.141728 | − | 0.245480i | ||||
\(791\) | −699983. | −0.0397783 | ||||||||
\(792\) | −45975.4 | + | 79631.7i | −0.00260443 | + | 0.00451100i | ||||
\(793\) | −9.17089e6 | + | 1.58844e7i | −0.517879 | + | 0.896993i | ||||
\(794\) | 1.09138e7 | − | 1.89032e7i | 0.614361 | − | 1.06410i | ||||
\(795\) | −4.46425e6 | − | 7.73232e6i | −0.250513 | − | 0.433902i | ||||
\(796\) | 1.68827e7 | + | 2.92418e7i | 0.944409 | + | 1.63576i | ||||
\(797\) | 2.86989e6 | − | 4.97080e6i | 0.160037 | − | 0.277192i | −0.774845 | − | 0.632151i | \(-0.782172\pi\) |
0.934882 | + | 0.354960i | \(0.115505\pi\) | |||||||
\(798\) | −3.43825e6 | + | 5.95522e6i | −0.191130 | + | 0.331048i | ||||
\(799\) | −3.02538e6 | + | 5.24012e6i | −0.167654 | + | 0.290385i | ||||
\(800\) | −3.14991e7 | −1.74009 | ||||||||
\(801\) | 1373.03 | + | 2378.16i | 7.56135e−5 | + | 0.000130966i | ||||
\(802\) | 2.22042e7 | − | 3.84588e7i | 1.21899 | − | 2.11135i | ||||
\(803\) | 824416. | 0.0451188 | ||||||||
\(804\) | −4.16398e7 | −2.27179 | ||||||||
\(805\) | −1.07499e6 | + | 1.86194e6i | −0.0584676 | + | 0.101269i | ||||
\(806\) | 4.36998e6 | 0.236942 | ||||||||
\(807\) | 8.37168e6 | + | 1.45002e7i | 0.452510 | + | 0.783771i | ||||
\(808\) | 8.78886e7 | 4.73592 | ||||||||
\(809\) | −6.71156e6 | − | 1.16248e7i | −0.360539 | − | 0.624472i | 0.627511 | − | 0.778608i | \(-0.284074\pi\) |
−0.988050 | + | 0.154136i | \(0.950741\pi\) | |||||||
\(810\) | −8.84725e6 | − | 1.53239e7i | −0.473801 | − | 0.820647i | ||||
\(811\) | 1.23269e7 | + | 2.13509e7i | 0.658117 | + | 1.13989i | 0.981103 | + | 0.193488i | \(0.0619801\pi\) |
−0.322986 | + | 0.946404i | \(0.604687\pi\) | |||||||
\(812\) | 4.60185e6 | − | 7.97064e6i | 0.244930 | − | 0.424231i | ||||
\(813\) | 1.72896e7 | 0.917399 | ||||||||
\(814\) | −4.64373e6 | + | 4.88507e6i | −0.245644 | + | 0.258410i | ||||
\(815\) | −3.14488e6 | −0.165848 | ||||||||
\(816\) | 5.09883e7 | − | 8.83144e7i | 2.68068 | − | 4.64308i | ||||
\(817\) | 4.07376e6 | + | 7.05596e6i | 0.213521 | + | 0.369829i | ||||
\(818\) | 6.25978e6 | + | 1.08423e7i | 0.327096 | + | 0.566547i | ||||
\(819\) | 19147.3 | + | 33164.1i | 0.000997465 | + | 0.00172766i | ||||
\(820\) | −1.54032e7 | −0.799975 | ||||||||
\(821\) | −1.41101e6 | − | 2.44394e6i | −0.0730587 | − | 0.126541i | 0.827182 | − | 0.561934i | \(-0.189943\pi\) |
−0.900240 | + | 0.435393i | \(0.856609\pi\) | |||||||
\(822\) | −8.70710e6 | −0.449463 | ||||||||
\(823\) | −1.23503e7 | + | 2.13914e7i | −0.635593 | + | 1.10088i | 0.350796 | + | 0.936452i | \(0.385911\pi\) |
−0.986389 | + | 0.164428i | \(0.947422\pi\) | |||||||
\(824\) | −1.75354e7 | −0.899700 | ||||||||
\(825\) | 2.73703e6 | 0.140005 | ||||||||
\(826\) | 5.02481e6 | − | 8.70323e6i | 0.256254 | − | 0.443844i | ||||
\(827\) | 4.43566e6 | + | 7.68279e6i | 0.225525 | + | 0.390621i | 0.956477 | − | 0.291808i | \(-0.0942569\pi\) |
−0.730952 | + | 0.682429i | \(0.760924\pi\) | |||||||
\(828\) | −662203. | −0.0335672 | ||||||||
\(829\) | −1.35873e7 | + | 2.35339e7i | −0.686669 | + | 1.18935i | 0.286240 | + | 0.958158i | \(0.407594\pi\) |
−0.972909 | + | 0.231188i | \(0.925739\pi\) | |||||||
\(830\) | −1.69857e7 | + | 2.94201e7i | −0.855830 | + | 1.48234i | ||||
\(831\) | 5.38571e6 | − | 9.32832e6i | 0.270545 | − | 0.468599i | ||||
\(832\) | 2.03682e7 | + | 3.52788e7i | 1.02010 | + | 1.76687i | ||||
\(833\) | −1.89971e7 | − | 3.29039e7i | −0.948580 | − | 1.64299i | ||||
\(834\) | 1.71164e7 | − | 2.96464e7i | 0.852112 | − | 1.47590i | ||||
\(835\) | 4.87867e6 | − | 8.45011e6i | 0.242151 | − | 0.419417i | ||||
\(836\) | −5.96486e6 | + | 1.03314e7i | −0.295178 | + | 0.511264i | ||||
\(837\) | 2.08245e6 | 0.102745 | ||||||||
\(838\) | −1.01577e7 | − | 1.75936e7i | −0.499672 | − | 0.865457i | ||||
\(839\) | −4.43563e6 | + | 7.68274e6i | −0.217546 | + | 0.376801i | −0.954057 | − | 0.299625i | \(-0.903139\pi\) |
0.736511 | + | 0.676425i | \(0.236472\pi\) | |||||||
\(840\) | 4.85195e6 | 0.237257 | ||||||||
\(841\) | 8.08181e6 | 0.394020 | ||||||||
\(842\) | 3.54773e7 | − | 6.14485e7i | 1.72453 | − | 2.98697i | ||||
\(843\) | 3.27067e7 | 1.58514 | ||||||||
\(844\) | 2.90675e7 | + | 5.03463e7i | 1.40459 | + | 2.43283i | ||||
\(845\) | −5.65472e6 | −0.272439 | ||||||||
\(846\) | −32549.8 | − | 56378.0i | −0.00156359 | − | 0.00270822i | ||||
\(847\) | −1.66768e6 | − | 2.88850e6i | −0.0798735 | − | 0.138345i | ||||
\(848\) | 2.84735e7 | + | 4.93176e7i | 1.35973 | + | 2.35512i | ||||
\(849\) | 1.40483e6 | − | 2.43323e6i | 0.0668888 | − | 0.115855i | ||||
\(850\) | 5.68002e7 | 2.69651 | ||||||||
\(851\) | −2.83356e7 | − | 6.82850e6i | −1.34125 | − | 0.323222i | ||||
\(852\) | −4.94778e7 | −2.33513 | ||||||||
\(853\) | −3.55767e6 | + | 6.16207e6i | −0.167415 | + | 0.289970i | −0.937510 | − | 0.347958i | \(-0.886875\pi\) |
0.770096 | + | 0.637929i | \(0.220208\pi\) | |||||||
\(854\) | −2.76587e6 | − | 4.79062e6i | −0.129774 | − | 0.224774i | ||||
\(855\) | 65773.9 | + | 113924.i | 0.00307707 | + | 0.00532965i | ||||
\(856\) | −4.51173e7 | − | 7.81455e7i | −2.10455 | − | 3.64519i | ||||
\(857\) | −2.59467e7 | −1.20679 | −0.603393 | − | 0.797444i | \(-0.706185\pi\) | ||||
−0.603393 | + | 0.797444i | \(0.706185\pi\) | |||||||
\(858\) | −4.73602e6 | − | 8.20302e6i | −0.219632 | − | 0.380413i | ||||
\(859\) | −1.01345e7 | −0.468620 | −0.234310 | − | 0.972162i | \(-0.575283\pi\) | ||||
−0.234310 | + | 0.972162i | \(0.575283\pi\) | |||||||
\(860\) | 4.78688e6 | − | 8.29113e6i | 0.220702 | − | 0.382268i | ||||
\(861\) | −2.24287e6 | −0.103109 | ||||||||
\(862\) | 1.99183e7 | 0.913027 | ||||||||
\(863\) | 2.08330e7 | − | 3.60839e7i | 0.952195 | − | 1.64925i | 0.211534 | − | 0.977371i | \(-0.432154\pi\) |
0.740661 | − | 0.671879i | \(-0.234513\pi\) | |||||||
\(864\) | 2.59733e7 | + | 4.49870e7i | 1.18370 | + | 2.05023i | ||||
\(865\) | −7.59942e6 | −0.345335 | ||||||||
\(866\) | 2.60711e7 | − | 4.51565e7i | 1.18131 | − | 2.04609i | ||||
\(867\) | −3.08960e7 | + | 5.35135e7i | −1.39590 | + | 2.41777i | ||||
\(868\) | −470855. | + | 815546.i | −0.0212123 | + | 0.0367408i | ||||
\(869\) | −628029. | − | 1.08778e6i | −0.0282118 | − | 0.0488642i | ||||
\(870\) | 1.25514e7 | + | 2.17396e7i | 0.562203 | + | 0.973764i | ||||
\(871\) | −1.26415e7 | + | 2.18957e7i | −0.564615 | + | 0.977941i | ||||
\(872\) | −2.71165e7 | + | 4.69671e7i | −1.20765 | + | 2.09172i | ||||
\(873\) | −18732.0 | + | 32444.8i | −0.000831856 | + | 0.00144082i | ||||
\(874\) | −7.22005e7 | −3.19714 | ||||||||
\(875\) | 1.66862e6 | + | 2.89013e6i | 0.0736777 | + | 0.127614i | ||||
\(876\) | 6.69937e6 | − | 1.16037e7i | 0.294967 | − | 0.510898i | ||||
\(877\) | 1.00493e7 | 0.441203 | 0.220601 | − | 0.975364i | \(-0.429198\pi\) | ||||
0.220601 | + | 0.975364i | \(0.429198\pi\) | |||||||
\(878\) | 5.97636e6 | 0.261638 | ||||||||
\(879\) | −9.27639e6 | + | 1.60672e7i | −0.404955 | + | 0.701403i | ||||
\(880\) | 6.17982e6 | 0.269011 | ||||||||
\(881\) | 1.72792e7 | + | 2.99284e7i | 0.750038 | + | 1.29910i | 0.947804 | + | 0.318855i | \(0.103298\pi\) |
−0.197765 | + | 0.980249i | \(0.563368\pi\) | |||||||
\(882\) | 408776. | 0.0176935 | ||||||||
\(883\) | −6.08836e6 | − | 1.05453e7i | −0.262784 | − | 0.455155i | 0.704197 | − | 0.710005i | \(-0.251307\pi\) |
−0.966981 | + | 0.254850i | \(0.917974\pi\) | |||||||
\(884\) | −7.02266e7 | − | 1.21636e8i | −3.02253 | − | 5.23518i | ||||
\(885\) | 9.79258e6 | + | 1.69612e7i | 0.420280 | + | 0.727946i | ||||
\(886\) | −2.98927e7 | + | 5.17757e7i | −1.27933 | + | 2.21586i | ||||
\(887\) | −5.36818e6 | −0.229096 | −0.114548 | − | 0.993418i | \(-0.536542\pi\) | ||||
−0.114548 | + | 0.993418i | \(0.536542\pi\) | |||||||
\(888\) | 1.86275e7 | + | 6.30840e7i | 0.792723 | + | 2.68465i | ||||
\(889\) | −4.48853e6 | −0.190480 | ||||||||
\(890\) | 175909. | − | 304683.i | 0.00744410 | − | 0.0128936i | ||||
\(891\) | −2.23493e6 | − | 3.87102e6i | −0.0943128 | − | 0.163355i | ||||
\(892\) | −1.01376e7 | − | 1.75588e7i | −0.426602 | − | 0.738896i | ||||
\(893\) | −2.53581e6 | − | 4.39214e6i | −0.106411 | − | 0.184310i | ||||
\(894\) | 4.36409e7 | 1.82621 | ||||||||
\(895\) | −3.94992e6 | − | 6.84146e6i | −0.164828 | − | 0.285490i | ||||
\(896\) | −2.90048e6 | −0.120698 | ||||||||
\(897\) | 2.04805e7 | − | 3.54734e7i | 0.849886 | − | 1.47205i | ||||
\(898\) | −1.98476e7 | −0.821329 | ||||||||
\(899\) | −2.92560e6 | −0.120730 | ||||||||
\(900\) | −218326. | + | 378152.i | −0.00898462 | + | 0.0155618i | ||||
\(901\) | −2.34032e7 | − | 4.05356e7i | −0.960426 | − | 1.66351i | ||||
\(902\) | −5.44565e6 | −0.222861 | ||||||||
\(903\) | 697022. | − | 1.20728e6i | 0.0284464 | − | 0.0492706i | ||||
\(904\) | −8.29301e6 | + | 1.43639e7i | −0.337514 | + | 0.584591i | ||||
\(905\) | 2.55721e6 | − | 4.42922e6i | 0.103787 | − | 0.179765i | ||||
\(906\) | −2.50358e7 | − | 4.33633e7i | −1.01331 | − | 1.75510i | ||||
\(907\) | 1.91740e7 | + | 3.32103e7i | 0.773915 | + | 1.34046i | 0.935402 | + | 0.353586i | \(0.115038\pi\) |
−0.161487 | + | 0.986875i | \(0.551629\pi\) | |||||||
\(908\) | −3.94204e6 | + | 6.82782e6i | −0.158674 | + | 0.274832i | ||||
\(909\) | 203854. | − | 353086.i | 0.00818296 | − | 0.0141733i | ||||
\(910\) | 2.45309e6 | − | 4.24888e6i | 0.0981997 | − | 0.170087i | ||||
\(911\) | −1.36375e7 | −0.544427 | −0.272213 | − | 0.962237i | \(-0.587756\pi\) | ||||
−0.272213 | + | 0.962237i | \(0.587756\pi\) | |||||||
\(912\) | 4.27373e7 | + | 7.40231e7i | 1.70145 | + | 2.94700i | ||||
\(913\) | −4.29081e6 | + | 7.43190e6i | −0.170358 | + | 0.295069i | ||||
\(914\) | −3.15714e6 | −0.125005 | ||||||||
\(915\) | 1.07805e7 | 0.425682 | ||||||||
\(916\) | 5.41060e7 | − | 9.37144e7i | 2.13062 | − | 3.69035i | ||||
\(917\) | −3.76462e6 | −0.147842 | ||||||||
\(918\) | −4.68358e7 | − | 8.11220e7i | −1.83430 | − | 3.17711i | ||||
\(919\) | −2.47693e7 | −0.967441 | −0.483720 | − | 0.875223i | \(-0.660715\pi\) | ||||
−0.483720 | + | 0.875223i | \(0.660715\pi\) | |||||||
\(920\) | 2.54718e7 | + | 4.41185e7i | 0.992180 | + | 1.71851i | ||||
\(921\) | 1.60349e7 | + | 2.77732e7i | 0.622898 | + | 1.07889i | ||||
\(922\) | 1.07810e7 | + | 1.86732e7i | 0.417667 | + | 0.723421i | ||||
\(923\) | −1.50210e7 | + | 2.60172e7i | −0.580358 | + | 1.00521i | ||||
\(924\) | 2.04118e6 | 0.0786504 | ||||||||
\(925\) | −1.32416e7 | + | 1.39298e7i | −0.508845 | + | 0.535290i | ||||
\(926\) | 5.59617e7 | 2.14468 | ||||||||
\(927\) | −40672.7 | + | 70447.2i | −0.00155455 | + | 0.00269256i | ||||
\(928\) | −3.64894e7 | − | 6.32014e7i | −1.39090 | − | 2.40911i | ||||
\(929\) | 1.85401e7 | + | 3.21124e7i | 0.704811 | + | 1.22077i | 0.966760 | + | 0.255686i | \(0.0823013\pi\) |
−0.261949 | + | 0.965082i | \(0.584365\pi\) | |||||||
\(930\) | −1.28424e6 | − | 2.22437e6i | −0.0486899 | − | 0.0843334i | ||||
\(931\) | 3.18458e7 | 1.20414 | ||||||||
\(932\) | 4.32351e7 | + | 7.48854e7i | 1.63041 | + | 2.82395i | ||||
\(933\) | 3.89264e7 | 1.46400 | ||||||||
\(934\) | −1.35363e7 | + | 2.34456e7i | −0.507730 | + | 0.879415i | ||||
\(935\) | −5.07938e6 | −0.190012 | ||||||||
\(936\) | 907387. | 0.0338534 | ||||||||
\(937\) | −2.28844e7 | + | 3.96370e7i | −0.851512 | + | 1.47486i | 0.0283307 | + | 0.999599i | \(0.490981\pi\) |
−0.879843 | + | 0.475264i | \(0.842352\pi\) | |||||||
\(938\) | −3.81256e6 | − | 6.60355e6i | −0.141485 | − | 0.245059i | ||||
\(939\) | −2.96474e7 | −1.09729 | ||||||||
\(940\) | −2.97970e6 | + | 5.16100e6i | −0.109990 | + | 0.190508i | ||||
\(941\) | 1.54209e7 | − | 2.67098e7i | 0.567723 | − | 0.983326i | −0.429067 | − | 0.903273i | \(-0.641158\pi\) |
0.996791 | − | 0.0800531i | \(-0.0255090\pi\) | |||||||
\(942\) | 9.07818e6 | − | 1.57239e7i | 0.333328 | − | 0.577341i | ||||
\(943\) | −1.17747e7 | − | 2.03943e7i | −0.431190 | − | 0.746843i | ||||
\(944\) | −6.24582e7 | − | 1.08181e8i | −2.28118 | − | 3.95112i | ||||
\(945\) | 1.16898e6 | − | 2.02474e6i | 0.0425823 | − | 0.0737546i | ||||
\(946\) | 1.69235e6 | − | 2.93124e6i | 0.0614842 | − | 0.106494i | ||||
\(947\) | −1.95006e6 | + | 3.37760e6i | −0.0706598 | + | 0.122386i | −0.899191 | − | 0.437557i | \(-0.855844\pi\) |
0.828531 | + | 0.559943i | \(0.189177\pi\) | |||||||
\(948\) | −2.04140e7 | −0.737746 | ||||||||
\(949\) | −4.06774e6 | − | 7.04554e6i | −0.146618 | − | 0.253950i | ||||
\(950\) | −2.38043e7 | + | 4.12302e7i | −0.855749 | + | 1.48220i | ||||
\(951\) | −7.43341e6 | −0.266524 | ||||||||
\(952\) | 2.54357e7 | 0.909601 | ||||||||
\(953\) | 7.91777e6 | − | 1.37140e7i | 0.282404 | − | 0.489138i | −0.689573 | − | 0.724217i | \(-0.742202\pi\) |
0.971976 | + | 0.235079i | \(0.0755349\pi\) | |||||||
\(954\) | 503587. | 0.0179144 | ||||||||
\(955\) | 1.02905e7 | + | 1.78236e7i | 0.365112 | + | 0.632393i | ||||
\(956\) | −2.87468e7 | −1.01729 | ||||||||
\(957\) | 3.17065e6 | + | 5.49172e6i | 0.111910 | + | 0.193833i | ||||
\(958\) | −1.35776e7 | − | 2.35170e7i | −0.477979 | − | 0.827883i | ||||
\(959\) | −569640. | − | 986646.i | −0.0200011 | − | 0.0346430i | ||||
\(960\) | 1.19715e7 | − | 2.07353e7i | 0.419248 | − | 0.726159i | ||||
\(961\) | −2.83298e7 | −0.989544 | ||||||||
\(962\) | 6.46608e7 | + | 1.55824e7i | 2.25270 | + | 0.542871i | ||||
\(963\) | −418592. | −0.0145454 | ||||||||
\(964\) | 5.61326e7 | − | 9.72245e7i | 1.94546 | − | 3.36964i | ||||
\(965\) | 1.70918e6 | + | 2.96039e6i | 0.0590840 | + | 0.102337i | ||||
\(966\) | 6.17677e6 | + | 1.06985e7i | 0.212970 | + | 0.368875i | ||||
\(967\) | −1.99527e7 | − | 3.45591e7i | −0.686177 | − | 1.18849i | −0.973065 | − | 0.230529i | \(-0.925954\pi\) |
0.286889 | − | 0.957964i | \(-0.407379\pi\) | |||||||
\(968\) | −7.90308e7 | −2.71086 | ||||||||
\(969\) | −3.51270e7 | − | 6.08417e7i | −1.20180 | − | 2.08158i | ||||
\(970\) | 4.79977e6 | 0.163791 | ||||||||
\(971\) | 1.23977e7 | − | 2.14734e7i | 0.421981 | − | 0.730893i | −0.574152 | − | 0.818749i | \(-0.694668\pi\) |
0.996133 | + | 0.0878560i | \(0.0280015\pi\) | |||||||
\(972\) | 1.43327e6 | 0.0486590 | ||||||||
\(973\) | 4.47918e6 | 0.151676 | ||||||||
\(974\) | −2.09494e7 | + | 3.62855e7i | −0.707579 | + | 1.22556i | ||||
\(975\) | −1.35047e7 | − | 2.33909e7i | −0.454962 | − | 0.788017i | ||||
\(976\) | −6.87592e7 | −2.31050 | ||||||||
\(977\) | −1.15986e7 | + | 2.00894e7i | −0.388750 | + | 0.673334i | −0.992282 | − | 0.124005i | \(-0.960426\pi\) |
0.603532 | + | 0.797339i | \(0.293760\pi\) | |||||||
\(978\) | −9.03504e6 | + | 1.56492e7i | −0.302053 | + | 0.523171i | ||||
\(979\) | 44436.9 | − | 76966.9i | 0.00148179 | − | 0.00256654i | ||||
\(980\) | −1.87102e7 | − | 3.24071e7i | −0.622321 | − | 1.07789i | ||||
\(981\) | 125791. | + | 217877.i | 0.00417329 | + | 0.00722834i | ||||
\(982\) | 1.69698e6 | − | 2.93926e6i | 0.0561563 | − | 0.0972655i | ||||
\(983\) | 3.71950e6 | − | 6.44236e6i | 0.122772 | − | 0.212648i | −0.798088 | − | 0.602541i | \(-0.794155\pi\) |
0.920860 | + | 0.389893i | \(0.127488\pi\) | |||||||
\(984\) | −2.65723e7 | + | 4.60246e7i | −0.874866 | + | 1.51531i | ||||
\(985\) | 1.79068e7 | 0.588067 | ||||||||
\(986\) | 6.57988e7 | + | 1.13967e8i | 2.15539 | + | 3.73324i | ||||
\(987\) | −433877. | + | 751497.i | −0.0141767 | + | 0.0245547i | ||||
\(988\) | 1.17725e8 | 3.83685 | ||||||||
\(989\) | 1.46369e7 | 0.475838 | ||||||||
\(990\) | 27324.3 | − | 47327.1i | 0.000886056 | − | 0.00153469i | ||||
\(991\) | 7.22842e6 | 0.233808 | 0.116904 | − | 0.993143i | \(-0.462703\pi\) | ||||
0.116904 | + | 0.993143i | \(0.462703\pi\) | |||||||
\(992\) | 3.73355e6 | + | 6.46669e6i | 0.120460 | + | 0.208643i | ||||
\(993\) | −1.53818e7 | −0.495032 | ||||||||
\(994\) | −4.53022e6 | − | 7.84658e6i | −0.145430 | − | 0.251892i | ||||
\(995\) | −6.02502e6 | − | 1.04356e7i | −0.192931 | − | 0.334166i | ||||
\(996\) | 6.97360e7 | + | 1.20786e8i | 2.22745 | + | 3.85806i | ||||
\(997\) | 2.92362e7 | − | 5.06387e7i | 0.931502 | − | 1.61341i | 0.150745 | − | 0.988573i | \(-0.451833\pi\) |
0.780756 | − | 0.624836i | \(-0.214834\pi\) | |||||||
\(998\) | −2.59595e6 | −0.0825030 | ||||||||
\(999\) | 3.08131e7 | + | 7.42555e6i | 0.976837 | + | 0.235405i |
(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 | 37.6.c.a.10.1 | ✓ | 30 | |
37.26 | even | 3 | inner | 37.6.c.a.26.1 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.6.c.a.10.1 | ✓ | 30 | 1.1 | even | 1 | trivial | |
37.6.c.a.26.1 | yes | 30 | 37.26 | even | 3 | inner |