Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,6,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, 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("74.47");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.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: | \(11.8684026662\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1317 x^{14} - 2712 x^{13} + 1206654 x^{12} - 2683704 x^{11} + 572597881 x^{10} + \cdots + 683643854869056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 63.5 | ||
Root | \(0.0781534 - 0.135366i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.63 |
Dual form | 74.6.c.b.47.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | + | 3.46410i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.578153 | + | 1.00139i | −0.0370886 | + | 0.0642393i | −0.883974 | − | 0.467536i | \(-0.845142\pi\) |
0.846885 | + | 0.531776i | \(0.178475\pi\) | |||||||
\(4\) | −8.00000 | + | 13.8564i | −0.250000 | + | 0.433013i | ||||
\(5\) | 40.4037 | − | 69.9813i | 0.722764 | − | 1.25186i | −0.237124 | − | 0.971479i | \(-0.576205\pi\) |
0.959888 | − | 0.280385i | \(-0.0904620\pi\) | |||||||
\(6\) | −4.62523 | −0.0524511 | ||||||||
\(7\) | −85.9598 | + | 148.887i | −0.663056 | + | 1.14845i | 0.316753 | + | 0.948508i | \(0.397408\pi\) |
−0.979808 | + | 0.199938i | \(0.935926\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 120.831 | + | 209.286i | 0.497249 | + | 0.861260i | ||||
\(10\) | 323.230 | 1.02214 | ||||||||
\(11\) | 646.275 | 1.61041 | 0.805204 | − | 0.592998i | \(-0.202056\pi\) | ||||
0.805204 | + | 0.592998i | \(0.202056\pi\) | |||||||
\(12\) | −9.25045 | − | 16.0223i | −0.0185443 | − | 0.0321196i | ||||
\(13\) | 176.561 | − | 305.813i | 0.289759 | − | 0.501877i | −0.683993 | − | 0.729488i | \(-0.739758\pi\) |
0.973752 | + | 0.227611i | \(0.0730916\pi\) | |||||||
\(14\) | −687.678 | −0.937703 | ||||||||
\(15\) | 46.7191 | + | 80.9199i | 0.0536125 | + | 0.0928596i | ||||
\(16\) | −128.000 | − | 221.703i | −0.125000 | − | 0.216506i | ||||
\(17\) | 890.829 | + | 1542.96i | 0.747605 | + | 1.29489i | 0.948968 | + | 0.315373i | \(0.102130\pi\) |
−0.201363 | + | 0.979517i | \(0.564537\pi\) | |||||||
\(18\) | −483.326 | + | 837.145i | −0.351608 | + | 0.609003i | ||||
\(19\) | −1131.30 | + | 1959.47i | −0.718941 | + | 1.24524i | 0.242479 | + | 0.970157i | \(0.422039\pi\) |
−0.961420 | + | 0.275085i | \(0.911294\pi\) | |||||||
\(20\) | 646.460 | + | 1119.70i | 0.361382 | + | 0.625932i | ||||
\(21\) | −99.3959 | − | 172.159i | −0.0491836 | − | 0.0851885i | ||||
\(22\) | 1292.55 | + | 2238.76i | 0.569365 | + | 0.986169i | ||||
\(23\) | −1204.39 | −0.474731 | −0.237366 | − | 0.971420i | \(-0.576284\pi\) | ||||
−0.237366 | + | 0.971420i | \(0.576284\pi\) | |||||||
\(24\) | 37.0018 | − | 64.0890i | 0.0131128 | − | 0.0227120i | ||||
\(25\) | −1702.42 | − | 2948.68i | −0.544776 | − | 0.943579i | ||||
\(26\) | 1412.49 | 0.409781 | ||||||||
\(27\) | −560.419 | −0.147946 | ||||||||
\(28\) | −1375.36 | − | 2382.19i | −0.331528 | − | 0.574223i | ||||
\(29\) | 7130.04 | 1.57433 | 0.787167 | − | 0.616740i | \(-0.211547\pi\) | ||||
0.787167 | + | 0.616740i | \(0.211547\pi\) | |||||||
\(30\) | −186.876 | + | 323.679i | −0.0379098 | + | 0.0656617i | ||||
\(31\) | −2669.15 | −0.498848 | −0.249424 | − | 0.968394i | \(-0.580241\pi\) | ||||
−0.249424 | + | 0.968394i | \(0.580241\pi\) | |||||||
\(32\) | 512.000 | − | 886.810i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −373.646 | + | 647.174i | −0.0597277 | + | 0.103451i | ||||
\(34\) | −3563.32 | + | 6171.84i | −0.528636 | + | 0.915625i | ||||
\(35\) | 6946.19 | + | 12031.2i | 0.958466 | + | 1.66011i | ||||
\(36\) | −3866.61 | −0.497249 | ||||||||
\(37\) | 912.234 | − | 8277.18i | 0.109547 | − | 0.993982i | ||||
\(38\) | −9050.38 | −1.01674 | ||||||||
\(39\) | 204.159 | + | 353.613i | 0.0214935 | + | 0.0372278i | ||||
\(40\) | −2585.84 | + | 4478.80i | −0.255536 | + | 0.442601i | ||||
\(41\) | 6201.74 | − | 10741.7i | 0.576175 | − | 0.997964i | −0.419738 | − | 0.907645i | \(-0.637878\pi\) |
0.995913 | − | 0.0903184i | \(-0.0287885\pi\) | |||||||
\(42\) | 397.583 | − | 688.635i | 0.0347780 | − | 0.0602373i | ||||
\(43\) | −17897.4 | −1.47611 | −0.738055 | − | 0.674740i | \(-0.764256\pi\) | ||||
−0.738055 | + | 0.674740i | \(0.764256\pi\) | |||||||
\(44\) | −5170.20 | + | 8955.05i | −0.402602 | + | 0.697327i | ||||
\(45\) | 19528.2 | 1.43757 | ||||||||
\(46\) | −2408.78 | − | 4172.13i | −0.167843 | − | 0.290712i | ||||
\(47\) | 17504.1 | 1.15583 | 0.577917 | − | 0.816096i | \(-0.303866\pi\) | ||||
0.577917 | + | 0.816096i | \(0.303866\pi\) | |||||||
\(48\) | 296.015 | 0.0185443 | ||||||||
\(49\) | −6374.67 | − | 11041.2i | −0.379286 | − | 0.656943i | ||||
\(50\) | 6809.69 | − | 11794.7i | 0.385214 | − | 0.667211i | ||||
\(51\) | −2060.14 | −0.110910 | ||||||||
\(52\) | 2824.98 | + | 4893.00i | 0.144879 | + | 0.250938i | ||||
\(53\) | −6660.30 | − | 11536.0i | −0.325690 | − | 0.564112i | 0.655962 | − | 0.754794i | \(-0.272263\pi\) |
−0.981652 | + | 0.190683i | \(0.938930\pi\) | |||||||
\(54\) | −1120.84 | − | 1941.35i | −0.0523068 | − | 0.0905981i | ||||
\(55\) | 26111.9 | − | 45227.2i | 1.16394 | − | 2.01601i | ||||
\(56\) | 5501.43 | − | 9528.75i | 0.234426 | − | 0.406037i | ||||
\(57\) | −1308.13 | − | 2265.74i | −0.0533289 | − | 0.0923684i | ||||
\(58\) | 14260.1 | + | 24699.2i | 0.556611 | + | 0.964079i | ||||
\(59\) | −3848.38 | − | 6665.59i | −0.143929 | − | 0.249292i | 0.785044 | − | 0.619440i | \(-0.212640\pi\) |
−0.928973 | + | 0.370148i | \(0.879307\pi\) | |||||||
\(60\) | −1495.01 | −0.0536125 | ||||||||
\(61\) | −7262.53 | + | 12579.1i | −0.249898 | + | 0.432837i | −0.963497 | − | 0.267718i | \(-0.913731\pi\) |
0.713599 | + | 0.700554i | \(0.247064\pi\) | |||||||
\(62\) | −5338.29 | − | 9246.20i | −0.176369 | − | 0.305481i | ||||
\(63\) | −41546.6 | −1.31882 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −14267.5 | − | 24711.9i | −0.418854 | − | 0.725477i | ||||
\(66\) | −2989.17 | −0.0844677 | ||||||||
\(67\) | −11231.9 | + | 19454.2i | −0.305680 | + | 0.529453i | −0.977412 | − | 0.211341i | \(-0.932217\pi\) |
0.671733 | + | 0.740794i | \(0.265550\pi\) | |||||||
\(68\) | −28506.5 | −0.747605 | ||||||||
\(69\) | 696.322 | − | 1206.07i | 0.0176071 | − | 0.0304964i | ||||
\(70\) | −27784.8 | + | 48124.6i | −0.677738 | + | 1.17388i | ||||
\(71\) | 14111.3 | − | 24441.5i | 0.332217 | − | 0.575416i | −0.650729 | − | 0.759310i | \(-0.725537\pi\) |
0.982946 | + | 0.183893i | \(0.0588701\pi\) | |||||||
\(72\) | −7733.21 | − | 13394.3i | −0.175804 | − | 0.304502i | ||||
\(73\) | 8460.37 | 0.185816 | 0.0929078 | − | 0.995675i | \(-0.470384\pi\) | ||||
0.0929078 | + | 0.995675i | \(0.470384\pi\) | |||||||
\(74\) | 30497.5 | − | 13394.3i | 0.647418 | − | 0.284342i | ||||
\(75\) | 3937.05 | 0.0808198 | ||||||||
\(76\) | −18100.8 | − | 31351.4i | −0.359470 | − | 0.622621i | ||||
\(77\) | −55553.7 | + | 96221.8i | −1.06779 | + | 1.84947i | ||||
\(78\) | −816.635 | + | 1414.45i | −0.0151982 | + | 0.0263240i | ||||
\(79\) | 44395.4 | − | 76895.1i | 0.800332 | − | 1.38622i | −0.119065 | − | 0.992886i | \(-0.537990\pi\) |
0.919397 | − | 0.393330i | \(-0.128677\pi\) | |||||||
\(80\) | −20686.7 | −0.361382 | ||||||||
\(81\) | −29038.0 | + | 50295.4i | −0.491762 | + | 0.851756i | ||||
\(82\) | 49613.9 | 0.814834 | ||||||||
\(83\) | 19980.5 | + | 34607.2i | 0.318354 | + | 0.551406i | 0.980145 | − | 0.198283i | \(-0.0635364\pi\) |
−0.661790 | + | 0.749689i | \(0.730203\pi\) | |||||||
\(84\) | 3180.67 | 0.0491836 | ||||||||
\(85\) | 143971. | 2.16137 | ||||||||
\(86\) | −35794.8 | − | 61998.4i | −0.521884 | − | 0.903929i | ||||
\(87\) | −4122.26 | + | 7139.96i | −0.0583898 | + | 0.101134i | ||||
\(88\) | −41361.6 | −0.569365 | ||||||||
\(89\) | −65715.7 | − | 113823.i | −0.879416 | − | 1.52319i | −0.851983 | − | 0.523570i | \(-0.824600\pi\) |
−0.0274331 | − | 0.999624i | \(-0.508733\pi\) | |||||||
\(90\) | 39056.3 | + | 67647.6i | 0.508259 | + | 0.880331i | ||||
\(91\) | 30354.3 | + | 52575.2i | 0.384252 | + | 0.665545i | ||||
\(92\) | 9635.12 | − | 16688.5i | 0.118683 | − | 0.205565i | ||||
\(93\) | 1543.18 | − | 2672.86i | 0.0185016 | − | 0.0320456i | ||||
\(94\) | 35008.2 | + | 60636.0i | 0.408649 | + | 0.707800i | ||||
\(95\) | 91417.3 | + | 158339.i | 1.03925 | + | 1.80003i | ||||
\(96\) | 592.029 | + | 1025.42i | 0.00655639 | + | 0.0113560i | ||||
\(97\) | −137338. | −1.48205 | −0.741023 | − | 0.671479i | \(-0.765659\pi\) | ||||
−0.741023 | + | 0.671479i | \(0.765659\pi\) | |||||||
\(98\) | 25498.7 | − | 44165.0i | 0.268196 | − | 0.464529i | ||||
\(99\) | 78090.4 | + | 135257.i | 0.800774 | + | 1.38698i | ||||
\(100\) | 54477.6 | 0.544776 | ||||||||
\(101\) | −110662. | −1.07943 | −0.539715 | − | 0.841848i | \(-0.681468\pi\) | ||||
−0.539715 | + | 0.841848i | \(0.681468\pi\) | |||||||
\(102\) | −4120.29 | − | 7136.55i | −0.0392127 | − | 0.0679184i | ||||
\(103\) | −68548.4 | −0.636655 | −0.318327 | − | 0.947981i | \(-0.603121\pi\) | ||||
−0.318327 | + | 0.947981i | \(0.603121\pi\) | |||||||
\(104\) | −11299.9 | + | 19572.0i | −0.102445 | + | 0.177440i | ||||
\(105\) | −16063.9 | −0.142192 | ||||||||
\(106\) | 26641.2 | − | 46143.9i | 0.230298 | − | 0.398887i | ||||
\(107\) | −13064.3 | + | 22628.1i | −0.110313 | + | 0.191068i | −0.915897 | − | 0.401414i | \(-0.868519\pi\) |
0.805583 | + | 0.592483i | \(0.201852\pi\) | |||||||
\(108\) | 4483.35 | − | 7765.39i | 0.0369865 | − | 0.0640625i | ||||
\(109\) | 102264. | + | 177126.i | 0.824433 | + | 1.42796i | 0.902352 | + | 0.431000i | \(0.141839\pi\) |
−0.0779187 | + | 0.996960i | \(0.524827\pi\) | |||||||
\(110\) | 208896. | 1.64607 | ||||||||
\(111\) | 7761.29 | + | 5698.99i | 0.0597897 | + | 0.0439026i | ||||
\(112\) | 44011.4 | 0.331528 | ||||||||
\(113\) | −95006.0 | − | 164555.i | −0.699930 | − | 1.21231i | −0.968490 | − | 0.249052i | \(-0.919881\pi\) |
0.268560 | − | 0.963263i | \(-0.413452\pi\) | |||||||
\(114\) | 5232.51 | − | 9062.97i | 0.0377093 | − | 0.0653143i | ||||
\(115\) | −48661.9 | + | 84284.8i | −0.343118 | + | 0.594299i | ||||
\(116\) | −57040.3 | + | 98796.7i | −0.393584 | + | 0.681707i | ||||
\(117\) | 85336.5 | 0.576329 | ||||||||
\(118\) | 15393.5 | − | 26662.3i | 0.101773 | − | 0.176276i | ||||
\(119\) | −306302. | −1.98282 | ||||||||
\(120\) | −2990.02 | − | 5178.87i | −0.0189549 | − | 0.0328308i | ||||
\(121\) | 256621. | 1.59341 | ||||||||
\(122\) | −58100.3 | −0.353410 | ||||||||
\(123\) | 7171.12 | + | 12420.7i | 0.0427390 | + | 0.0740261i | ||||
\(124\) | 21353.2 | − | 36984.8i | 0.124712 | − | 0.216008i | ||||
\(125\) | −22613.7 | −0.129449 | ||||||||
\(126\) | −83093.2 | − | 143922.i | −0.466272 | − | 0.807606i | ||||
\(127\) | −22053.8 | − | 38198.3i | −0.121332 | − | 0.210152i | 0.798961 | − | 0.601382i | \(-0.205383\pi\) |
−0.920293 | + | 0.391230i | \(0.872050\pi\) | |||||||
\(128\) | 8192.00 | + | 14189.0i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 10347.4 | − | 17922.3i | 0.0547468 | − | 0.0948243i | ||||
\(130\) | 57069.8 | − | 98847.8i | 0.296175 | − | 0.512990i | ||||
\(131\) | 8743.52 | + | 15144.2i | 0.0445152 | + | 0.0771025i | 0.887425 | − | 0.460953i | \(-0.152492\pi\) |
−0.842909 | + | 0.538056i | \(0.819159\pi\) | |||||||
\(132\) | −5978.34 | − | 10354.8i | −0.0298639 | − | 0.0517257i | ||||
\(133\) | −194492. | − | 336870.i | −0.953396 | − | 1.65133i | ||||
\(134\) | −89855.3 | −0.432297 | ||||||||
\(135\) | −22643.0 | + | 39218.9i | −0.106930 | + | 0.185208i | ||||
\(136\) | −57013.1 | − | 98749.5i | −0.264318 | − | 0.457813i | ||||
\(137\) | 93337.3 | 0.424868 | 0.212434 | − | 0.977175i | \(-0.431861\pi\) | ||||
0.212434 | + | 0.977175i | \(0.431861\pi\) | |||||||
\(138\) | 5570.58 | 0.0249002 | ||||||||
\(139\) | 37483.1 | + | 64922.6i | 0.164550 | + | 0.285009i | 0.936495 | − | 0.350680i | \(-0.114049\pi\) |
−0.771945 | + | 0.635689i | \(0.780716\pi\) | |||||||
\(140\) | −222278. | −0.958466 | ||||||||
\(141\) | −10120.1 | + | 17528.5i | −0.0428682 | + | 0.0742499i | ||||
\(142\) | 112891. | 0.469825 | ||||||||
\(143\) | 114107. | − | 197639.i | 0.466630 | − | 0.808226i | ||||
\(144\) | 30932.9 | − | 53577.3i | 0.124312 | − | 0.215315i | ||||
\(145\) | 288080. | − | 498970.i | 1.13787 | − | 1.97085i | ||||
\(146\) | 16920.7 | + | 29307.6i | 0.0656958 | + | 0.113788i | ||||
\(147\) | 14742.1 | 0.0562687 | ||||||||
\(148\) | 107394. | + | 78857.8i | 0.403020 | + | 0.295931i | ||||
\(149\) | −267249. | −0.986166 | −0.493083 | − | 0.869982i | \(-0.664130\pi\) | ||||
−0.493083 | + | 0.869982i | \(0.664130\pi\) | |||||||
\(150\) | 7874.10 | + | 13638.3i | 0.0285741 | + | 0.0494918i | ||||
\(151\) | −221144. | + | 383032.i | −0.789282 | + | 1.36708i | 0.137125 | + | 0.990554i | \(0.456214\pi\) |
−0.926407 | + | 0.376523i | \(0.877120\pi\) | |||||||
\(152\) | 72403.1 | − | 125406.i | 0.254184 | − | 0.440259i | ||||
\(153\) | −215280. | + | 372877.i | −0.743491 | + | 1.28776i | ||||
\(154\) | −444430. | −1.51008 | ||||||||
\(155\) | −107844. | + | 186790.i | −0.360549 | + | 0.624490i | ||||
\(156\) | −6533.08 | −0.0214935 | ||||||||
\(157\) | −190368. | − | 329726.i | −0.616373 | − | 1.06759i | −0.990142 | − | 0.140068i | \(-0.955268\pi\) |
0.373769 | − | 0.927522i | \(-0.378065\pi\) | |||||||
\(158\) | 355163. | 1.13184 | ||||||||
\(159\) | 15402.7 | 0.0483175 | ||||||||
\(160\) | −41373.4 | − | 71660.9i | −0.127768 | − | 0.221300i | ||||
\(161\) | 103529. | − | 179318.i | 0.314773 | − | 0.545203i | ||||
\(162\) | −232304. | −0.695456 | ||||||||
\(163\) | −100143. | − | 173454.i | −0.295225 | − | 0.511345i | 0.679812 | − | 0.733386i | \(-0.262061\pi\) |
−0.975037 | + | 0.222041i | \(0.928728\pi\) | |||||||
\(164\) | 99227.9 | + | 171868.i | 0.288087 | + | 0.498982i | ||||
\(165\) | 30193.4 | + | 52296.5i | 0.0863381 | + | 0.149542i | ||||
\(166\) | −79922.0 | + | 138429.i | −0.225111 | + | 0.389903i | ||||
\(167\) | 295943. | − | 512588.i | 0.821139 | − | 1.42225i | −0.0836956 | − | 0.996491i | \(-0.526672\pi\) |
0.904835 | − | 0.425763i | \(-0.139994\pi\) | |||||||
\(168\) | 6361.34 | + | 11018.2i | 0.0173890 | + | 0.0301187i | ||||
\(169\) | 123299. | + | 213560.i | 0.332080 | + | 0.575179i | ||||
\(170\) | 287943. | + | 498731.i | 0.764159 | + | 1.32356i | ||||
\(171\) | −546786. | −1.42997 | ||||||||
\(172\) | 143179. | − | 247994.i | 0.369028 | − | 0.639175i | ||||
\(173\) | −32890.1 | − | 56967.2i | −0.0835506 | − | 0.144714i | 0.821222 | − | 0.570609i | \(-0.193293\pi\) |
−0.904773 | + | 0.425895i | \(0.859959\pi\) | |||||||
\(174\) | −32978.1 | −0.0825756 | ||||||||
\(175\) | 585360. | 1.44487 | ||||||||
\(176\) | −82723.2 | − | 143281.i | −0.201301 | − | 0.348664i | ||||
\(177\) | 8899.81 | 0.0213524 | ||||||||
\(178\) | 262863. | − | 455292.i | 0.621841 | − | 1.07706i | ||||
\(179\) | 747782. | 1.74439 | 0.872193 | − | 0.489163i | \(-0.162698\pi\) | ||||
0.872193 | + | 0.489163i | \(0.162698\pi\) | |||||||
\(180\) | −156225. | + | 270590.i | −0.359394 | + | 0.622488i | ||||
\(181\) | 223818. | − | 387665.i | 0.507808 | − | 0.879549i | −0.492152 | − | 0.870510i | \(-0.663789\pi\) |
0.999959 | − | 0.00903904i | \(-0.00287726\pi\) | |||||||
\(182\) | −121417. | + | 210301.i | −0.271708 | + | 0.470611i | ||||
\(183\) | −8397.72 | − | 14545.3i | −0.0185367 | − | 0.0321066i | ||||
\(184\) | 77081.0 | 0.167843 | ||||||||
\(185\) | −542391. | − | 398269.i | −1.16515 | − | 0.855553i | ||||
\(186\) | 12345.4 | 0.0261651 | ||||||||
\(187\) | 575721. | + | 997178.i | 1.20395 | + | 2.08530i | ||||
\(188\) | −140033. | + | 242544.i | −0.288958 | + | 0.500491i | ||||
\(189\) | 48173.5 | − | 83438.9i | 0.0980965 | − | 0.169908i | ||||
\(190\) | −365669. | + | 633358.i | −0.734860 | + | 1.27281i | ||||
\(191\) | 622992. | 1.23566 | 0.617830 | − | 0.786312i | \(-0.288012\pi\) | ||||
0.617830 | + | 0.786312i | \(0.288012\pi\) | |||||||
\(192\) | −2368.12 | + | 4101.70i | −0.00463607 | + | 0.00802991i | ||||
\(193\) | 523859. | 1.01233 | 0.506164 | − | 0.862437i | \(-0.331063\pi\) | ||||
0.506164 | + | 0.862437i | \(0.331063\pi\) | |||||||
\(194\) | −274676. | − | 475753.i | −0.523983 | − | 0.907564i | ||||
\(195\) | 32995.1 | 0.0621388 | ||||||||
\(196\) | 203989. | 0.379286 | ||||||||
\(197\) | 45111.8 | + | 78135.9i | 0.0828180 | + | 0.143445i | 0.904459 | − | 0.426560i | \(-0.140275\pi\) |
−0.821641 | + | 0.570005i | \(0.806941\pi\) | |||||||
\(198\) | −312362. | + | 541026.i | −0.566232 | + | 0.980743i | ||||
\(199\) | −168650. | −0.301893 | −0.150946 | − | 0.988542i | \(-0.548232\pi\) | ||||
−0.150946 | + | 0.988542i | \(0.548232\pi\) | |||||||
\(200\) | 108955. | + | 188716.i | 0.192607 | + | 0.333606i | ||||
\(201\) | −12987.5 | − | 22495.1i | −0.0226744 | − | 0.0392733i | ||||
\(202\) | −221324. | − | 383344.i | −0.381636 | − | 0.661013i | ||||
\(203\) | −612897. | + | 1.06157e6i | −1.04387 | + | 1.80804i | ||||
\(204\) | 16481.1 | − | 28546.2i | 0.0277276 | − | 0.0480256i | ||||
\(205\) | −501147. | − | 868012.i | −0.832876 | − | 1.44258i | ||||
\(206\) | −137097. | − | 237459.i | −0.225092 | − | 0.389870i | ||||
\(207\) | −145528. | − | 252062.i | −0.236059 | − | 0.408867i | ||||
\(208\) | −90399.3 | −0.144879 | ||||||||
\(209\) | −731130. | + | 1.26635e6i | −1.15779 | + | 2.00535i | ||||
\(210\) | −32127.7 | − | 55646.8i | −0.0502726 | − | 0.0870747i | ||||
\(211\) | 315198. | 0.487391 | 0.243695 | − | 0.969852i | \(-0.421640\pi\) | ||||
0.243695 | + | 0.969852i | \(0.421640\pi\) | |||||||
\(212\) | 213130. | 0.325690 | ||||||||
\(213\) | 16317.0 | + | 28261.9i | 0.0246429 | + | 0.0426827i | ||||
\(214\) | −104515. | −0.156007 | ||||||||
\(215\) | −723122. | + | 1.25248e6i | −1.06688 | + | 1.84789i | ||||
\(216\) | 35866.8 | 0.0523068 | ||||||||
\(217\) | 229439. | − | 397401.i | 0.330764 | − | 0.572900i | ||||
\(218\) | −409055. | + | 708504.i | −0.582962 | + | 1.00972i | ||||
\(219\) | −4891.39 | + | 8472.14i | −0.00689164 | + | 0.0119367i | ||||
\(220\) | 417791. | + | 723635.i | 0.581972 | + | 1.00801i | ||||
\(221\) | 629143. | 0.866500 | ||||||||
\(222\) | −4219.29 | + | 38283.9i | −0.00574589 | + | 0.0521355i | ||||
\(223\) | 108302. | 0.145839 | 0.0729196 | − | 0.997338i | \(-0.476768\pi\) | ||||
0.0729196 | + | 0.997338i | \(0.476768\pi\) | |||||||
\(224\) | 88022.8 | + | 152460.i | 0.117213 | + | 0.203019i | ||||
\(225\) | 411413. | − | 712588.i | 0.541778 | − | 0.938387i | ||||
\(226\) | 380024. | − | 658221.i | 0.494925 | − | 0.857236i | ||||
\(227\) | −28009.3 | + | 48513.5i | −0.0360776 | + | 0.0624882i | −0.883500 | − | 0.468430i | \(-0.844820\pi\) |
0.847423 | + | 0.530919i | \(0.178153\pi\) | |||||||
\(228\) | 41860.1 | 0.0533289 | ||||||||
\(229\) | 162338. | − | 281177.i | 0.204565 | − | 0.354316i | −0.745429 | − | 0.666585i | \(-0.767755\pi\) |
0.949994 | + | 0.312268i | \(0.101089\pi\) | |||||||
\(230\) | −389295. | −0.485243 | ||||||||
\(231\) | −64237.1 | − | 111262.i | −0.0792056 | − | 0.137188i | ||||
\(232\) | −456323. | −0.556611 | ||||||||
\(233\) | 803296. | 0.969361 | 0.484681 | − | 0.874691i | \(-0.338936\pi\) | ||||
0.484681 | + | 0.874691i | \(0.338936\pi\) | |||||||
\(234\) | 170673. | + | 295614.i | 0.203763 | + | 0.352928i | ||||
\(235\) | 707231. | − | 1.22496e6i | 0.835395 | − | 1.44695i | ||||
\(236\) | 123148. | 0.143929 | ||||||||
\(237\) | 51334.7 | + | 88914.3i | 0.0593663 | + | 0.102826i | ||||
\(238\) | −612604. | − | 1.06106e6i | −0.701031 | − | 1.21422i | ||||
\(239\) | −577166. | − | 999680.i | −0.653591 | − | 1.13205i | −0.982245 | − | 0.187602i | \(-0.939929\pi\) |
0.328655 | − | 0.944450i | \(-0.393405\pi\) | |||||||
\(240\) | 11960.1 | − | 20715.5i | 0.0134031 | − | 0.0232149i | ||||
\(241\) | −37865.0 | + | 65584.2i | −0.0419948 | + | 0.0727372i | −0.886259 | − | 0.463190i | \(-0.846705\pi\) |
0.844264 | + | 0.535927i | \(0.180038\pi\) | |||||||
\(242\) | 513242. | + | 888961.i | 0.563357 | + | 0.975763i | ||||
\(243\) | −101668. | − | 176094.i | −0.110451 | − | 0.191306i | ||||
\(244\) | −116201. | − | 201265.i | −0.124949 | − | 0.216418i | ||||
\(245\) | −1.03024e6 | −1.09654 | ||||||||
\(246\) | −28684.5 | + | 49682.9i | −0.0302210 | + | 0.0523443i | ||||
\(247\) | 399486. | + | 691931.i | 0.416639 | + | 0.721639i | ||||
\(248\) | 170825. | 0.176369 | ||||||||
\(249\) | −46207.2 | −0.0472292 | ||||||||
\(250\) | −45227.5 | − | 78336.3i | −0.0457670 | − | 0.0792708i | ||||
\(251\) | −592206. | −0.593319 | −0.296660 | − | 0.954983i | \(-0.595873\pi\) | ||||
−0.296660 | + | 0.954983i | \(0.595873\pi\) | |||||||
\(252\) | 332373. | − | 575686.i | 0.329704 | − | 0.571064i | ||||
\(253\) | −778368. | −0.764511 | ||||||||
\(254\) | 88215.1 | − | 152793.i | 0.0857944 | − | 0.148600i | ||||
\(255\) | −83237.5 | + | 144172.i | −0.0801620 | + | 0.138845i | ||||
\(256\) | −32768.0 | + | 56755.8i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −231855. | − | 401585.i | −0.218970 | − | 0.379267i | 0.735523 | − | 0.677499i | \(-0.236936\pi\) |
−0.954493 | + | 0.298232i | \(0.903603\pi\) | |||||||
\(258\) | 82779.6 | 0.0774237 | ||||||||
\(259\) | 1.15395e6 | + | 847325.i | 1.06890 | + | 0.784875i | ||||
\(260\) | 456558. | 0.418854 | ||||||||
\(261\) | 861533. | + | 1.49222e6i | 0.782836 | + | 1.35591i | ||||
\(262\) | −34974.1 | + | 60576.9i | −0.0314770 | + | 0.0545197i | ||||
\(263\) | −462933. | + | 801823.i | −0.412694 | + | 0.714808i | −0.995183 | − | 0.0980309i | \(-0.968746\pi\) |
0.582489 | + | 0.812839i | \(0.302079\pi\) | |||||||
\(264\) | 23913.4 | − | 41419.2i | 0.0211169 | − | 0.0365756i | ||||
\(265\) | −1.07640e6 | −0.941588 | ||||||||
\(266\) | 777969. | − | 1.34748e6i | 0.674153 | − | 1.16767i | ||||
\(267\) | 151975. | 0.130465 | ||||||||
\(268\) | −179711. | − | 311268.i | −0.152840 | − | 0.264727i | ||||
\(269\) | −63285.0 | −0.0533237 | −0.0266618 | − | 0.999645i | \(-0.508488\pi\) | ||||
−0.0266618 | + | 0.999645i | \(0.508488\pi\) | |||||||
\(270\) | −181144. | −0.151222 | ||||||||
\(271\) | −59466.1 | − | 102998.i | −0.0491865 | − | 0.0851936i | 0.840384 | − | 0.541992i | \(-0.182330\pi\) |
−0.889570 | + | 0.456798i | \(0.848996\pi\) | |||||||
\(272\) | 228052. | − | 394998.i | 0.186901 | − | 0.323722i | ||||
\(273\) | −70197.8 | −0.0570055 | ||||||||
\(274\) | 186675. | + | 323330.i | 0.150213 | + | 0.260177i | ||||
\(275\) | −1.10023e6 | − | 1.90566e6i | −0.877311 | − | 1.51955i | ||||
\(276\) | 11141.2 | + | 19297.0i | 0.00880354 | + | 0.0152482i | ||||
\(277\) | 206212. | − | 357170.i | 0.161478 | − | 0.279689i | −0.773921 | − | 0.633283i | \(-0.781707\pi\) |
0.935399 | + | 0.353594i | \(0.115040\pi\) | |||||||
\(278\) | −149932. | + | 259690.i | −0.116355 | + | 0.201532i | ||||
\(279\) | −322517. | − | 558616.i | −0.248052 | − | 0.429638i | ||||
\(280\) | −444556. | − | 769994.i | −0.338869 | − | 0.586938i | ||||
\(281\) | −857708. | − | 1.48559e6i | −0.647998 | − | 1.12237i | −0.983600 | − | 0.180362i | \(-0.942273\pi\) |
0.335602 | − | 0.942004i | \(-0.391060\pi\) | |||||||
\(282\) | −80960.4 | −0.0606248 | ||||||||
\(283\) | 1.20304e6 | − | 2.08372e6i | 0.892921 | − | 1.54658i | 0.0565642 | − | 0.998399i | \(-0.481985\pi\) |
0.836357 | − | 0.548186i | \(-0.184681\pi\) | |||||||
\(284\) | 225781. | + | 391064.i | 0.166108 | + | 0.287708i | ||||
\(285\) | −211413. | −0.154177 | ||||||||
\(286\) | 912856. | 0.659914 | ||||||||
\(287\) | 1.06620e6 | + | 1.84671e6i | 0.764072 | + | 1.32341i | ||||
\(288\) | 247463. | 0.175804 | ||||||||
\(289\) | −877224. | + | 1.51940e6i | −0.617826 | + | 1.07011i | ||||
\(290\) | 2.30464e6 | 1.60919 | ||||||||
\(291\) | 79402.5 | − | 137529.i | 0.0549670 | − | 0.0952056i | ||||
\(292\) | −67683.0 | + | 117230.i | −0.0464539 | + | 0.0804605i | ||||
\(293\) | 329763. | − | 571166.i | 0.224405 | − | 0.388681i | −0.731736 | − | 0.681588i | \(-0.761289\pi\) |
0.956141 | + | 0.292908i | \(0.0946228\pi\) | |||||||
\(294\) | 29484.3 | + | 51068.3i | 0.0198940 | + | 0.0344574i | ||||
\(295\) | −621955. | −0.416106 | ||||||||
\(296\) | −58383.0 | + | 529740.i | −0.0387309 | + | 0.351426i | ||||
\(297\) | −362185. | −0.238254 | ||||||||
\(298\) | −534498. | − | 925777.i | −0.348662 | − | 0.603901i | ||||
\(299\) | −212648. | + | 368318.i | −0.137557 | + | 0.238256i | ||||
\(300\) | −31496.4 | + | 54553.3i | −0.0202049 | + | 0.0349960i | ||||
\(301\) | 1.53846e6 | − | 2.66469e6i | 0.978744 | − | 1.69523i | ||||
\(302\) | −1.76915e6 | −1.11621 | ||||||||
\(303\) | 63979.5 | − | 110816.i | 0.0400345 | − | 0.0693418i | ||||
\(304\) | 579225. | 0.359470 | ||||||||
\(305\) | 586867. | + | 1.01648e6i | 0.361235 | + | 0.625678i | ||||
\(306\) | −1.72224e6 | −1.05146 | ||||||||
\(307\) | −2.68684e6 | −1.62703 | −0.813514 | − | 0.581545i | \(-0.802448\pi\) | ||||
−0.813514 | + | 0.581545i | \(0.802448\pi\) | |||||||
\(308\) | −888859. | − | 1.53955e6i | −0.533895 | − | 0.924734i | ||||
\(309\) | 39631.5 | − | 68643.7i | 0.0236126 | − | 0.0408982i | ||||
\(310\) | −862748. | −0.509894 | ||||||||
\(311\) | 481189. | + | 833444.i | 0.282108 | + | 0.488625i | 0.971904 | − | 0.235379i | \(-0.0756331\pi\) |
−0.689796 | + | 0.724004i | \(0.742300\pi\) | |||||||
\(312\) | −13066.2 | − | 22631.2i | −0.00759909 | − | 0.0131620i | ||||
\(313\) | 310564. | + | 537913.i | 0.179180 | + | 0.310349i | 0.941600 | − | 0.336733i | \(-0.109322\pi\) |
−0.762420 | + | 0.647083i | \(0.775989\pi\) | |||||||
\(314\) | 761470. | − | 1.31891e6i | 0.435842 | − | 0.754900i | ||||
\(315\) | −1.67864e6 | + | 2.90749e6i | −0.953192 | + | 1.65098i | ||||
\(316\) | 710327. | + | 1.23032e6i | 0.400166 | + | 0.693108i | ||||
\(317\) | 117139. | + | 202890.i | 0.0654714 | + | 0.113400i | 0.896903 | − | 0.442227i | \(-0.145812\pi\) |
−0.831432 | + | 0.555627i | \(0.812478\pi\) | |||||||
\(318\) | 30805.4 | + | 53356.5i | 0.0170828 | + | 0.0295883i | ||||
\(319\) | 4.60797e6 | 2.53532 | ||||||||
\(320\) | 165494. | − | 286643.i | 0.0903455 | − | 0.156483i | ||||
\(321\) | −15106.4 | − | 26165.0i | −0.00818273 | − | 0.0141729i | ||||
\(322\) | 828233. | 0.445157 | ||||||||
\(323\) | −4.03117e6 | −2.14993 | ||||||||
\(324\) | −464609. | − | 804726.i | −0.245881 | − | 0.425878i | ||||
\(325\) | −1.20233e6 | −0.631414 | ||||||||
\(326\) | 400574. | − | 693814.i | 0.208756 | − | 0.361576i | ||||
\(327\) | −236496. | −0.122308 | ||||||||
\(328\) | −396911. | + | 687471.i | −0.203708 | + | 0.352833i | ||||
\(329\) | −1.50465e6 | + | 2.60613e6i | −0.766382 | + | 1.32741i | ||||
\(330\) | −120774. | + | 209186.i | −0.0610502 | + | 0.105742i | ||||
\(331\) | 37012.9 | + | 64108.2i | 0.0185688 | + | 0.0321620i | 0.875160 | − | 0.483833i | \(-0.160756\pi\) |
−0.856592 | + | 0.515995i | \(0.827422\pi\) | |||||||
\(332\) | −639376. | −0.318354 | ||||||||
\(333\) | 1.84253e6 | − | 809226.i | 0.910549 | − | 0.399907i | ||||
\(334\) | 2.36754e6 | 1.16127 | ||||||||
\(335\) | 907623. | + | 1.57205e6i | 0.441869 | + | 0.765339i | ||||
\(336\) | −25445.3 | + | 44072.6i | −0.0122959 | + | 0.0212971i | ||||
\(337\) | −42100.9 | + | 72920.9i | −0.0201937 | + | 0.0349766i | −0.875946 | − | 0.482410i | \(-0.839762\pi\) |
0.855752 | + | 0.517386i | \(0.173095\pi\) | |||||||
\(338\) | −493196. | + | 854240.i | −0.234816 | + | 0.406713i | ||||
\(339\) | 219712. | 0.103838 | ||||||||
\(340\) | −1.15177e6 | + | 1.99492e6i | −0.540342 | + | 0.935899i | ||||
\(341\) | −1.72500e6 | −0.803349 | ||||||||
\(342\) | −1.09357e6 | − | 1.89412e6i | −0.505571 | − | 0.875674i | ||||
\(343\) | −697592. | −0.320159 | ||||||||
\(344\) | 1.14543e6 | 0.521884 | ||||||||
\(345\) | −56268.0 | − | 97459.1i | −0.0254515 | − | 0.0440834i | ||||
\(346\) | 131560. | − | 227869.i | 0.0590792 | − | 0.102328i | ||||
\(347\) | 1.60416e6 | 0.715195 | 0.357598 | − | 0.933876i | \(-0.383596\pi\) | ||||
0.357598 | + | 0.933876i | \(0.383596\pi\) | |||||||
\(348\) | −65956.1 | − | 114239.i | −0.0291949 | − | 0.0505670i | ||||
\(349\) | 1.25971e6 | + | 2.18188e6i | 0.553613 | + | 0.958887i | 0.998010 | + | 0.0630564i | \(0.0200848\pi\) |
−0.444397 | + | 0.895830i | \(0.646582\pi\) | |||||||
\(350\) | 1.17072e6 | + | 2.02775e6i | 0.510838 | + | 0.884797i | ||||
\(351\) | −98948.2 | + | 171383.i | −0.0428687 | + | 0.0742507i | ||||
\(352\) | 330893. | − | 573123.i | 0.142341 | − | 0.246542i | ||||
\(353\) | −200443. | − | 347178.i | −0.0856159 | − | 0.148291i | 0.820038 | − | 0.572310i | \(-0.193952\pi\) |
−0.905654 | + | 0.424019i | \(0.860619\pi\) | |||||||
\(354\) | 17799.6 | + | 30829.8i | 0.00754923 | + | 0.0130756i | ||||
\(355\) | −1.14030e6 | − | 1.97506e6i | −0.480229 | − | 0.831780i | ||||
\(356\) | 2.10290e6 | 0.879416 | ||||||||
\(357\) | 177089. | − | 306728.i | 0.0735398 | − | 0.127375i | ||||
\(358\) | 1.49556e6 | + | 2.59039e6i | 0.616733 | + | 1.06821i | ||||
\(359\) | 1.27839e6 | 0.523513 | 0.261756 | − | 0.965134i | \(-0.415698\pi\) | ||||
0.261756 | + | 0.965134i | \(0.415698\pi\) | |||||||
\(360\) | −1.24980e6 | −0.508259 | ||||||||
\(361\) | −1.32162e6 | − | 2.28911e6i | −0.533751 | − | 0.924484i | ||||
\(362\) | 1.79055e6 | 0.718148 | ||||||||
\(363\) | −148366. | + | 256978.i | −0.0590974 | + | 0.102360i | ||||
\(364\) | −971337. | −0.384252 | ||||||||
\(365\) | 341831. | − | 592068.i | 0.134301 | − | 0.232616i | ||||
\(366\) | 33590.9 | − | 58181.1i | 0.0131075 | − | 0.0227028i | ||||
\(367\) | −135636. | + | 234929.i | −0.0525666 | + | 0.0910480i | −0.891111 | − | 0.453785i | \(-0.850074\pi\) |
0.838545 | + | 0.544833i | \(0.183407\pi\) | |||||||
\(368\) | 154162. | + | 267016.i | 0.0593414 | + | 0.102782i | ||||
\(369\) | 2.99746e6 | 1.14601 | ||||||||
\(370\) | 294861. | − | 2.67543e6i | 0.111973 | − | 1.01599i | ||||
\(371\) | 2.29007e6 | 0.863803 | ||||||||
\(372\) | 24690.8 | + | 42765.8i | 0.00925078 | + | 0.0160228i | ||||
\(373\) | −1.04342e6 | + | 1.80725e6i | −0.388317 | + | 0.672585i | −0.992223 | − | 0.124471i | \(-0.960277\pi\) |
0.603906 | + | 0.797055i | \(0.293610\pi\) | |||||||
\(374\) | −2.30288e6 | + | 3.98871e6i | −0.851320 | + | 1.47453i | ||||
\(375\) | 13074.2 | − | 22645.2i | 0.00480106 | − | 0.00831569i | ||||
\(376\) | −1.12026e6 | −0.408649 | ||||||||
\(377\) | 1.25889e6 | − | 2.18046e6i | 0.456177 | − | 0.790122i | ||||
\(378\) | 385388. | 0.138729 | ||||||||
\(379\) | 1.32483e6 | + | 2.29467e6i | 0.473763 | + | 0.820581i | 0.999549 | − | 0.0300357i | \(-0.00956208\pi\) |
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(380\) | −2.92535e6 | −1.03925 | ||||||||
\(381\) | 51001.9 | 0.0180001 | ||||||||
\(382\) | 1.24598e6 | + | 2.15811e6i | 0.436872 | + | 0.756684i | ||||
\(383\) | −704251. | + | 1.21980e6i | −0.245319 | + | 0.424904i | −0.962221 | − | 0.272269i | \(-0.912226\pi\) |
0.716902 | + | 0.697173i | \(0.245559\pi\) | |||||||
\(384\) | −18944.9 | −0.00655639 | ||||||||
\(385\) | 4.48915e6 | + | 7.77544e6i | 1.54352 | + | 2.67346i | ||||
\(386\) | 1.04772e6 | + | 1.81470e6i | 0.357912 | + | 0.619922i | ||||
\(387\) | −2.16257e6 | − | 3.74568e6i | −0.733994 | − | 1.27132i | ||||
\(388\) | 1.09871e6 | − | 1.90301e6i | 0.370512 | − | 0.641745i | ||||
\(389\) | −1.78520e6 | + | 3.09205e6i | −0.598153 | + | 1.03603i | 0.394940 | + | 0.918707i | \(0.370765\pi\) |
−0.993094 | + | 0.117325i | \(0.962568\pi\) | |||||||
\(390\) | 65990.2 | + | 114298.i | 0.0219694 | + | 0.0380521i | ||||
\(391\) | −1.07291e6 | − | 1.85833e6i | −0.354911 | − | 0.614724i | ||||
\(392\) | 407979. | + | 706640.i | 0.134098 | + | 0.232265i | ||||
\(393\) | −20220.4 | −0.00660401 | ||||||||
\(394\) | −180447. | + | 312544.i | −0.0585612 | + | 0.101431i | ||||
\(395\) | −3.58748e6 | − | 6.21370e6i | −1.15690 | − | 2.00381i | ||||
\(396\) | −2.49889e6 | −0.800774 | ||||||||
\(397\) | −813002. | −0.258890 | −0.129445 | − | 0.991587i | \(-0.541320\pi\) | ||||
−0.129445 | + | 0.991587i | \(0.541320\pi\) | |||||||
\(398\) | −337299. | − | 584219.i | −0.106735 | − | 0.184871i | ||||
\(399\) | 449785. | 0.141440 | ||||||||
\(400\) | −435820. | + | 754863.i | −0.136194 | + | 0.235895i | ||||
\(401\) | 3.40545e6 | 1.05758 | 0.528790 | − | 0.848753i | \(-0.322646\pi\) | ||||
0.528790 | + | 0.848753i | \(0.322646\pi\) | |||||||
\(402\) | 51950.2 | − | 89980.3i | 0.0160333 | − | 0.0277704i | ||||
\(403\) | −471267. | + | 816259.i | −0.144546 | + | 0.250360i | ||||
\(404\) | 885295. | − | 1.53338e6i | 0.269857 | − | 0.467407i | ||||
\(405\) | 2.34649e6 | + | 4.06424e6i | 0.710855 | + | 1.23124i | ||||
\(406\) | −4.90317e6 | −1.47626 | ||||||||
\(407\) | 589555. | − | 5.34934e6i | 0.176416 | − | 1.60072i | ||||
\(408\) | 131849. | 0.0392127 | ||||||||
\(409\) | −987071. | − | 1.70966e6i | −0.291770 | − | 0.505360i | 0.682459 | − | 0.730924i | \(-0.260911\pi\) |
−0.974228 | + | 0.225564i | \(0.927577\pi\) | |||||||
\(410\) | 2.00459e6 | − | 3.47205e6i | 0.588933 | − | 1.02006i | ||||
\(411\) | −53963.2 | + | 93467.1i | −0.0157577 | + | 0.0272932i | ||||
\(412\) | 548387. | − | 949834.i | 0.159164 | − | 0.275680i | ||||
\(413\) | 1.32322e6 | 0.381731 | ||||||||
\(414\) | 582113. | − | 1.00825e6i | 0.166919 | − | 0.289113i | ||||
\(415\) | 3.22915e6 | 0.920381 | ||||||||
\(416\) | −180799. | − | 313152.i | −0.0512226 | − | 0.0887201i | ||||
\(417\) | −86683.9 | −0.0244117 | ||||||||
\(418\) | −5.84904e6 | −1.63736 | ||||||||
\(419\) | −1.93595e6 | − | 3.35316e6i | −0.538714 | − | 0.933080i | −0.998974 | − | 0.0452957i | \(-0.985577\pi\) |
0.460260 | − | 0.887784i | \(-0.347756\pi\) | |||||||
\(420\) | 128511. | − | 222587.i | 0.0355481 | − | 0.0615711i | ||||
\(421\) | 1.22230e6 | 0.336102 | 0.168051 | − | 0.985778i | \(-0.446253\pi\) | ||||
0.168051 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(422\) | 630396. | + | 1.09188e6i | 0.172319 | + | 0.298465i | ||||
\(423\) | 2.11505e6 | + | 3.66337e6i | 0.574737 | + | 0.995473i | ||||
\(424\) | 426259. | + | 738303.i | 0.115149 | + | 0.199444i | ||||
\(425\) | 3.03314e6 | − | 5.25355e6i | 0.814554 | − | 1.41085i | ||||
\(426\) | −65268.0 | + | 113048.i | −0.0174251 | + | 0.0301812i | ||||
\(427\) | −1.24857e6 | − | 2.16259e6i | −0.331393 | − | 0.573990i | ||||
\(428\) | −209030. | − | 362050.i | −0.0551567 | − | 0.0955342i | ||||
\(429\) | 131943. | + | 228532.i | 0.0346132 | + | 0.0599519i | ||||
\(430\) | −5.78498e6 | −1.50880 | ||||||||
\(431\) | 1.98291e6 | − | 3.43450e6i | 0.514174 | − | 0.890575i | −0.485691 | − | 0.874131i | \(-0.661432\pi\) |
0.999865 | − | 0.0164447i | \(-0.00523475\pi\) | |||||||
\(432\) | 71733.6 | + | 124246.i | 0.0184933 | + | 0.0320313i | ||||
\(433\) | −1.91179e6 | −0.490027 | −0.245013 | − | 0.969520i | \(-0.578792\pi\) | ||||
−0.245013 | + | 0.969520i | \(0.578792\pi\) | |||||||
\(434\) | 1.83551e6 | 0.467771 | ||||||||
\(435\) | 333109. | + | 576962.i | 0.0844041 | + | 0.146192i | ||||
\(436\) | −3.27244e6 | −0.824433 | ||||||||
\(437\) | 1.36252e6 | − | 2.35996e6i | 0.341303 | − | 0.591155i | ||||
\(438\) | −39131.1 | −0.00974624 | ||||||||
\(439\) | 100272. | − | 173676.i | 0.0248324 | − | 0.0430110i | −0.853342 | − | 0.521351i | \(-0.825428\pi\) |
0.878175 | + | 0.478340i | \(0.158761\pi\) | |||||||
\(440\) | −1.67116e6 | + | 2.89454e6i | −0.411517 | + | 0.712768i | ||||
\(441\) | 1.54052e6 | − | 2.66826e6i | 0.377200 | − | 0.653329i | ||||
\(442\) | 1.25829e6 | + | 2.17941e6i | 0.306354 | + | 0.530621i | ||||
\(443\) | −7.13297e6 | −1.72688 | −0.863438 | − | 0.504454i | \(-0.831694\pi\) | ||||
−0.863438 | + | 0.504454i | \(0.831694\pi\) | |||||||
\(444\) | −141058. | + | 61951.7i | −0.0339578 | + | 0.0149140i | ||||
\(445\) | −1.06206e7 | −2.54244 | ||||||||
\(446\) | 216604. | + | 375169.i | 0.0515619 | + | 0.0893079i | ||||
\(447\) | 154511. | − | 267621.i | 0.0365755 | − | 0.0633506i | ||||
\(448\) | −352091. | + | 609840.i | −0.0828820 | + | 0.143556i | ||||
\(449\) | 781564. | − | 1.35371e6i | 0.182957 | − | 0.316891i | −0.759929 | − | 0.650006i | \(-0.774766\pi\) |
0.942886 | + | 0.333115i | \(0.108100\pi\) | |||||||
\(450\) | 3.29130e6 | 0.766190 | ||||||||
\(451\) | 4.00803e6 | − | 6.94212e6i | 0.927876 | − | 1.60713i | ||||
\(452\) | 3.04019e6 | 0.699930 | ||||||||
\(453\) | −255710. | − | 442903.i | −0.0585467 | − | 0.101406i | ||||
\(454\) | −224074. | −0.0510214 | ||||||||
\(455\) | 4.90571e6 | 1.11090 | ||||||||
\(456\) | 83720.2 | + | 145008.i | 0.0188546 | + | 0.0326572i | ||||
\(457\) | −1.22319e6 | + | 2.11862e6i | −0.273969 | + | 0.474529i | −0.969875 | − | 0.243605i | \(-0.921670\pi\) |
0.695905 | + | 0.718134i | \(0.255003\pi\) | |||||||
\(458\) | 1.29870e6 | 0.289298 | ||||||||
\(459\) | −499238. | − | 864705.i | −0.110605 | − | 0.191574i | ||||
\(460\) | −778590. | − | 1.34856e6i | −0.171559 | − | 0.297149i | ||||
\(461\) | 1.03062e6 | + | 1.78508e6i | 0.225863 | + | 0.391205i | 0.956578 | − | 0.291477i | \(-0.0941466\pi\) |
−0.730715 | + | 0.682682i | \(0.760813\pi\) | |||||||
\(462\) | 256948. | − | 445048.i | 0.0560068 | − | 0.0970067i | ||||
\(463\) | −3.63356e6 | + | 6.29350e6i | −0.787734 | + | 1.36439i | 0.139619 | + | 0.990205i | \(0.455412\pi\) |
−0.927352 | + | 0.374189i | \(0.877921\pi\) | |||||||
\(464\) | −912645. | − | 1.58075e6i | −0.196792 | − | 0.340853i | ||||
\(465\) | −124700. | − | 215987.i | −0.0267445 | − | 0.0463229i | ||||
\(466\) | 1.60659e6 | + | 2.78270e6i | 0.342721 | + | 0.593610i | ||||
\(467\) | −5.98917e6 | −1.27079 | −0.635396 | − | 0.772186i | \(-0.719163\pi\) | ||||
−0.635396 | + | 0.772186i | \(0.719163\pi\) | |||||||
\(468\) | −682692. | + | 1.18246e6i | −0.144082 | + | 0.249558i | ||||
\(469\) | −1.93099e6 | − | 3.34457e6i | −0.405366 | − | 0.702114i | ||||
\(470\) | 5.65785e6 | 1.18143 | ||||||||
\(471\) | 440247. | 0.0914416 | ||||||||
\(472\) | 246296. | + | 426598.i | 0.0508865 | + | 0.0881380i | ||||
\(473\) | −1.15667e7 | −2.37714 | ||||||||
\(474\) | −205339. | + | 355657.i | −0.0419783 | + | 0.0727086i | ||||
\(475\) | 7.70379e6 | 1.56664 | ||||||||
\(476\) | 2.45042e6 | − | 4.24424e6i | 0.495704 | − | 0.858584i | ||||
\(477\) | 1.60955e6 | − | 2.78782e6i | 0.323898 | − | 0.561008i | ||||
\(478\) | 2.30866e6 | − | 3.99872e6i | 0.462158 | − | 0.800482i | ||||
\(479\) | −4.77027e6 | − | 8.26234e6i | −0.949957 | − | 1.64537i | −0.745508 | − | 0.666496i | \(-0.767793\pi\) |
−0.204448 | − | 0.978877i | \(-0.565540\pi\) | |||||||
\(480\) | 95680.7 | 0.0189549 | ||||||||
\(481\) | −2.37020e6 | − | 1.74040e6i | −0.467114 | − | 0.342994i | ||||
\(482\) | −302920. | −0.0593896 | ||||||||
\(483\) | 119711. | + | 207346.i | 0.0233490 | + | 0.0404416i | ||||
\(484\) | −2.05297e6 | + | 3.55584e6i | −0.398353 | + | 0.689968i | ||||
\(485\) | −5.54897e6 | + | 9.61110e6i | −1.07117 | + | 1.85532i | ||||
\(486\) | 406671. | − | 704375.i | 0.0781003 | − | 0.135274i | ||||
\(487\) | −2.44745e6 | −0.467618 | −0.233809 | − | 0.972283i | \(-0.575119\pi\) | ||||
−0.233809 | + | 0.972283i | \(0.575119\pi\) | |||||||
\(488\) | 464802. | − | 805061.i | 0.0883524 | − | 0.153031i | ||||
\(489\) | 231593. | 0.0437979 | ||||||||
\(490\) | −2.06048e6 | − | 3.56886e6i | −0.387685 | − | 0.671490i | ||||
\(491\) | 8.94639e6 | 1.67473 | 0.837364 | − | 0.546646i | \(-0.184095\pi\) | ||||
0.837364 | + | 0.546646i | \(0.184095\pi\) | |||||||
\(492\) | −229476. | −0.0427390 | ||||||||
\(493\) | 6.35165e6 | + | 1.10014e7i | 1.17698 | + | 2.03859i | ||||
\(494\) | −1.59795e6 | + | 2.76772e6i | −0.294608 | + | 0.510276i | ||||
\(495\) | 1.26206e7 | 2.31508 | ||||||||
\(496\) | 341651. | + | 591757.i | 0.0623560 | + | 0.108004i | ||||
\(497\) | 2.42601e6 | + | 4.20197e6i | 0.440557 | + | 0.763066i | ||||
\(498\) | −92414.3 | − | 160066.i | −0.0166981 | − | 0.0289219i | ||||
\(499\) | 425263. | − | 736577.i | 0.0764550 | − | 0.132424i | −0.825263 | − | 0.564748i | \(-0.808973\pi\) |
0.901718 | + | 0.432325i | \(0.142307\pi\) | |||||||
\(500\) | 180910. | − | 313345.i | 0.0323622 | − | 0.0560529i | ||||
\(501\) | 342201. | + | 592709.i | 0.0609097 | + | 0.105499i | ||||
\(502\) | −1.18441e6 | − | 2.05146e6i | −0.209770 | − | 0.363332i | ||||
\(503\) | 679867. | + | 1.17756e6i | 0.119813 | + | 0.207522i | 0.919693 | − | 0.392637i | \(-0.128437\pi\) |
−0.799880 | + | 0.600159i | \(0.795104\pi\) | |||||||
\(504\) | 2.65898e6 | 0.466272 | ||||||||
\(505\) | −4.47115e6 | + | 7.74426e6i | −0.780173 | + | 1.35130i | ||||
\(506\) | −1.55674e6 | − | 2.69634e6i | −0.270295 | − | 0.468165i | ||||
\(507\) | −285143. | −0.0492654 | ||||||||
\(508\) | 705721. | 0.121332 | ||||||||
\(509\) | 1.48874e6 | + | 2.57857e6i | 0.254697 | + | 0.441148i | 0.964813 | − | 0.262937i | \(-0.0846910\pi\) |
−0.710116 | + | 0.704084i | \(0.751358\pi\) | |||||||
\(510\) | −665900. | −0.113366 | ||||||||
\(511\) | −727252. | + | 1.25964e6i | −0.123206 | + | 0.213399i | ||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 634001. | − | 1.09812e6i | 0.106364 | − | 0.184229i | ||||
\(514\) | 927421. | − | 1.60634e6i | 0.154835 | − | 0.268182i | ||||
\(515\) | −2.76961e6 | + | 4.79711e6i | −0.460151 | + | 0.797005i | ||||
\(516\) | 165559. | + | 286757.i | 0.0273734 | + | 0.0474121i | ||||
\(517\) | 1.13125e7 | 1.86136 | ||||||||
\(518\) | −627324. | + | 5.69204e6i | −0.102723 | + | 0.932059i | ||||
\(519\) | 76062.0 | 0.0123951 | ||||||||
\(520\) | 913117. | + | 1.58156e6i | 0.148087 | + | 0.256495i | ||||
\(521\) | 3.41479e6 | − | 5.91458e6i | 0.551149 | − | 0.954618i | −0.447043 | − | 0.894513i | \(-0.647523\pi\) |
0.998192 | − | 0.0601057i | \(-0.0191438\pi\) | |||||||
\(522\) | −3.44613e6 | + | 5.96888e6i | −0.553549 | + | 0.958774i | ||||
\(523\) | −2.06235e6 | + | 3.57209e6i | −0.329691 | + | 0.571042i | −0.982451 | − | 0.186523i | \(-0.940278\pi\) |
0.652759 | + | 0.757565i | \(0.273611\pi\) | |||||||
\(524\) | −279793. | −0.0445152 | ||||||||
\(525\) | −338428. | + | 586174.i | −0.0535880 | + | 0.0928172i | ||||
\(526\) | −3.70346e6 | −0.583638 | ||||||||
\(527\) | −2.37775e6 | − | 4.11839e6i | −0.372941 | − | 0.645953i | ||||
\(528\) | 191307. | 0.0298639 | ||||||||
\(529\) | −4.98579e6 | −0.774630 | ||||||||
\(530\) | −2.15281e6 | − | 3.72878e6i | −0.332902 | − | 0.576602i | ||||
\(531\) | 930010. | − | 1.61083e6i | 0.143137 | − | 0.247920i | ||||
\(532\) | 6.22375e6 | 0.953396 | ||||||||
\(533\) | −2.18997e6 | − | 3.79314e6i | −0.333903 | − | 0.578337i | ||||
\(534\) | 303950. | + | 526457.i | 0.0461264 | + | 0.0798932i | ||||
\(535\) | 1.05570e6 | + | 1.82852e6i | 0.159461 | + | 0.276195i | ||||
\(536\) | 718843. | − | 1.24507e6i | 0.108074 | − | 0.187190i | ||||
\(537\) | −432333. | + | 748822.i | −0.0646967 | + | 0.112058i | ||||
\(538\) | −126570. | − | 219226.i | −0.0188528 | − | 0.0326540i | ||||
\(539\) | −4.11979e6 | − | 7.13569e6i | −0.610806 | − | 1.05795i | ||||
\(540\) | −362288. | − | 627502.i | −0.0534650 | − | 0.0926042i | ||||
\(541\) | 1.04365e7 | 1.53307 | 0.766533 | − | 0.642205i | \(-0.221980\pi\) | ||||
0.766533 | + | 0.642205i | \(0.221980\pi\) | |||||||
\(542\) | 237864. | − | 411993.i | 0.0347801 | − | 0.0602410i | ||||
\(543\) | 258803. | + | 448259.i | 0.0376677 | + | 0.0652424i | ||||
\(544\) | 1.82442e6 | 0.264318 | ||||||||
\(545\) | 1.65273e7 | 2.38348 | ||||||||
\(546\) | −140396. | − | 243172.i | −0.0201545 | − | 0.0349086i | ||||
\(547\) | −9.43501e6 | −1.34826 | −0.674130 | − | 0.738612i | \(-0.735481\pi\) | ||||
−0.674130 | + | 0.738612i | \(0.735481\pi\) | |||||||
\(548\) | −746698. | + | 1.29332e6i | −0.106217 | + | 0.183973i | ||||
\(549\) | −3.51017e6 | −0.497047 | ||||||||
\(550\) | 4.40094e6 | − | 7.62265e6i | 0.620352 | − | 1.07448i | ||||
\(551\) | −8.06620e6 | + | 1.39711e7i | −1.13185 | + | 1.96043i | ||||
\(552\) | −44564.6 | + | 77188.2i | −0.00622505 | + | 0.0107821i | ||||
\(553\) | 7.63244e6 | + | 1.32198e7i | 1.06133 | + | 1.83828i | ||||
\(554\) | 1.64970e6 | 0.228365 | ||||||||
\(555\) | 712408. | − | 312885.i | 0.0981739 | − | 0.0431173i | ||||
\(556\) | −1.19946e6 | −0.164550 | ||||||||
\(557\) | 4.75436e6 | + | 8.23479e6i | 0.649313 | + | 1.12464i | 0.983287 | + | 0.182060i | \(0.0582766\pi\) |
−0.333975 | + | 0.942582i | \(0.608390\pi\) | |||||||
\(558\) | 1.29007e6 | − | 2.23446e6i | 0.175399 | − | 0.303800i | ||||
\(559\) | −3.15998e6 | + | 5.47325e6i | −0.427716 | + | 0.740826i | ||||
\(560\) | 1.77823e6 | − | 3.07998e6i | 0.239616 | − | 0.415028i | ||||
\(561\) | −1.33142e6 | −0.178611 | ||||||||
\(562\) | 3.43083e6 | − | 5.94238e6i | 0.458204 | − | 0.793633i | ||||
\(563\) | −8.61074e6 | −1.14490 | −0.572452 | − | 0.819938i | \(-0.694008\pi\) | ||||
−0.572452 | + | 0.819938i | \(0.694008\pi\) | |||||||
\(564\) | −161921. | − | 280455.i | −0.0214341 | − | 0.0371249i | ||||
\(565\) | −1.53544e7 | −2.02354 | ||||||||
\(566\) | 9.62430e6 | 1.26278 | ||||||||
\(567\) | −4.99221e6 | − | 8.64676e6i | −0.652131 | − | 1.12952i | ||||
\(568\) | −903124. | + | 1.56426e6i | −0.117456 | + | 0.203440i | ||||
\(569\) | −1.52294e7 | −1.97198 | −0.985992 | − | 0.166793i | \(-0.946659\pi\) | ||||
−0.985992 | + | 0.166793i | \(0.946659\pi\) | |||||||
\(570\) | −422826. | − | 732356.i | −0.0545098 | − | 0.0944137i | ||||
\(571\) | 3.67655e6 | + | 6.36798e6i | 0.471901 | + | 0.817356i | 0.999483 | − | 0.0321478i | \(-0.0102347\pi\) |
−0.527582 | + | 0.849504i | \(0.676901\pi\) | |||||||
\(572\) | 1.82571e6 | + | 3.16223e6i | 0.233315 | + | 0.404113i | ||||
\(573\) | −360185. | + | 623859.i | −0.0458288 | + | 0.0793779i | ||||
\(574\) | −4.26480e6 | + | 7.38686e6i | −0.540280 | + | 0.935793i | ||||
\(575\) | 2.05038e6 | + | 3.55137e6i | 0.258622 | + | 0.447946i | ||||
\(576\) | 494926. | + | 857237.i | 0.0621561 | + | 0.107658i | ||||
\(577\) | 2.65338e6 | + | 4.59578e6i | 0.331787 | + | 0.574672i | 0.982862 | − | 0.184341i | \(-0.0590151\pi\) |
−0.651075 | + | 0.759013i | \(0.725682\pi\) | |||||||
\(578\) | −7.01780e6 | −0.873738 | ||||||||
\(579\) | −302871. | + | 524588.i | −0.0375458 | + | 0.0650312i | ||||
\(580\) | 4.60928e6 | + | 7.98351e6i | 0.568936 | + | 0.985426i | ||||
\(581\) | −6.87008e6 | −0.844347 | ||||||||
\(582\) | 635220. | 0.0777350 | ||||||||
\(583\) | −4.30439e6 | − | 7.45542e6i | −0.524494 | − | 0.908450i | ||||
\(584\) | −541464. | −0.0656958 | ||||||||
\(585\) | 3.44791e6 | − | 5.97196e6i | 0.416550 | − | 0.721485i | ||||
\(586\) | 2.63810e6 | 0.317357 | ||||||||
\(587\) | 1.12598e6 | − | 1.95026e6i | 0.134876 | − | 0.233613i | −0.790674 | − | 0.612238i | \(-0.790270\pi\) |
0.925550 | + | 0.378625i | \(0.123603\pi\) | |||||||
\(588\) | −117937. | + | 204273.i | −0.0140672 | + | 0.0243651i | ||||
\(589\) | 3.01960e6 | − | 5.23010e6i | 0.358642 | − | 0.621186i | ||||
\(590\) | −1.24391e6 | − | 2.15452e6i | −0.147116 | − | 0.254812i | ||||
\(591\) | −104326. | −0.0122864 | ||||||||
\(592\) | −1.95184e6 | + | 857235.i | −0.228897 | + | 0.100530i | ||||
\(593\) | −2.90482e6 | −0.339220 | −0.169610 | − | 0.985511i | \(-0.554251\pi\) | ||||
−0.169610 | + | 0.985511i | \(0.554251\pi\) | |||||||
\(594\) | −724370. | − | 1.25465e6i | −0.0842353 | − | 0.145900i | ||||
\(595\) | −1.23757e7 | + | 2.14354e7i | −1.43311 | + | 2.48221i | ||||
\(596\) | 2.13799e6 | − | 3.70311e6i | 0.246542 | − | 0.427023i | ||||
\(597\) | 97505.3 | − | 168884.i | 0.0111968 | − | 0.0193934i | ||||
\(598\) | −1.70119e6 | −0.194536 | ||||||||
\(599\) | 2.85327e6 | − | 4.94201e6i | 0.324919 | − | 0.562777i | −0.656577 | − | 0.754259i | \(-0.727996\pi\) |
0.981496 | + | 0.191482i | \(0.0613295\pi\) | |||||||
\(600\) | −251971. | −0.0285741 | ||||||||
\(601\) | −7.43246e6 | − | 1.28734e7i | −0.839357 | − | 1.45381i | −0.890433 | − | 0.455113i | \(-0.849599\pi\) |
0.0510769 | − | 0.998695i | \(-0.483735\pi\) | |||||||
\(602\) | 1.23077e7 | 1.38415 | ||||||||
\(603\) | −5.42868e6 | −0.607996 | ||||||||
\(604\) | −3.53830e6 | − | 6.12851e6i | −0.394641 | − | 0.683538i | ||||
\(605\) | 1.03684e7 | − | 1.79587e7i | 1.15166 | − | 1.99474i | ||||
\(606\) | 511836. | 0.0566173 | ||||||||
\(607\) | −1.99749e6 | − | 3.45975e6i | −0.220045 | − | 0.381130i | 0.734776 | − | 0.678310i | \(-0.237287\pi\) |
−0.954822 | + | 0.297180i | \(0.903954\pi\) | |||||||
\(608\) | 1.15845e6 | + | 2.00649e6i | 0.127092 | + | 0.220130i | ||||
\(609\) | −708697. | − | 1.22750e6i | −0.0774314 | − | 0.134115i | ||||
\(610\) | −2.34747e6 | + | 4.06593e6i | −0.255432 | + | 0.442421i | ||||
\(611\) | 3.09054e6 | − | 5.35298e6i | 0.334913 | − | 0.580086i | ||||
\(612\) | −3.44449e6 | − | 5.96603e6i | −0.371746 | − | 0.643882i | ||||
\(613\) | −5.97713e6 | − | 1.03527e7i | −0.642453 | − | 1.11276i | −0.984883 | − | 0.173219i | \(-0.944583\pi\) |
0.342430 | − | 0.939543i | \(-0.388750\pi\) | |||||||
\(614\) | −5.37367e6 | − | 9.30747e6i | −0.575241 | − | 0.996347i | ||||
\(615\) | 1.15896e6 | 0.123561 | ||||||||
\(616\) | 3.55544e6 | − | 6.15820e6i | 0.377521 | − | 0.653886i | ||||
\(617\) | 7.75753e6 | + | 1.34364e7i | 0.820372 | + | 1.42093i | 0.905406 | + | 0.424547i | \(0.139567\pi\) |
−0.0850342 | + | 0.996378i | \(0.527100\pi\) | |||||||
\(618\) | 317052. | 0.0333933 | ||||||||
\(619\) | 1.13670e7 | 1.19240 | 0.596199 | − | 0.802837i | \(-0.296677\pi\) | ||||
0.596199 | + | 0.802837i | \(0.296677\pi\) | |||||||
\(620\) | −1.72550e6 | − | 2.98865e6i | −0.180275 | − | 0.312245i | ||||
\(621\) | 674963. | 0.0702346 | ||||||||
\(622\) | −1.92476e6 | + | 3.33378e6i | −0.199480 | + | 0.345510i | ||||
\(623\) | 2.25956e7 | 2.33241 | ||||||||
\(624\) | 52264.6 | − | 90525.0i | 0.00537337 | − | 0.00930694i | ||||
\(625\) | 4.40639e6 | − | 7.63210e6i | 0.451215 | − | 0.781527i | ||||
\(626\) | −1.24226e6 | + | 2.15165e6i | −0.126700 | + | 0.219450i | ||||
\(627\) | −845411. | − | 1.46429e6i | −0.0858813 | − | 0.148751i | ||||
\(628\) | 6.09176e6 | 0.616373 | ||||||||
\(629\) | 1.35840e7 | − | 5.96601e6i | 1.36899 | − | 0.601254i | ||||
\(630\) | −1.34291e7 | −1.34802 | ||||||||
\(631\) | 1.69526e6 | + | 2.93628e6i | 0.169498 | + | 0.293579i | 0.938243 | − | 0.345976i | \(-0.112452\pi\) |
−0.768746 | + | 0.639555i | \(0.779119\pi\) | |||||||
\(632\) | −2.84131e6 | + | 4.92129e6i | −0.282960 | + | 0.490102i | ||||
\(633\) | −182233. | + | 315636.i | −0.0180766 | + | 0.0313096i | ||||
\(634\) | −468554. | + | 811560.i | −0.0462953 | + | 0.0801858i | ||||
\(635\) | −3.56422e6 | −0.350776 | ||||||||
\(636\) | −123222. | + | 213426.i | −0.0120794 | + | 0.0209221i | ||||
\(637\) | −4.50207e6 | −0.439606 | ||||||||
\(638\) | 9.21594e6 | + | 1.59625e7i | 0.896371 | + | 1.55256i | ||||
\(639\) | 6.82036e6 | 0.660778 | ||||||||
\(640\) | 1.32395e6 | 0.127768 | ||||||||
\(641\) | 1.57548e6 | + | 2.72881e6i | 0.151449 | + | 0.262318i | 0.931761 | − | 0.363073i | \(-0.118273\pi\) |
−0.780311 | + | 0.625392i | \(0.784939\pi\) | |||||||
\(642\) | 60425.6 | − | 104660.i | 0.00578606 | − | 0.0100218i | ||||
\(643\) | −1.07323e7 | −1.02368 | −0.511841 | − | 0.859080i | \(-0.671036\pi\) | ||||
−0.511841 | + | 0.859080i | \(0.671036\pi\) | |||||||
\(644\) | 1.65647e6 | + | 2.86908e6i | 0.157387 | + | 0.272602i | ||||
\(645\) | −836151. | − | 1.44826e6i | −0.0791380 | − | 0.137071i | ||||
\(646\) | −8.06234e6 | − | 1.39644e7i | −0.760116 | − | 1.31656i | ||||
\(647\) | 3.85774e6 | − | 6.68181e6i | 0.362304 | − | 0.627528i | −0.626036 | − | 0.779794i | \(-0.715324\pi\) |
0.988340 | + | 0.152266i | \(0.0486570\pi\) | |||||||
\(648\) | 1.85843e6 | − | 3.21890e6i | 0.173864 | − | 0.301141i | ||||
\(649\) | −2.48711e6 | − | 4.30780e6i | −0.231784 | − | 0.401462i | ||||
\(650\) | −2.40465e6 | − | 4.16498e6i | −0.223239 | − | 0.386660i | ||||
\(651\) | 265302. | + | 459517.i | 0.0245351 | + | 0.0424961i | ||||
\(652\) | 3.20459e6 | 0.295225 | ||||||||
\(653\) | −4.10964e6 | + | 7.11810e6i | −0.377156 | + | 0.653253i | −0.990647 | − | 0.136448i | \(-0.956431\pi\) |
0.613491 | + | 0.789701i | \(0.289765\pi\) | |||||||
\(654\) | −472993. | − | 819248.i | −0.0432425 | − | 0.0748981i | ||||
\(655\) | 1.41308e6 | 0.128696 | ||||||||
\(656\) | −3.17529e6 | −0.288087 | ||||||||
\(657\) | 1.02228e6 | + | 1.77064e6i | 0.0923966 | + | 0.160036i | ||||
\(658\) | −1.20372e7 | −1.08383 | ||||||||
\(659\) | −4.84529e6 | + | 8.39229e6i | −0.434617 | + | 0.752778i | −0.997264 | − | 0.0739187i | \(-0.976449\pi\) |
0.562648 | + | 0.826697i | \(0.309783\pi\) | |||||||
\(660\) | −966189. | −0.0863381 | ||||||||
\(661\) | 7.77971e6 | − | 1.34749e7i | 0.692564 | − | 1.19956i | −0.278431 | − | 0.960456i | \(-0.589814\pi\) |
0.970995 | − | 0.239100i | \(-0.0768523\pi\) | |||||||
\(662\) | −148051. | + | 256433.i | −0.0131301 | + | 0.0227420i | ||||
\(663\) | −363741. | + | 630018.i | −0.0321372 | + | 0.0556633i | ||||
\(664\) | −1.27875e6 | − | 2.21486e6i | −0.112555 | − | 0.194952i | ||||
\(665\) | −3.14329e7 | −2.75632 | ||||||||
\(666\) | 6.48830e6 | + | 4.76425e6i | 0.566820 | + | 0.416207i | ||||
\(667\) | −8.58735e6 | −0.747385 | ||||||||
\(668\) | 4.73509e6 | + | 8.20141e6i | 0.410570 | + | 0.711127i | ||||
\(669\) | −62615.1 | + | 108453.i | −0.00540896 | + | 0.00936860i | ||||
\(670\) | −3.63049e6 | + | 6.28819e6i | −0.312448 | + | 0.541176i | ||||
\(671\) | −4.69360e6 | + | 8.12955e6i | −0.402438 | + | 0.697044i | ||||
\(672\) | −203563. | −0.0173890 | ||||||||
\(673\) | 4.31854e6 | − | 7.47994e6i | 0.367536 | − | 0.636591i | −0.621644 | − | 0.783300i | \(-0.713535\pi\) |
0.989180 | + | 0.146709i | \(0.0468682\pi\) | |||||||
\(674\) | −336807. | −0.0285582 | ||||||||
\(675\) | 954071. | + | 1.65250e6i | 0.0805974 | + | 0.139599i | ||||
\(676\) | −3.94556e6 | −0.332080 | ||||||||
\(677\) | 1.23212e7 | 1.03319 | 0.516597 | − | 0.856228i | \(-0.327198\pi\) | ||||
0.516597 | + | 0.856228i | \(0.327198\pi\) | |||||||
\(678\) | 439424. | + | 761105.i | 0.0367121 | + | 0.0635873i | ||||
\(679\) | 1.18056e7 | − | 2.04478e7i | 0.982680 | − | 1.70205i | ||||
\(680\) | −9.21416e6 | −0.764159 | ||||||||
\(681\) | −32387.3 | − | 56096.5i | −0.00267613 | − | 0.00463520i | ||||
\(682\) | −3.45001e6 | − | 5.97559e6i | −0.284027 | − | 0.491949i | ||||
\(683\) | 4.17008e6 | + | 7.22279e6i | 0.342052 | + | 0.592452i | 0.984814 | − | 0.173614i | \(-0.0555446\pi\) |
−0.642761 | + | 0.766067i | \(0.722211\pi\) | |||||||
\(684\) | 4.37428e6 | − | 7.57648e6i | 0.357492 | − | 0.619195i | ||||
\(685\) | 3.77117e6 | − | 6.53186e6i | 0.307079 | − | 0.531876i | ||||
\(686\) | −1.39518e6 | − | 2.41653e6i | −0.113193 | − | 0.196057i | ||||
\(687\) | 187712. | + | 325127.i | 0.0151740 | + | 0.0262822i | ||||
\(688\) | 2.29087e6 | + | 3.96790e6i | 0.184514 | + | 0.319587i | ||||
\(689\) | −4.70380e6 | −0.377486 | ||||||||
\(690\) | 225072. | − | 389836.i | 0.0179970 | − | 0.0311716i | ||||
\(691\) | 6.43958e6 | + | 1.11537e7i | 0.513053 | + | 0.888635i | 0.999885 | + | 0.0151389i | \(0.00481905\pi\) |
−0.486832 | + | 0.873496i | \(0.661848\pi\) | |||||||
\(692\) | 1.05248e6 | 0.0835506 | ||||||||
\(693\) | −2.68505e7 | −2.12383 | ||||||||
\(694\) | 3.20833e6 | + | 5.55698e6i | 0.252860 | + | 0.437966i | ||||
\(695\) | 6.05783e6 | 0.475724 | ||||||||
\(696\) | 263824. | − | 456957.i | 0.0206439 | − | 0.0357563i | ||||
\(697\) | 2.20988e7 | 1.72300 | ||||||||
\(698\) | −5.03884e6 | + | 8.72752e6i | −0.391464 | + | 0.678035i | ||||
\(699\) | −464428. | + | 804413.i | −0.0359522 | + | 0.0622710i | ||||
\(700\) | −4.68288e6 | + | 8.11098e6i | −0.361217 | + | 0.625646i | ||||
\(701\) | 9.63151e6 | + | 1.66823e7i | 0.740286 | + | 1.28221i | 0.952365 | + | 0.304960i | \(0.0986432\pi\) |
−0.212079 | + | 0.977252i | \(0.568023\pi\) | |||||||
\(702\) | −791585. | −0.0606254 | ||||||||
\(703\) | 1.51868e7 | + | 1.11515e7i | 1.15899 | + | 0.851027i | ||||
\(704\) | 2.64714e6 | 0.201301 | ||||||||
\(705\) | 817776. | + | 1.41643e6i | 0.0619672 | + | 0.107330i | ||||
\(706\) | 801773. | − | 1.38871e6i | 0.0605396 | − | 0.104858i | ||||
\(707\) | 9.51247e6 | − | 1.64761e7i | 0.715722 | − | 1.23967i | ||||
\(708\) | −71198.5 | + | 123319.i | −0.00533811 | + | 0.00924588i | ||||
\(709\) | −1.74809e7 | −1.30602 | −0.653008 | − | 0.757351i | \(-0.726493\pi\) | ||||
−0.653008 | + | 0.757351i | \(0.726493\pi\) | |||||||
\(710\) | 4.56120e6 | − | 7.90023e6i | 0.339573 | − | 0.588158i | ||||
\(711\) | 2.14575e7 | 1.59186 | ||||||||
\(712\) | 4.20581e6 | + | 7.28467e6i | 0.310921 | + | 0.538530i | ||||
\(713\) | 3.21469e6 | 0.236819 | ||||||||
\(714\) | 1.41672e6 | 0.104001 | ||||||||
\(715\) | −9.22070e6 | − | 1.59707e7i | −0.674526 | − | 1.16831i | ||||
\(716\) | −5.98226e6 | + | 1.03616e7i | −0.436096 | + | 0.755341i | ||||
\(717\) | 1.33476e6 | 0.0969629 | ||||||||
\(718\) | 2.55678e6 | + | 4.42847e6i | 0.185090 | + | 0.320585i | ||||
\(719\) | −1.24013e6 | − | 2.14796e6i | −0.0894631 | − | 0.154955i | 0.817821 | − | 0.575472i | \(-0.195182\pi\) |
−0.907284 | + | 0.420518i | \(0.861848\pi\) | |||||||
\(720\) | −2.49961e6 | − | 4.32944e6i | −0.179697 | − | 0.311244i | ||||
\(721\) | 5.89240e6 | − | 1.02059e7i | 0.422138 | − | 0.731164i | ||||
\(722\) | 5.28648e6 | − | 9.15646e6i | 0.377419 | − | 0.653709i | ||||
\(723\) | −43783.6 | − | 75835.4i | −0.00311505 | − | 0.00539543i | ||||
\(724\) | 3.58109e6 | + | 6.20264e6i | 0.253904 | + | 0.439774i | ||||
\(725\) | −1.21383e7 | − | 2.10242e7i | −0.857659 | − | 1.48551i | ||||
\(726\) | −1.18693e6 | −0.0835764 | ||||||||
\(727\) | 4.38234e6 | − | 7.59044e6i | 0.307518 | − | 0.532636i | −0.670301 | − | 0.742089i | \(-0.733835\pi\) |
0.977819 | + | 0.209453i | \(0.0671683\pi\) | |||||||
\(728\) | −1.94267e6 | − | 3.36481e6i | −0.135854 | − | 0.235306i | ||||
\(729\) | −1.38774e7 | −0.967138 | ||||||||
\(730\) | 2.73465e6 | 0.189930 | ||||||||
\(731\) | −1.59435e7 | − | 2.76150e7i | −1.10355 | − | 1.91140i | ||||
\(732\) | 268727. | 0.0185367 | ||||||||
\(733\) | −5.13017e6 | + | 8.88572e6i | −0.352673 | + | 0.610847i | −0.986717 | − | 0.162450i | \(-0.948060\pi\) |
0.634044 | + | 0.773297i | \(0.281394\pi\) | |||||||
\(734\) | −1.08509e6 | −0.0743404 | ||||||||
\(735\) | 595638. | − | 1.03167e6i | 0.0406690 | − | 0.0704408i | ||||
\(736\) | −616648. | + | 1.06807e6i | −0.0419607 | + | 0.0726780i | ||||
\(737\) | −7.25891e6 | + | 1.25728e7i | −0.492269 | + | 0.852635i | ||||
\(738\) | 5.99493e6 | + | 1.03835e7i | 0.405175 | + | 0.701784i | ||||
\(739\) | 1.00671e6 | 0.0678098 | 0.0339049 | − | 0.999425i | \(-0.489206\pi\) | ||||
0.0339049 | + | 0.999425i | \(0.489206\pi\) | |||||||
\(740\) | 9.85770e6 | − | 4.32944e6i | 0.661753 | − | 0.290638i | ||||
\(741\) | −923857. | −0.0618101 | ||||||||
\(742\) | 4.58015e6 | + | 7.93305e6i | 0.305400 | + | 0.528969i | ||||
\(743\) | −2.39829e6 | + | 4.15395e6i | −0.159378 | + | 0.276051i | −0.934645 | − | 0.355583i | \(-0.884282\pi\) |
0.775266 | + | 0.631634i | \(0.217616\pi\) | |||||||
\(744\) | −98763.3 | + | 171063.i | −0.00654129 | + | 0.0113298i | ||||
\(745\) | −1.07979e7 | + | 1.87024e7i | −0.712766 | + | 1.23455i | ||||
\(746\) | −8.34735e6 | −0.549163 | ||||||||
\(747\) | −4.82855e6 | + | 8.36329e6i | −0.316603 | + | 0.548372i | ||||
\(748\) | −1.84231e7 | −1.20395 | ||||||||
\(749\) | −2.24602e6 | − | 3.89022e6i | −0.146288 | − | 0.253378i | ||||
\(750\) | 104594. | 0.00678973 | ||||||||
\(751\) | 2.28611e6 | 0.147910 | 0.0739551 | − | 0.997262i | \(-0.476438\pi\) | ||||
0.0739551 | + | 0.997262i | \(0.476438\pi\) | |||||||
\(752\) | −2.24053e6 | − | 3.88070e6i | −0.144479 | − | 0.250245i | ||||
\(753\) | 342386. | − | 593030.i | 0.0220054 | − | 0.0381144i | ||||
\(754\) | 1.00711e7 | 0.645132 | ||||||||
\(755\) | 1.78701e7 | + | 3.09519e7i | 1.14093 | + | 1.97615i | ||||
\(756\) | 770776. | + | 1.33502e6i | 0.0490483 | + | 0.0849541i | ||||
\(757\) | 1.77608e6 | + | 3.07626e6i | 0.112648 | + | 0.195111i | 0.916837 | − | 0.399262i | \(-0.130734\pi\) |
−0.804189 | + | 0.594373i | \(0.797400\pi\) | |||||||
\(758\) | −5.29931e6 | + | 9.17867e6i | −0.335001 | + | 0.580239i | ||||
\(759\) | 450016. | − | 779450.i | 0.0283546 | − | 0.0491116i | ||||
\(760\) | −5.85071e6 | − | 1.01337e7i | −0.367430 | − | 0.636407i | ||||
\(761\) | 9.71882e6 | + | 1.68335e7i | 0.608348 | + | 1.05369i | 0.991513 | + | 0.130009i | \(0.0415008\pi\) |
−0.383165 | + | 0.923680i | \(0.625166\pi\) | |||||||
\(762\) | 102004. | + | 176676.i | 0.00636398 | + | 0.0110227i | ||||
\(763\) | −3.51623e7 | −2.18658 | ||||||||
\(764\) | −4.98394e6 | + | 8.63243e6i | −0.308915 | + | 0.535057i | ||||
\(765\) | 1.73963e7 | + | 3.01312e7i | 1.07474 | + | 1.86150i | ||||
\(766\) | −5.63401e6 | −0.346933 | ||||||||
\(767\) | −2.71789e6 | −0.166818 | ||||||||
\(768\) | −37889.9 | − | 65627.2i | −0.00231803 | − | 0.00401495i | ||||
\(769\) | 2.92450e7 | 1.78335 | 0.891674 | − | 0.452678i | \(-0.149531\pi\) | ||||
0.891674 | + | 0.452678i | \(0.149531\pi\) | |||||||
\(770\) | −1.79566e7 | + | 3.11018e7i | −1.09143 | + | 1.89042i | ||||
\(771\) | 536192. | 0.0324851 | ||||||||
\(772\) | −4.19087e6 | + | 7.25881e6i | −0.253082 | + | 0.438351i | ||||
\(773\) | −5.86383e6 | + | 1.01565e7i | −0.352966 | + | 0.611355i | −0.986768 | − | 0.162141i | \(-0.948160\pi\) |
0.633802 | + | 0.773496i | \(0.281494\pi\) | |||||||
\(774\) | 8.65028e6 | − | 1.49827e7i | 0.519012 | − | 0.898956i | ||||
\(775\) | 4.54402e6 | + | 7.87047e6i | 0.271760 | + | 0.470703i | ||||
\(776\) | 8.78964e6 | 0.523983 | ||||||||
\(777\) | −1.51566e6 | + | 665669.i | −0.0900637 | + | 0.0395554i | ||||
\(778\) | −1.42816e7 | −0.845917 | ||||||||
\(779\) | 1.40320e7 | + | 2.43042e7i | 0.828470 | + | 1.43495i | ||||
\(780\) | −263961. | + | 457193.i | −0.0155347 | + | 0.0269069i | ||||
\(781\) | 9.11979e6 | − | 1.57959e7i | 0.535005 | − | 0.926655i | ||||
\(782\) | 4.29162e6 | − | 7.43331e6i | 0.250960 | − | 0.434676i | ||||
\(783\) | −3.99581e6 | −0.232917 | ||||||||
\(784\) | −1.63191e6 | + | 2.82656e6i | −0.0948216 | + | 0.164236i | ||||
\(785\) | −3.07662e7 | −1.78197 | ||||||||
\(786\) | −40440.8 | − | 70045.4i | −0.00233487 | − | 0.00404412i | ||||
\(787\) | −6.28779e6 | −0.361877 | −0.180939 | − | 0.983494i | \(-0.557914\pi\) | ||||
−0.180939 | + | 0.983494i | \(0.557914\pi\) | |||||||
\(788\) | −1.44358e6 | −0.0828180 | ||||||||
\(789\) | −535292. | − | 927154.i | −0.0306125 | − | 0.0530224i | ||||
\(790\) | 1.43499e7 | − | 2.48548e7i | 0.818054 | − | 1.41691i | ||||
\(791\) | 3.26668e7 | 1.85637 | ||||||||
\(792\) | −4.99779e6 | − | 8.65642e6i | −0.283116 | − | 0.490372i | ||||
\(793\) | 2.56456e6 | + | 4.44195e6i | 0.144820 | + | 0.250836i | ||||
\(794\) | −1.62600e6 | − | 2.81632e6i | −0.0915315 | − | 0.158537i | ||||
\(795\) | 622327. | − | 1.07790e6i | 0.0349221 | − | 0.0604869i | ||||
\(796\) | 1.34920e6 | − | 2.33688e6i | 0.0754732 | − | 0.130723i | ||||
\(797\) | −1.63958e7 | − | 2.83984e7i | −0.914296 | − | 1.58361i | −0.807928 | − | 0.589281i | \(-0.799411\pi\) |
−0.106368 | − | 0.994327i | \(-0.533922\pi\) | |||||||
\(798\) | 899571. | + | 1.55810e6i | 0.0500067 | + | 0.0866141i | ||||
\(799\) | 1.55932e7 | + | 2.70082e7i | 0.864107 | + | 1.49668i | ||||
\(800\) | −3.48656e6 | −0.192607 | ||||||||
\(801\) | 1.58811e7 | − | 2.75068e7i | 0.874577 | − | 1.51481i | ||||
\(802\) | 6.81089e6 | + | 1.17968e7i | 0.373911 | + | 0.647632i | ||||
\(803\) | 5.46773e6 | 0.299239 | ||||||||
\(804\) | 415601. | 0.0226744 | ||||||||
\(805\) | −8.36593e6 | − | 1.44902e7i | −0.455014 | − | 0.788107i | ||||
\(806\) | −3.77014e6 | −0.204418 | ||||||||
\(807\) | 36588.4 | − | 63373.0i | 0.00197770 | − | 0.00342547i | ||||
\(808\) | 7.08236e6 | 0.381636 | ||||||||
\(809\) | 5.68955e6 | − | 9.85459e6i | 0.305637 | − | 0.529380i | −0.671766 | − | 0.740764i | \(-0.734464\pi\) |
0.977403 | + | 0.211384i | \(0.0677971\pi\) | |||||||
\(810\) | −9.38596e6 | + | 1.62570e7i | −0.502651 | + | 0.870617i | ||||
\(811\) | 2.04693e6 | − | 3.54538e6i | 0.109282 | − | 0.189283i | −0.806197 | − | 0.591647i | \(-0.798478\pi\) |
0.915480 | + | 0.402364i | \(0.131811\pi\) | |||||||
\(812\) | −9.80635e6 | − | 1.69851e7i | −0.521936 | − | 0.904020i | ||||
\(813\) | 137522. | 0.00729703 | ||||||||
\(814\) | 1.97098e7 | − | 8.65640e6i | 1.04261 | − | 0.457906i | ||||
\(815\) | −1.61847e7 | −0.853513 | ||||||||
\(816\) | 263698. | + | 456739.i | 0.0138638 | + | 0.0240128i | ||||
\(817\) | 2.02473e7 | − | 3.50693e7i | 1.06124 | − | 1.83811i | ||||
\(818\) | 3.94828e6 | − | 6.83863e6i | 0.206312 | − | 0.357343i | ||||
\(819\) | −7.33551e6 | + | 1.27055e7i | −0.382138 | + | 0.661883i | ||||
\(820\) | 1.60367e7 | 0.832876 | ||||||||
\(821\) | −9.93209e6 | + | 1.72029e7i | −0.514260 | + | 0.890724i | 0.485603 | + | 0.874179i | \(0.338600\pi\) |
−0.999863 | + | 0.0165448i | \(0.994733\pi\) | |||||||
\(822\) | −431706. | −0.0222848 | ||||||||
\(823\) | 8.68045e6 | + | 1.50350e7i | 0.446728 | + | 0.773755i | 0.998171 | − | 0.0604575i | \(-0.0192560\pi\) |
−0.551443 | + | 0.834212i | \(0.685923\pi\) | |||||||
\(824\) | 4.38710e6 | 0.225092 | ||||||||
\(825\) | 2.54442e6 | 0.130153 | ||||||||
\(826\) | 2.64645e6 | + | 4.58378e6i | 0.134962 | + | 0.233762i | ||||
\(827\) | −2.30400e6 | + | 3.99064e6i | −0.117144 | + | 0.202899i | −0.918635 | − | 0.395108i | \(-0.870707\pi\) |
0.801491 | + | 0.598007i | \(0.204040\pi\) | |||||||
\(828\) | 4.65690e6 | 0.236059 | ||||||||
\(829\) | 8.58810 | + | 14.8750i | 4.34021e−7 | + | 7.51747e-7i | 0.866026 | − | 0.500000i | \(-0.166667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(830\) | 6.45829e6 | + | 1.11861e7i | 0.325404 | + | 0.563616i | ||||
\(831\) | 238444. | + | 412998.i | 0.0119780 | + | 0.0207465i | ||||
\(832\) | 723194. | − | 1.25261e6i | 0.0362198 | − | 0.0627346i | ||||
\(833\) | 1.13575e7 | − | 1.96717e7i | 0.567113 | − | 0.982268i | ||||
\(834\) | −173368. | − | 300282.i | −0.00863084 | − | 0.0149491i | ||||
\(835\) | −2.39144e7 | − | 4.14209e7i | −1.18698 | − | 2.05591i | ||||
\(836\) | −1.16981e7 | − | 2.02617e7i | −0.578894 | − | 1.00267i | ||||
\(837\) | 1.49584e6 | 0.0738026 | ||||||||
\(838\) | 7.74379e6 | − | 1.34126e7i | 0.380928 | − | 0.659787i | ||||
\(839\) | −58416.1 | − | 101180.i | −0.00286502 | − | 0.00496236i | 0.864589 | − | 0.502479i | \(-0.167579\pi\) |
−0.867454 | + | 0.497517i | \(0.834245\pi\) | |||||||
\(840\) | 1.02809e6 | 0.0502726 | ||||||||
\(841\) | 3.03263e7 | 1.47853 | ||||||||
\(842\) | 2.44459e6 | + | 4.23415e6i | 0.118830 | + | 0.205819i | ||||
\(843\) | 1.98355e6 | 0.0961333 | ||||||||
\(844\) | −2.52158e6 | + | 4.36751e6i | −0.121848 | + | 0.211046i | ||||
\(845\) | 1.99269e7 | 0.960061 | ||||||||
\(846\) | −8.46019e6 | + | 1.46535e7i | −0.406400 | + | 0.703906i | ||||
\(847\) | −2.20591e7 | + | 3.82074e7i | −1.05652 | + | 1.82995i | ||||
\(848\) | −1.70504e6 | + | 2.95321e6i | −0.0814225 | + | 0.141028i | ||||
\(849\) | 1.39108e6 | + | 2.40942e6i | 0.0662343 | + | 0.114721i | ||||
\(850\) | 2.42651e7 | 1.15195 | ||||||||
\(851\) | −1.09869e6 | + | 9.96896e6i | −0.0520056 | + | 0.471874i | ||||
\(852\) | −522144. | −0.0246429 | ||||||||
\(853\) | 1.72333e6 | + | 2.98490e6i | 0.0810954 | + | 0.140461i | 0.903721 | − | 0.428123i | \(-0.140825\pi\) |
−0.822625 | + | 0.568584i | \(0.807491\pi\) | |||||||
\(854\) | 4.99429e6 | − | 8.65036e6i | 0.234330 | − | 0.405872i | ||||
\(855\) | −2.20922e7 | + | 3.82648e7i | −1.03353 | + | 1.79013i | ||||
\(856\) | 836118. | − | 1.44820e6i | 0.0390017 | − | 0.0675529i | ||||
\(857\) | −3.98074e7 | −1.85145 | −0.925725 | − | 0.378198i | \(-0.876544\pi\) | ||||
−0.925725 | + | 0.378198i | \(0.876544\pi\) | |||||||
\(858\) | −527771. | + | 914126.i | −0.0244753 | + | 0.0423924i | ||||
\(859\) | −3.26940e7 | −1.51177 | −0.755884 | − | 0.654706i | \(-0.772793\pi\) | ||||
−0.755884 | + | 0.654706i | \(0.772793\pi\) | |||||||
\(860\) | −1.15700e7 | − | 2.00397e7i | −0.533440 | − | 0.923945i | ||||
\(861\) | −2.46571e6 | −0.113353 | ||||||||
\(862\) | 1.58633e7 | 0.727152 | ||||||||
\(863\) | 5.48612e6 | + | 9.50225e6i | 0.250749 | + | 0.434309i | 0.963732 | − | 0.266871i | \(-0.0859899\pi\) |
−0.712983 | + | 0.701181i | \(0.752657\pi\) | |||||||
\(864\) | −286935. | + | 496985.i | −0.0130767 | + | 0.0226495i | ||||
\(865\) | −5.31552e6 | −0.241549 | ||||||||
\(866\) | −3.82358e6 | − | 6.62263e6i | −0.173251 | − | 0.300079i | ||||
\(867\) | −1.01434e6 | − | 1.75689e6i | −0.0458285 | − | 0.0793774i | ||||
\(868\) | 3.67103e6 | + | 6.35841e6i | 0.165382 | + | 0.286450i | ||||
\(869\) | 2.86917e7 | − | 4.96954e7i | 1.28886 | − | 2.23237i | ||||
\(870\) | −1.33244e6 | + | 2.30785e6i | −0.0596827 | + | 0.103373i | ||||
\(871\) | 3.96624e6 | + | 6.86972e6i | 0.177147 | + | 0.306827i | ||||
\(872\) | −6.54488e6 | − | 1.13361e7i | −0.291481 | − | 0.504860i | ||||
\(873\) | −1.65948e7 | − | 2.87430e7i | −0.736946 | − | 1.27643i | ||||
\(874\) | 1.09002e7 | 0.482676 | ||||||||
\(875\) | 1.94387e6 | − | 3.36689e6i | 0.0858317 | − | 0.148665i | ||||
\(876\) | −78262.3 | − | 135554.i | −0.00344582 | − | 0.00596833i | ||||
\(877\) | −2.27367e7 | −0.998227 | −0.499113 | − | 0.866537i | \(-0.666341\pi\) | ||||
−0.499113 | + | 0.866537i | \(0.666341\pi\) | |||||||
\(878\) | 802176. | 0.0351183 | ||||||||
\(879\) | 381307. | + | 660443.i | 0.0166457 | + | 0.0288312i | ||||
\(880\) | −1.33693e7 | −0.581972 | ||||||||
\(881\) | −5.91581e6 | + | 1.02465e7i | −0.256788 | + | 0.444769i | −0.965380 | − | 0.260849i | \(-0.915997\pi\) |
0.708592 | + | 0.705619i | \(0.249331\pi\) | |||||||
\(882\) | 1.23242e7 | 0.533441 | ||||||||
\(883\) | 7.08676e6 | − | 1.22746e7i | 0.305876 | − | 0.529793i | −0.671580 | − | 0.740932i | \(-0.734384\pi\) |
0.977456 | + | 0.211139i | \(0.0677173\pi\) | |||||||
\(884\) | −5.03314e6 | + | 8.71766e6i | −0.216625 | + | 0.375206i | ||||
\(885\) | 359586. | − | 622820.i | 0.0154328 | − | 0.0267304i | ||||
\(886\) | −1.42659e7 | − | 2.47093e7i | −0.610543 | − | 1.05749i | ||||
\(887\) | −2.46798e7 | −1.05325 | −0.526626 | − | 0.850097i | \(-0.676543\pi\) | ||||
−0.526626 | + | 0.850097i | \(0.676543\pi\) | |||||||
\(888\) | −496722. | − | 364735.i | −0.0211388 | − | 0.0155219i | ||||
\(889\) | 7.58295e6 | 0.321799 | ||||||||
\(890\) | −2.12413e7 | − | 3.67910e7i | −0.898889 | − | 1.55692i | ||||
\(891\) | −1.87666e7 | + | 3.25047e7i | −0.791937 | + | 1.37168i | ||||
\(892\) | −866415. | + | 1.50068e6i | −0.0364598 | + | 0.0631502i | ||||
\(893\) | −1.98024e7 | + | 3.42987e7i | −0.830975 | + | 1.43929i | ||||
\(894\) | 1.23609e6 | 0.0517256 | ||||||||
\(895\) | 3.02132e7 | − | 5.23308e7i | 1.26078 | − | 2.18373i | ||||
\(896\) | −2.81673e6 | −0.117213 | ||||||||
\(897\) | −245887. | − | 425888.i | −0.0102036 | − | 0.0176732i | ||||
\(898\) | 6.25251e6 | 0.258740 | ||||||||
\(899\) | −1.90311e7 | −0.785354 | ||||||||
\(900\) | 6.58260e6 | + | 1.14014e7i | 0.270889 | + | 0.469194i | ||||
\(901\) | 1.18664e7 | − | 2.05532e7i | 0.486975 | − | 0.843465i | ||||
\(902\) | 3.20643e7 | 1.31221 | ||||||||
\(903\) | 1.77893e6 | + | 3.08119e6i | 0.0726004 | + | 0.125748i | ||||
\(904\) | 6.08038e6 | + | 1.05315e7i | 0.247463 | + | 0.428618i | ||||
\(905\) | −1.80862e7 | − | 3.13262e7i | −0.734050 | − | 1.27141i | ||||
\(906\) | 1.02284e6 | − | 1.77161e6i | 0.0413987 | − | 0.0717047i | ||||
\(907\) | 6.17443e6 | − | 1.06944e7i | 0.249218 | − | 0.431658i | −0.714091 | − | 0.700053i | \(-0.753160\pi\) |
0.963309 | + | 0.268395i | \(0.0864932\pi\) | |||||||
\(908\) | −448149. | − | 776216.i | −0.0180388 | − | 0.0312441i | ||||
\(909\) | −1.33714e7 | − | 2.31600e7i | −0.536745 | − | 0.929670i | ||||
\(910\) | 9.81142e6 | + | 1.69939e7i | 0.392761 | + | 0.680282i | ||||
\(911\) | −1.14971e7 | −0.458977 | −0.229488 | − | 0.973311i | \(-0.573705\pi\) | ||||
−0.229488 | + | 0.973311i | \(0.573705\pi\) | |||||||
\(912\) | −334881. | + | 580030.i | −0.0133322 | + | 0.0230921i | ||||
\(913\) | 1.29129e7 | + | 2.23658e7i | 0.512681 | + | 0.887989i | ||||
\(914\) | −9.78549e6 | −0.387451 | ||||||||
\(915\) | −1.35720e6 | −0.0535908 | ||||||||
\(916\) | 2.59740e6 | + | 4.49883e6i | 0.102282 | + | 0.177158i | ||||
\(917\) | −3.00636e6 | −0.118064 | ||||||||
\(918\) | 1.99695e6 | − | 3.45882e6i | 0.0782097 | − | 0.135463i | ||||
\(919\) | −3.35738e7 | −1.31133 | −0.655665 | − | 0.755052i | \(-0.727612\pi\) | ||||
−0.655665 | + | 0.755052i | \(0.727612\pi\) | |||||||
\(920\) | 3.11436e6 | − | 5.39423e6i | 0.121311 | − | 0.210116i | ||||
\(921\) | 1.55340e6 | − | 2.69057e6i | 0.0603441 | − | 0.104519i | ||||
\(922\) | −4.12246e6 | + | 7.14031e6i | −0.159709 | + | 0.276624i | ||||
\(923\) | −4.98302e6 | − | 8.63084e6i | −0.192525 | − | 0.333464i | ||||
\(924\) | 2.05559e6 | 0.0792056 | ||||||||
\(925\) | −2.59598e7 | + | 1.14014e7i | −0.997579 | + | 0.438130i | ||||
\(926\) | −2.90685e7 | −1.11402 | ||||||||
\(927\) | −8.28280e6 | − | 1.43462e7i | −0.316576 | − | 0.548326i | ||||
\(928\) | 3.65058e6 | − | 6.32299e6i | 0.139153 | − | 0.241020i | ||||
\(929\) | −2.24384e7 | + | 3.88644e7i | −0.853005 | + | 1.47745i | 0.0254782 | + | 0.999675i | \(0.491889\pi\) |
−0.878483 | + | 0.477773i | \(0.841444\pi\) | |||||||
\(930\) | 498801. | − | 863948.i | 0.0189112 | − | 0.0327552i | ||||
\(931\) | 2.88466e7 | 1.09074 | ||||||||
\(932\) | −6.42636e6 | + | 1.11308e7i | −0.242340 | + | 0.419746i | ||||
\(933\) | −1.11281e6 | −0.0418519 | ||||||||
\(934\) | −1.19783e7 | − | 2.07471e7i | −0.449293 | − | 0.778198i | ||||
\(935\) | 9.30451e7 | 3.48068 | ||||||||
\(936\) | −5.46154e6 | −0.203763 | ||||||||
\(937\) | 1.04005e7 | + | 1.80141e7i | 0.386994 | + | 0.670293i | 0.992044 | − | 0.125895i | \(-0.0401802\pi\) |
−0.605050 | + | 0.796187i | \(0.706847\pi\) | |||||||
\(938\) | 7.72394e6 | − | 1.33783e7i | 0.286637 | − | 0.496470i | ||||
\(939\) | −718214. | −0.0265822 | ||||||||
\(940\) | 1.13157e7 | + | 1.95994e7i | 0.417697 | + | 0.723473i | ||||
\(941\) | 1.12683e7 | + | 1.95173e7i | 0.414844 | + | 0.718530i | 0.995412 | − | 0.0956813i | \(-0.0305030\pi\) |
−0.580568 | + | 0.814211i | \(0.697170\pi\) | |||||||
\(942\) | 880493. | + | 1.52506e6i | 0.0323295 | + | 0.0559963i | ||||
\(943\) | −7.46932e6 | + | 1.29372e7i | −0.273528 | + | 0.473764i | ||||
\(944\) | −985185. | + | 1.70639e6i | −0.0359822 | + | 0.0623230i | ||||
\(945\) | −3.89278e6 | − | 6.74249e6i | −0.141801 | − | 0.245607i | ||||
\(946\) | −2.31333e7 | − | 4.00681e7i | −0.840446 | − | 1.45570i | ||||
\(947\) | 1.16609e7 | + | 2.01972e7i | 0.422529 | + | 0.731841i | 0.996186 | − | 0.0872544i | \(-0.0278093\pi\) |
−0.573658 | + | 0.819095i | \(0.694476\pi\) | |||||||
\(948\) | −1.64271e6 | −0.0593663 | ||||||||
\(949\) | 1.49377e6 | − | 2.58729e6i | 0.0538417 | − | 0.0932566i | ||||
\(950\) | 1.54076e7 | + | 2.66867e7i | 0.553893 | + | 0.959370i | ||||
\(951\) | −270896. | −0.00971296 | ||||||||
\(952\) | 1.96033e7 | 0.701031 | ||||||||
\(953\) | 1.08727e7 | + | 1.88320e7i | 0.387797 | + | 0.671683i | 0.992153 | − | 0.125031i | \(-0.0399030\pi\) |
−0.604356 | + | 0.796714i | \(0.706570\pi\) | |||||||
\(954\) | 1.28764e7 | 0.458061 | ||||||||
\(955\) | 2.51712e7 | − | 4.35978e7i | 0.893091 | − | 1.54688i | ||||
\(956\) | 1.84693e7 | 0.653591 | ||||||||
\(957\) | −2.66411e6 | + | 4.61438e6i | −0.0940314 | + | 0.162867i | ||||
\(958\) | 1.90811e7 | − | 3.30494e7i | 0.671721 | − | 1.16345i | ||||
\(959\) | −8.02325e6 | + | 1.38967e7i | −0.281711 | + | 0.487938i | ||||
\(960\) | 191361. | + | 331448.i | 0.00670157 | + | 0.0116075i | ||||
\(961\) | −2.15048e7 | −0.751151 | ||||||||
\(962\) | 1.28852e6 | − | 1.16914e7i | 0.0448904 | − | 0.407314i | ||||
\(963\) | −6.31434e6 | −0.219413 | ||||||||
\(964\) | −605840. | − | 1.04935e6i | −0.0209974 | − | 0.0363686i | ||||
\(965\) | 2.11659e7 | − | 3.66604e7i | 0.731674 | − | 1.26730i | ||||
\(966\) | −478846. | + | 829385.i | −0.0165102 | + | 0.0285965i | ||||
\(967\) | −4.04106e6 | + | 6.99933e6i | −0.138973 | + | 0.240708i | −0.927108 | − | 0.374794i | \(-0.877713\pi\) |
0.788135 | + | 0.615502i | \(0.211047\pi\) | |||||||
\(968\) | −1.64237e7 | −0.563357 | ||||||||
\(969\) | 2.33064e6 | − | 4.03678e6i | 0.0797379 | − | 0.138110i | ||||
\(970\) | −4.43918e7 | −1.51486 | ||||||||
\(971\) | −6.82405e6 | − | 1.18196e7i | −0.232271 | − | 0.402304i | 0.726205 | − | 0.687478i | \(-0.241282\pi\) |
−0.958476 | + | 0.285173i | \(0.907949\pi\) | |||||||
\(972\) | 3.25337e6 | 0.110451 | ||||||||
\(973\) | −1.28881e7 | −0.436424 | ||||||||
\(974\) | −4.89490e6 | − | 8.47821e6i | −0.165328 | − | 0.286356i | ||||
\(975\) | 695129. | − | 1.20400e6i | 0.0234182 | − | 0.0405616i | ||||
\(976\) | 3.71842e6 | 0.124949 | ||||||||
\(977\) | 6.06644e6 | + | 1.05074e7i | 0.203328 | + | 0.352175i | 0.949599 | − | 0.313468i | \(-0.101491\pi\) |
−0.746271 | + | 0.665643i | \(0.768158\pi\) | |||||||
\(978\) | 463186. | + | 802262.i | 0.0154849 | + | 0.0268206i | ||||
\(979\) | −4.24705e7 | − | 7.35610e7i | −1.41622 | − | 2.45296i | ||||
\(980\) | 8.24193e6 | − | 1.42754e7i | 0.274135 | − | 0.474815i | ||||
\(981\) | −2.47134e7 | + | 4.28048e7i | −0.819897 | + | 1.42010i | ||||
\(982\) | 1.78928e7 | + | 3.09912e7i | 0.592106 | + | 1.02556i | ||||
\(983\) | 2.06117e7 | + | 3.57004e7i | 0.680345 | + | 1.17839i | 0.974876 | + | 0.222750i | \(0.0715034\pi\) |
−0.294531 | + | 0.955642i | \(0.595163\pi\) | |||||||
\(984\) | −458951. | − | 794927.i | −0.0151105 | − | 0.0261722i | ||||
\(985\) | 7.29074e6 | 0.239431 | ||||||||
\(986\) | −2.54066e7 | + | 4.40055e7i | −0.832251 | + | 1.44150i | ||||
\(987\) | −1.73984e6 | − | 3.01348e6i | −0.0568480 | − | 0.0984637i | ||||
\(988\) | −1.27836e7 | −0.416639 | ||||||||
\(989\) | 2.15555e7 | 0.700755 | ||||||||
\(990\) | 2.52412e7 | + | 4.37190e7i | 0.818505 | + | 1.41769i | ||||
\(991\) | 1.11763e7 | 0.361504 | 0.180752 | − | 0.983529i | \(-0.442147\pi\) | ||||
0.180752 | + | 0.983529i | \(0.442147\pi\) | |||||||
\(992\) | −1.36660e6 | + | 2.36703e6i | −0.0440924 | + | 0.0763702i | ||||
\(993\) | −85596.5 | −0.00275475 | ||||||||
\(994\) | −9.70404e6 | + | 1.68079e7i | −0.311521 | + | 0.539569i | ||||
\(995\) | −6.81407e6 | + | 1.18023e7i | −0.218197 | + | 0.377929i | ||||
\(996\) | 369657. | − | 640265.i | 0.0118073 | − | 0.0204509i | ||||
\(997\) | 2.47017e7 | + | 4.27845e7i | 0.787024 | + | 1.36317i | 0.927782 | + | 0.373122i | \(0.121713\pi\) |
−0.140758 | + | 0.990044i | \(0.544954\pi\) | |||||||
\(998\) | 3.40210e6 | 0.108124 | ||||||||
\(999\) | −511234. | + | 4.63869e6i | −0.0162071 | + | 0.147056i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 74.6.c.b.63.5 | yes | 16 | |
37.10 | even | 3 | inner | 74.6.c.b.47.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.6.c.b.47.5 | ✓ | 16 | 37.10 | even | 3 | inner | |
74.6.c.b.63.5 | yes | 16 | 1.1 | even | 1 | trivial |