Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,6,Mod(11,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.11");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.e (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: | \(5.61343369345\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 110 x^{10} + 27 x^{9} + 9714 x^{8} - 3257 x^{7} + 240269 x^{6} - 608504 x^{5} + 5067668 x^{4} - 7120352 x^{3} + 9029136 x^{2} - 1794240 x + 313600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Root | \(2.06025 + 3.56846i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.11 |
Dual form | 35.6.e.a.16.2 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56025 | − | 2.70243i | −0.275816 | − | 0.477727i | 0.694525 | − | 0.719469i | \(-0.255615\pi\) |
−0.970341 | + | 0.241742i | \(0.922281\pi\) | |||||||
\(3\) | −13.9359 | + | 24.1376i | −0.893986 | + | 1.54843i | −0.0589307 | + | 0.998262i | \(0.518769\pi\) |
−0.835055 | + | 0.550166i | \(0.814564\pi\) | |||||||
\(4\) | 11.1312 | − | 19.2799i | 0.347851 | − | 0.602496i | ||||
\(5\) | 12.5000 | + | 21.6506i | 0.223607 | + | 0.387298i | ||||
\(6\) | 86.9736 | 0.986301 | ||||||||
\(7\) | −89.4698 | − | 93.8198i | −0.690131 | − | 0.723685i | ||||
\(8\) | −169.326 | −0.935403 | ||||||||
\(9\) | −266.916 | − | 462.312i | −1.09842 | − | 1.90252i | ||||
\(10\) | 39.0062 | − | 67.5608i | 0.123349 | − | 0.213646i | ||||
\(11\) | 202.629 | − | 350.963i | 0.504916 | − | 0.874541i | −0.495067 | − | 0.868855i | \(-0.664857\pi\) |
0.999984 | − | 0.00568632i | \(-0.00181002\pi\) | |||||||
\(12\) | 310.247 | + | 537.363i | 0.621948 | + | 1.07725i | ||||
\(13\) | −931.313 | −1.52840 | −0.764200 | − | 0.644979i | \(-0.776866\pi\) | ||||
−0.764200 | + | 0.644979i | \(0.776866\pi\) | |||||||
\(14\) | −113.946 | + | 388.168i | −0.155375 | + | 0.529298i | ||||
\(15\) | −696.793 | −0.799605 | ||||||||
\(16\) | −92.0091 | − | 159.364i | −0.0898526 | − | 0.155629i | ||||
\(17\) | 368.146 | − | 637.648i | 0.308957 | − | 0.535130i | −0.669177 | − | 0.743103i | \(-0.733353\pi\) |
0.978135 | + | 0.207973i | \(0.0666867\pi\) | |||||||
\(18\) | −832.912 | + | 1442.65i | −0.605923 | + | 1.04949i | ||||
\(19\) | 497.114 | + | 861.027i | 0.315917 | + | 0.547184i | 0.979632 | − | 0.200802i | \(-0.0643547\pi\) |
−0.663715 | + | 0.747985i | \(0.731021\pi\) | |||||||
\(20\) | 556.562 | 0.311128 | ||||||||
\(21\) | 3511.42 | − | 852.127i | 1.73754 | − | 0.421654i | ||||
\(22\) | −1264.61 | −0.557055 | ||||||||
\(23\) | −612.416 | − | 1060.74i | −0.241394 | − | 0.418107i | 0.719717 | − | 0.694267i | \(-0.244271\pi\) |
−0.961112 | + | 0.276160i | \(0.910938\pi\) | |||||||
\(24\) | 2359.70 | − | 4087.13i | 0.836237 | − | 1.44840i | ||||
\(25\) | −312.500 | + | 541.266i | −0.100000 | + | 0.173205i | ||||
\(26\) | 1453.08 | + | 2516.81i | 0.421557 | + | 0.730158i | ||||
\(27\) | 8106.00 | 2.13992 | ||||||||
\(28\) | −2804.75 | + | 680.635i | −0.676080 | + | 0.164066i | ||||
\(29\) | −5585.88 | −1.23338 | −0.616689 | − | 0.787207i | \(-0.711527\pi\) | ||||
−0.616689 | + | 0.787207i | \(0.711527\pi\) | |||||||
\(30\) | 1087.17 | + | 1883.03i | 0.220544 | + | 0.381993i | ||||
\(31\) | −1574.79 | + | 2727.61i | −0.294319 | + | 0.509775i | −0.974826 | − | 0.222966i | \(-0.928426\pi\) |
0.680507 | + | 0.732741i | \(0.261759\pi\) | |||||||
\(32\) | −2996.33 | + | 5189.80i | −0.517267 | + | 0.895933i | ||||
\(33\) | 5647.61 | + | 9781.95i | 0.902776 | + | 1.56365i | ||||
\(34\) | −2297.60 | −0.340861 | ||||||||
\(35\) | 912.887 | − | 3109.83i | 0.125964 | − | 0.429107i | ||||
\(36\) | −11884.4 | −1.52835 | ||||||||
\(37\) | 4806.89 | + | 8325.78i | 0.577245 | + | 0.999817i | 0.995794 | + | 0.0916228i | \(0.0292054\pi\) |
−0.418549 | + | 0.908194i | \(0.637461\pi\) | |||||||
\(38\) | 1551.24 | − | 2686.83i | 0.174269 | − | 0.301844i | ||||
\(39\) | 12978.6 | − | 22479.7i | 1.36637 | − | 2.36662i | ||||
\(40\) | −2116.58 | − | 3666.02i | −0.209162 | − | 0.362280i | ||||
\(41\) | −14680.2 | −1.36387 | −0.681933 | − | 0.731414i | \(-0.738861\pi\) | ||||
−0.681933 | + | 0.731414i | \(0.738861\pi\) | |||||||
\(42\) | −7781.51 | − | 8159.85i | −0.680677 | − | 0.713771i | ||||
\(43\) | 3526.05 | 0.290815 | 0.145408 | − | 0.989372i | \(-0.453551\pi\) | ||||
0.145408 | + | 0.989372i | \(0.453551\pi\) | |||||||
\(44\) | −4511.02 | − | 7813.32i | −0.351272 | − | 0.608421i | ||||
\(45\) | 6672.91 | − | 11557.8i | 0.491229 | − | 0.850833i | ||||
\(46\) | −1911.04 | + | 3310.03i | −0.133161 | + | 0.230641i | ||||
\(47\) | −9283.82 | − | 16080.1i | −0.613031 | − | 1.06180i | −0.990727 | − | 0.135870i | \(-0.956617\pi\) |
0.377696 | − | 0.925930i | \(-0.376716\pi\) | |||||||
\(48\) | 5128.90 | 0.321308 | ||||||||
\(49\) | −797.318 | + | 16788.1i | −0.0474396 | + | 0.998874i | ||||
\(50\) | 1950.31 | 0.110326 | ||||||||
\(51\) | 10260.9 | + | 17772.4i | 0.552407 | + | 0.956796i | ||||
\(52\) | −10366.7 | + | 17955.6i | −0.531656 | + | 0.920856i | ||||
\(53\) | 2728.99 | − | 4726.75i | 0.133448 | − | 0.231139i | −0.791555 | − | 0.611097i | \(-0.790728\pi\) |
0.925004 | + | 0.379958i | \(0.124062\pi\) | |||||||
\(54\) | −12647.4 | − | 21905.9i | −0.590223 | − | 1.02230i | ||||
\(55\) | 10131.4 | 0.451611 | ||||||||
\(56\) | 15149.6 | + | 15886.1i | 0.645550 | + | 0.676937i | ||||
\(57\) | −27710.9 | −1.12970 | ||||||||
\(58\) | 8715.36 | + | 15095.5i | 0.340185 | + | 0.589218i | ||||
\(59\) | 3883.98 | − | 6727.24i | 0.145260 | − | 0.251598i | −0.784210 | − | 0.620496i | \(-0.786931\pi\) |
0.929470 | + | 0.368898i | \(0.120265\pi\) | |||||||
\(60\) | −7756.17 | + | 13434.1i | −0.278144 | + | 0.481759i | ||||
\(61\) | −9437.36 | − | 16346.0i | −0.324733 | − | 0.562453i | 0.656726 | − | 0.754130i | \(-0.271941\pi\) |
−0.981458 | + | 0.191676i | \(0.938608\pi\) | |||||||
\(62\) | 9828.25 | 0.324711 | ||||||||
\(63\) | −19493.1 | + | 66405.0i | −0.618772 | + | 2.10790i | ||||
\(64\) | 12811.5 | 0.390976 | ||||||||
\(65\) | −11641.4 | − | 20163.5i | −0.341761 | − | 0.591947i | ||||
\(66\) | 17623.4 | − | 30524.6i | 0.498000 | − | 0.862561i | ||||
\(67\) | 33352.2 | − | 57767.7i | 0.907691 | − | 1.57217i | 0.0904261 | − | 0.995903i | \(-0.471177\pi\) |
0.817264 | − | 0.576263i | \(-0.195490\pi\) | |||||||
\(68\) | −8195.86 | − | 14195.6i | −0.214942 | − | 0.372291i | ||||
\(69\) | 34138.2 | 0.863212 | ||||||||
\(70\) | −9828.42 | + | 2385.09i | −0.239739 | + | 0.0581781i | ||||
\(71\) | 30994.2 | 0.729683 | 0.364842 | − | 0.931070i | \(-0.381123\pi\) | ||||
0.364842 | + | 0.931070i | \(0.381123\pi\) | |||||||
\(72\) | 45195.9 | + | 78281.5i | 1.02747 | + | 1.77962i | ||||
\(73\) | −18657.3 | + | 32315.3i | −0.409771 | + | 0.709743i | −0.994864 | − | 0.101223i | \(-0.967725\pi\) |
0.585093 | + | 0.810966i | \(0.301058\pi\) | |||||||
\(74\) | 14999.9 | − | 25980.6i | 0.318426 | − | 0.551530i | ||||
\(75\) | −8709.91 | − | 15086.0i | −0.178797 | − | 0.309686i | ||||
\(76\) | 22134.0 | 0.439568 | ||||||||
\(77\) | −51056.5 | + | 12390.0i | −0.981350 | + | 0.238147i | ||||
\(78\) | −80999.7 | −1.50746 | ||||||||
\(79\) | 7830.73 | + | 13563.2i | 0.141167 | + | 0.244509i | 0.927937 | − | 0.372738i | \(-0.121581\pi\) |
−0.786769 | + | 0.617247i | \(0.788248\pi\) | |||||||
\(80\) | 2300.23 | − | 3984.11i | 0.0401833 | − | 0.0695995i | ||||
\(81\) | −48103.4 | + | 83317.5i | −0.814635 | + | 1.41099i | ||||
\(82\) | 22904.7 | + | 39672.2i | 0.376176 | + | 0.651556i | ||||
\(83\) | 70001.9 | 1.11536 | 0.557679 | − | 0.830057i | \(-0.311692\pi\) | ||||
0.557679 | + | 0.830057i | \(0.311692\pi\) | |||||||
\(84\) | 22657.6 | − | 77185.1i | 0.350361 | − | 1.19354i | ||||
\(85\) | 18407.3 | 0.276340 | ||||||||
\(86\) | −5501.52 | − | 9528.90i | −0.0802114 | − | 0.138930i | ||||
\(87\) | 77844.0 | − | 134830.i | 1.10262 | − | 1.90980i | ||||
\(88\) | −34310.3 | + | 59427.2i | −0.472300 | + | 0.818048i | ||||
\(89\) | 3952.08 | + | 6845.21i | 0.0528873 | + | 0.0916034i | 0.891257 | − | 0.453499i | \(-0.149824\pi\) |
−0.838370 | + | 0.545102i | \(0.816491\pi\) | |||||||
\(90\) | −41645.6 | −0.541954 | ||||||||
\(91\) | 83324.4 | + | 87375.6i | 1.05480 | + | 1.10608i | ||||
\(92\) | −27267.8 | −0.335877 | ||||||||
\(93\) | −43892.0 | − | 76023.3i | −0.526233 | − | 0.911463i | ||||
\(94\) | −28970.2 | + | 50177.8i | −0.338167 | + | 0.585722i | ||||
\(95\) | −12427.9 | + | 21525.7i | −0.141282 | + | 0.244708i | ||||
\(96\) | −83512.9 | − | 144649.i | −0.924858 | − | 1.60190i | ||||
\(97\) | −149459. | −1.61284 | −0.806420 | − | 0.591343i | \(-0.798598\pi\) | ||||
−0.806420 | + | 0.591343i | \(0.798598\pi\) | |||||||
\(98\) | 46612.6 | − | 24038.9i | 0.490274 | − | 0.252842i | ||||
\(99\) | −216340. | −2.21844 | ||||||||
\(100\) | 6957.03 | + | 12049.9i | 0.0695703 | + | 0.120499i | ||||
\(101\) | 63466.3 | − | 109927.i | 0.619070 | − | 1.07226i | −0.370586 | − | 0.928798i | \(-0.620843\pi\) |
0.989656 | − | 0.143462i | \(-0.0458235\pi\) | |||||||
\(102\) | 32019.0 | − | 55458.6i | 0.304725 | − | 0.527799i | ||||
\(103\) | −6750.25 | − | 11691.8i | −0.0626941 | − | 0.108589i | 0.832975 | − | 0.553311i | \(-0.186636\pi\) |
−0.895669 | + | 0.444722i | \(0.853303\pi\) | |||||||
\(104\) | 157696. | 1.42967 | ||||||||
\(105\) | 62341.9 | + | 65373.0i | 0.551832 | + | 0.578662i | ||||
\(106\) | −17031.6 | −0.147228 | ||||||||
\(107\) | −37215.8 | − | 64459.6i | −0.314245 | − | 0.544287i | 0.665032 | − | 0.746815i | \(-0.268418\pi\) |
−0.979277 | + | 0.202527i | \(0.935085\pi\) | |||||||
\(108\) | 90229.9 | − | 156283.i | 0.744373 | − | 1.28929i | ||||
\(109\) | −68840.7 | + | 119236.i | −0.554982 | + | 0.961257i | 0.442923 | + | 0.896560i | \(0.353942\pi\) |
−0.997905 | + | 0.0646973i | \(0.979392\pi\) | |||||||
\(110\) | −15807.6 | − | 27379.5i | −0.124561 | − | 0.215747i | ||||
\(111\) | −267953. | −2.06419 | ||||||||
\(112\) | −6719.51 | + | 22890.6i | −0.0506165 | + | 0.172429i | ||||
\(113\) | 62258.8 | 0.458674 | 0.229337 | − | 0.973347i | \(-0.426344\pi\) | ||||
0.229337 | + | 0.973347i | \(0.426344\pi\) | |||||||
\(114\) | 43235.9 | + | 74886.7i | 0.311589 | + | 0.539688i | ||||
\(115\) | 15310.4 | − | 26518.4i | 0.107955 | − | 0.186983i | ||||
\(116\) | −62177.8 | + | 107695.i | −0.429033 | + | 0.743106i | ||||
\(117\) | 248583. | + | 430558.i | 1.67883 | + | 2.90781i | ||||
\(118\) | −24239.9 | −0.160260 | ||||||||
\(119\) | −92762.0 | + | 22510.8i | −0.600486 | + | 0.145722i | ||||
\(120\) | 117985. | 0.747953 | ||||||||
\(121\) | −1591.37 | − | 2756.34i | −0.00988117 | − | 0.0171147i | ||||
\(122\) | −29449.3 | + | 51007.6i | −0.179133 | + | 0.310267i | ||||
\(123\) | 204581. | − | 354345.i | 1.21928 | − | 2.11185i | ||||
\(124\) | 35058.7 | + | 60723.5i | 0.204758 | + | 0.354652i | ||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 209869. | − | 50929.5i | 1.17767 | − | 0.285788i | ||||
\(127\) | −264361. | −1.45442 | −0.727208 | − | 0.686417i | \(-0.759183\pi\) | ||||
−0.727208 | + | 0.686417i | \(0.759183\pi\) | |||||||
\(128\) | 75893.4 | + | 131451.i | 0.409430 | + | 0.709153i | ||||
\(129\) | −49138.5 | + | 85110.4i | −0.259985 | + | 0.450307i | ||||
\(130\) | −36327.0 | + | 62920.2i | −0.188526 | + | 0.326537i | ||||
\(131\) | −54997.2 | − | 95258.0i | −0.280003 | − | 0.484979i | 0.691382 | − | 0.722489i | \(-0.257002\pi\) |
−0.971385 | + | 0.237510i | \(0.923669\pi\) | |||||||
\(132\) | 251460. | 1.25613 | ||||||||
\(133\) | 36304.7 | − | 123675.i | 0.177965 | − | 0.606252i | ||||
\(134\) | −208151. | −1.00142 | ||||||||
\(135\) | 101325. | + | 175500.i | 0.478500 | + | 0.828787i | ||||
\(136\) | −62336.8 | + | 107970.i | −0.288999 | + | 0.500562i | ||||
\(137\) | 140940. | − | 244115.i | 0.641552 | − | 1.11120i | −0.343535 | − | 0.939140i | \(-0.611624\pi\) |
0.985086 | − | 0.172060i | \(-0.0550424\pi\) | |||||||
\(138\) | −53264.1 | − | 92256.1i | −0.238088 | − | 0.412380i | ||||
\(139\) | 236209. | 1.03696 | 0.518478 | − | 0.855091i | \(-0.326499\pi\) | ||||
0.518478 | + | 0.855091i | \(0.326499\pi\) | |||||||
\(140\) | −49795.5 | − | 52216.6i | −0.214719 | − | 0.225158i | ||||
\(141\) | 517512. | 2.19216 | ||||||||
\(142\) | −48358.6 | − | 83759.6i | −0.201258 | − | 0.348589i | ||||
\(143\) | −188711. | + | 326857.i | −0.771715 | + | 1.33665i | ||||
\(144\) | −49117.4 | + | 85073.9i | −0.197392 | + | 0.341893i | ||||
\(145\) | −69823.5 | − | 120938.i | −0.275792 | − | 0.477686i | ||||
\(146\) | 116440. | 0.452085 | ||||||||
\(147\) | −394113. | − | 253202.i | −1.50427 | − | 0.966436i | ||||
\(148\) | 214027. | 0.803181 | ||||||||
\(149\) | 12819.9 | + | 22204.8i | 0.0473064 | + | 0.0819371i | 0.888709 | − | 0.458472i | \(-0.151603\pi\) |
−0.841403 | + | 0.540409i | \(0.818270\pi\) | |||||||
\(150\) | −27179.3 | + | 47075.9i | −0.0986301 | + | 0.170832i | ||||
\(151\) | −131289. | + | 227399.i | −0.468581 | + | 0.811606i | −0.999355 | − | 0.0359071i | \(-0.988568\pi\) |
0.530774 | + | 0.847513i | \(0.321901\pi\) | |||||||
\(152\) | −84174.4 | − | 145794.i | −0.295509 | − | 0.511837i | ||||
\(153\) | −393057. | −1.35746 | ||||||||
\(154\) | 113144. | + | 118645.i | 0.384441 | + | 0.403133i | ||||
\(155\) | −78739.4 | −0.263247 | ||||||||
\(156\) | −288937. | − | 500453.i | −0.950586 | − | 1.64646i | ||||
\(157\) | −131131. | + | 227126.i | −0.424578 | + | 0.735391i | −0.996381 | − | 0.0849999i | \(-0.972911\pi\) |
0.571803 | + | 0.820391i | \(0.306244\pi\) | |||||||
\(158\) | 24435.8 | − | 42324.0i | 0.0778724 | − | 0.134879i | ||||
\(159\) | 76061.7 | + | 131743.i | 0.238602 | + | 0.413270i | ||||
\(160\) | −149817. | −0.462658 | ||||||||
\(161\) | −44725.3 | + | 152361.i | −0.135984 | + | 0.463242i | ||||
\(162\) | 300213. | 0.898757 | ||||||||
\(163\) | −142691. | − | 247148.i | −0.420656 | − | 0.728598i | 0.575348 | − | 0.817909i | \(-0.304867\pi\) |
−0.996004 | + | 0.0893112i | \(0.971533\pi\) | |||||||
\(164\) | −163409. | + | 283032.i | −0.474423 | + | 0.821725i | ||||
\(165\) | −141190. | + | 244549.i | −0.403734 | + | 0.699287i | ||||
\(166\) | −109220. | − | 189175.i | −0.307633 | − | 0.532837i | ||||
\(167\) | 467133. | 1.29613 | 0.648067 | − | 0.761583i | \(-0.275578\pi\) | ||||
0.648067 | + | 0.761583i | \(0.275578\pi\) | |||||||
\(168\) | −594576. | + | 144287.i | −1.62530 | + | 0.394416i | ||||
\(169\) | 496051. | 1.33601 | ||||||||
\(170\) | −28720.0 | − | 49744.5i | −0.0762188 | − | 0.132015i | ||||
\(171\) | 265376. | − | 459644.i | 0.694019 | − | 1.20208i | ||||
\(172\) | 39249.3 | − | 67981.8i | 0.101161 | − | 0.175215i | ||||
\(173\) | 15082.1 | + | 26123.0i | 0.0383132 | + | 0.0663603i | 0.884546 | − | 0.466453i | \(-0.154468\pi\) |
−0.846233 | + | 0.532813i | \(0.821135\pi\) | |||||||
\(174\) | −485824. | −1.21648 | ||||||||
\(175\) | 78740.8 | − | 19108.2i | 0.194359 | − | 0.0471656i | ||||
\(176\) | −74574.8 | −0.181472 | ||||||||
\(177\) | 108253. | + | 187500.i | 0.259721 | + | 0.449850i | ||||
\(178\) | 12332.5 | − | 21360.5i | 0.0291743 | − | 0.0505313i | ||||
\(179\) | 297188. | − | 514745.i | 0.693265 | − | 1.20077i | −0.277497 | − | 0.960727i | \(-0.589505\pi\) |
0.970762 | − | 0.240044i | \(-0.0771618\pi\) | |||||||
\(180\) | −148555. | − | 257306.i | −0.341749 | − | 0.591927i | ||||
\(181\) | 155232. | 0.352197 | 0.176099 | − | 0.984373i | \(-0.443652\pi\) | ||||
0.176099 | + | 0.984373i | \(0.443652\pi\) | |||||||
\(182\) | 106120. | − | 361506.i | 0.237475 | − | 0.808979i | ||||
\(183\) | 526071. | 1.16123 | ||||||||
\(184\) | 103698. | + | 179610.i | 0.225801 | + | 0.391099i | ||||
\(185\) | −120172. | + | 208144.i | −0.258152 | + | 0.447132i | ||||
\(186\) | −136965. | + | 237230.i | −0.290287 | + | 0.502792i | ||||
\(187\) | −149194. | − | 258412.i | −0.311995 | − | 0.540391i | ||||
\(188\) | −413362. | −0.852974 | ||||||||
\(189\) | −725242. | − | 760503.i | −1.47682 | − | 1.54863i | ||||
\(190\) | 77562.2 | 0.155871 | ||||||||
\(191\) | −160480. | − | 277960.i | −0.318302 | − | 0.551314i | 0.661832 | − | 0.749652i | \(-0.269779\pi\) |
−0.980134 | + | 0.198338i | \(0.936446\pi\) | |||||||
\(192\) | −178539. | + | 309239.i | −0.349527 | + | 0.605399i | ||||
\(193\) | 363618. | − | 629804.i | 0.702670 | − | 1.21706i | −0.264855 | − | 0.964288i | \(-0.585324\pi\) |
0.967526 | − | 0.252773i | \(-0.0813424\pi\) | |||||||
\(194\) | 233193. | + | 403901.i | 0.444847 | + | 0.770497i | ||||
\(195\) | 648932. | 1.22212 | ||||||||
\(196\) | 314797. | + | 202244.i | 0.585316 | + | 0.376042i | ||||
\(197\) | −752919. | −1.38224 | −0.691119 | − | 0.722741i | \(-0.742882\pi\) | ||||
−0.691119 | + | 0.722741i | \(0.742882\pi\) | |||||||
\(198\) | 337544. | + | 584643.i | 0.611881 | + | 1.05981i | ||||
\(199\) | −48317.7 | + | 83688.7i | −0.0864915 | + | 0.149808i | −0.906026 | − | 0.423222i | \(-0.860899\pi\) |
0.819534 | + | 0.573030i | \(0.194232\pi\) | |||||||
\(200\) | 52914.4 | − | 91650.4i | 0.0935403 | − | 0.162017i | ||||
\(201\) | 929584. | + | 1.61009e6i | 1.62292 | + | 2.81099i | ||||
\(202\) | −396093. | −0.682996 | ||||||||
\(203\) | 499767. | + | 524066.i | 0.851193 | + | 0.892578i | ||||
\(204\) | 456865. | 0.768622 | ||||||||
\(205\) | −183502. | − | 317835.i | −0.304970 | − | 0.528223i | ||||
\(206\) | −21064.2 | + | 36484.2i | −0.0345841 | + | 0.0599013i | ||||
\(207\) | −326928. | + | 566255.i | −0.530305 | + | 0.918515i | ||||
\(208\) | 85689.2 | + | 148418.i | 0.137331 | + | 0.237864i | ||||
\(209\) | 402919. | 0.638046 | ||||||||
\(210\) | 79397.1 | − | 270473.i | 0.124239 | − | 0.423229i | ||||
\(211\) | −373868. | −0.578112 | −0.289056 | − | 0.957312i | \(-0.593341\pi\) | ||||
−0.289056 | + | 0.957312i | \(0.593341\pi\) | |||||||
\(212\) | −60754.2 | − | 105229.i | −0.0928403 | − | 0.160804i | ||||
\(213\) | −431930. | + | 748126.i | −0.652326 | + | 1.12986i | ||||
\(214\) | −116132. | + | 201146.i | −0.173347 | + | 0.300246i | ||||
\(215\) | 44075.6 | + | 76341.2i | 0.0650283 | + | 0.112632i | ||||
\(216\) | −1.37256e6 | −2.00169 | ||||||||
\(217\) | 396800. | − | 96292.6i | 0.572035 | − | 0.138817i | ||||
\(218\) | 429634. | 0.612291 | ||||||||
\(219\) | −520010. | − | 900684.i | −0.732658 | − | 1.26900i | ||||
\(220\) | 112776. | − | 195333.i | 0.157094 | − | 0.272094i | ||||
\(221\) | −342860. | + | 593850.i | −0.472210 | + | 0.817892i | ||||
\(222\) | 418073. | + | 724123.i | 0.569337 | + | 0.986121i | ||||
\(223\) | 545786. | 0.734954 | 0.367477 | − | 0.930033i | \(-0.380222\pi\) | ||||
0.367477 | + | 0.930033i | \(0.380222\pi\) | |||||||
\(224\) | 754987. | − | 183215.i | 1.00535 | − | 0.243972i | ||||
\(225\) | 333645. | 0.439368 | ||||||||
\(226\) | −97139.2 | − | 168250.i | −0.126510 | − | 0.219121i | ||||
\(227\) | 61638.3 | − | 106761.i | 0.0793937 | − | 0.137514i | −0.823595 | − | 0.567179i | \(-0.808035\pi\) |
0.902989 | + | 0.429665i | \(0.141368\pi\) | |||||||
\(228\) | −308456. | + | 534262.i | −0.392968 | + | 0.680640i | ||||
\(229\) | −539166. | − | 933862.i | −0.679412 | − | 1.17678i | −0.975158 | − | 0.221510i | \(-0.928901\pi\) |
0.295746 | − | 0.955267i | \(-0.404432\pi\) | |||||||
\(230\) | −95552.2 | −0.119103 | ||||||||
\(231\) | 412450. | − | 1.40505e6i | 0.508559 | − | 1.73245i | ||||
\(232\) | 945835. | 1.15371 | ||||||||
\(233\) | −70604.2 | − | 122290.i | −0.0852002 | − | 0.147571i | 0.820276 | − | 0.571967i | \(-0.193820\pi\) |
−0.905476 | + | 0.424396i | \(0.860486\pi\) | |||||||
\(234\) | 775701. | − | 1.34355e6i | 0.926094 | − | 1.60404i | ||||
\(235\) | 232096. | − | 402001.i | 0.274156 | − | 0.474851i | ||||
\(236\) | −86467.0 | − | 149765.i | −0.101058 | − | 0.175037i | ||||
\(237\) | −436512. | −0.504807 | ||||||||
\(238\) | 205566. | + | 215560.i | 0.235239 | + | 0.246676i | ||||
\(239\) | −508655. | −0.576008 | −0.288004 | − | 0.957629i | \(-0.592992\pi\) | ||||
−0.288004 | + | 0.957629i | \(0.592992\pi\) | |||||||
\(240\) | 64111.3 | + | 111044.i | 0.0718466 | + | 0.124442i | ||||
\(241\) | 12848.0 | − | 22253.5i | 0.0142493 | − | 0.0246806i | −0.858813 | − | 0.512290i | \(-0.828797\pi\) |
0.873062 | + | 0.487609i | \(0.162131\pi\) | |||||||
\(242\) | −4965.87 | + | 8601.15i | −0.00545076 | + | 0.00944100i | ||||
\(243\) | −355845. | − | 616342.i | −0.386586 | − | 0.669586i | ||||
\(244\) | −420198. | −0.451835 | ||||||||
\(245\) | −373439. | + | 192589.i | −0.397470 | + | 0.204982i | ||||
\(246\) | −1.27679e6 | −1.34518 | ||||||||
\(247\) | −462969. | − | 801886.i | −0.482847 | − | 0.836316i | ||||
\(248\) | 266653. | − | 461856.i | 0.275307 | − | 0.476845i | ||||
\(249\) | −975536. | + | 1.68968e6i | −0.997114 | + | 1.72705i | ||||
\(250\) | 24378.9 | + | 42225.5i | 0.0246697 | + | 0.0427292i | ||||
\(251\) | −30939.4 | −0.0309975 | −0.0154988 | − | 0.999880i | \(-0.504934\pi\) | ||||
−0.0154988 | + | 0.999880i | \(0.504934\pi\) | |||||||
\(252\) | 1.06330e6 | + | 1.11500e6i | 1.05476 | + | 1.10604i | ||||
\(253\) | −496373. | −0.487536 | ||||||||
\(254\) | 412470. | + | 714419.i | 0.401151 | + | 0.694814i | ||||
\(255\) | −256522. | + | 444309.i | −0.247044 | + | 0.427892i | ||||
\(256\) | 441809. | − | 765236.i | 0.421342 | − | 0.729786i | ||||
\(257\) | −128055. | − | 221797.i | −0.120938 | − | 0.209471i | 0.799200 | − | 0.601065i | \(-0.205257\pi\) |
−0.920138 | + | 0.391595i | \(0.871924\pi\) | |||||||
\(258\) | 306673. | 0.286831 | ||||||||
\(259\) | 351052. | − | 1.19589e6i | 0.325178 | − | 1.10775i | ||||
\(260\) | −518334. | −0.475528 | ||||||||
\(261\) | 1.49096e6 | + | 2.58242e6i | 1.35477 | + | 2.34653i | ||||
\(262\) | −171619. | + | 297252.i | −0.154458 | + | 0.267530i | ||||
\(263\) | −510371. | + | 883989.i | −0.454985 | + | 0.788056i | −0.998687 | − | 0.0512214i | \(-0.983689\pi\) |
0.543703 | + | 0.839278i | \(0.317022\pi\) | |||||||
\(264\) | −956288. | − | 1.65634e6i | −0.844459 | − | 1.46265i | ||||
\(265\) | 136450. | 0.119360 | ||||||||
\(266\) | −390868. | + | 94853.0i | −0.338708 | + | 0.0821953i | ||||
\(267\) | −220303. | −0.189122 | ||||||||
\(268\) | −742504. | − | 1.28605e6i | −0.631483 | − | 1.09376i | ||||
\(269\) | 246883. | − | 427613.i | 0.208022 | − | 0.360305i | −0.743069 | − | 0.669215i | \(-0.766631\pi\) |
0.951091 | + | 0.308909i | \(0.0999640\pi\) | |||||||
\(270\) | 316184. | − | 547648.i | 0.263956 | − | 0.457185i | ||||
\(271\) | 737896. | + | 1.27807e6i | 0.610340 | + | 1.05714i | 0.991183 | + | 0.132500i | \(0.0423004\pi\) |
−0.380843 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(272\) | −135491. | −0.111042 | ||||||||
\(273\) | −3.27024e6 | + | 793597.i | −2.65566 | + | 0.644456i | ||||
\(274\) | −879604. | −0.707800 | ||||||||
\(275\) | 126643. | + | 219352.i | 0.100983 | + | 0.174908i | ||||
\(276\) | 380000. | − | 658180.i | 0.300270 | − | 0.520082i | ||||
\(277\) | 438956. | − | 760293.i | 0.343733 | − | 0.595363i | −0.641390 | − | 0.767215i | \(-0.721642\pi\) |
0.985123 | + | 0.171852i | \(0.0549752\pi\) | |||||||
\(278\) | −368546. | − | 638340.i | −0.286009 | − | 0.495382i | ||||
\(279\) | 1.68135e6 | 1.29314 | ||||||||
\(280\) | −154575. | + | 526574.i | −0.117827 | + | 0.401388i | ||||
\(281\) | −1.46598e6 | −1.10755 | −0.553774 | − | 0.832667i | \(-0.686813\pi\) | ||||
−0.553774 | + | 0.832667i | \(0.686813\pi\) | |||||||
\(282\) | −807448. | − | 1.39854e6i | −0.604633 | − | 1.04725i | ||||
\(283\) | −865539. | + | 1.49916e6i | −0.642422 | + | 1.11271i | 0.342468 | + | 0.939530i | \(0.388737\pi\) |
−0.984890 | + | 0.173179i | \(0.944596\pi\) | |||||||
\(284\) | 345004. | − | 597564.i | 0.253821 | − | 0.439631i | ||||
\(285\) | −346386. | − | 599958.i | −0.252608 | − | 0.437531i | ||||
\(286\) | 1.17774e6 | 0.851404 | ||||||||
\(287\) | 1.31343e6 | + | 1.37729e6i | 0.941246 | + | 0.987010i | ||||
\(288\) | 3.19908e6 | 2.27271 | ||||||||
\(289\) | 438865. | + | 760136.i | 0.309091 | + | 0.535361i | ||||
\(290\) | −217884. | + | 377386.i | −0.152135 | + | 0.263506i | ||||
\(291\) | 2.08283e6 | − | 3.60757e6i | 1.44186 | − | 2.49737i | ||||
\(292\) | 415357. | + | 719420.i | 0.285079 | + | 0.493771i | ||||
\(293\) | −623726. | −0.424449 | −0.212224 | − | 0.977221i | \(-0.568071\pi\) | ||||
−0.212224 | + | 0.977221i | \(0.568071\pi\) | |||||||
\(294\) | −69345.7 | + | 1.46012e6i | −0.0467898 | + | 0.985191i | ||||
\(295\) | 194199. | 0.129925 | ||||||||
\(296\) | −813931. | − | 1.40977e6i | −0.539956 | − | 0.935232i | ||||
\(297\) | 1.64251e6 | − | 2.84491e6i | 1.08048 | − | 1.87145i | ||||
\(298\) | 40004.6 | − | 69289.9i | 0.0260957 | − | 0.0451991i | ||||
\(299\) | 570351. | + | 987877.i | 0.368947 | + | 0.639036i | ||||
\(300\) | −387809. | −0.248779 | ||||||||
\(301\) | −315475. | − | 330813.i | −0.200701 | − | 0.210459i | ||||
\(302\) | 819372. | 0.516968 | ||||||||
\(303\) | 1.76891e6 | + | 3.06385e6i | 1.10688 | + | 1.91717i | ||||
\(304\) | 91478.1 | − | 158445.i | 0.0567718 | − | 0.0983317i | ||||
\(305\) | 235934. | − | 408650.i | 0.145225 | − | 0.251537i | ||||
\(306\) | 613267. | + | 1.06221e6i | 0.374409 | + | 0.648495i | ||||
\(307\) | −1.92297e6 | −1.16446 | −0.582232 | − | 0.813022i | \(-0.697821\pi\) | ||||
−0.582232 | + | 0.813022i | \(0.697821\pi\) | |||||||
\(308\) | −329444. | + | 1.12228e6i | −0.197881 | + | 0.674100i | ||||
\(309\) | 376282. | 0.224191 | ||||||||
\(310\) | 122853. | + | 212788.i | 0.0726076 | + | 0.125760i | ||||
\(311\) | −1.05152e6 | + | 1.82129e6i | −0.616478 | + | 1.06777i | 0.373645 | + | 0.927572i | \(0.378108\pi\) |
−0.990123 | + | 0.140200i | \(0.955226\pi\) | |||||||
\(312\) | −2.19762e6 | + | 3.80639e6i | −1.27810 | + | 2.21374i | ||||
\(313\) | −1.37176e6 | − | 2.37595e6i | −0.791437 | − | 1.37081i | −0.925077 | − | 0.379779i | \(-0.876000\pi\) |
0.133640 | − | 0.991030i | \(-0.457333\pi\) | |||||||
\(314\) | 818391. | 0.468422 | ||||||||
\(315\) | −1.68138e6 | + | 408024.i | −0.954747 | + | 0.231691i | ||||
\(316\) | 348663. | 0.196421 | ||||||||
\(317\) | 756053. | + | 1.30952e6i | 0.422575 | + | 0.731922i | 0.996191 | − | 0.0872031i | \(-0.0277929\pi\) |
−0.573615 | + | 0.819125i | \(0.694460\pi\) | |||||||
\(318\) | 237350. | − | 411103.i | 0.131620 | − | 0.227973i | ||||
\(319\) | −1.13186e6 | + | 1.96044e6i | −0.622753 | + | 1.07864i | ||||
\(320\) | 160144. | + | 277377.i | 0.0874249 | + | 0.151424i | ||||
\(321\) | 2.07454e6 | 1.12372 | ||||||||
\(322\) | 481527. | − | 116853.i | 0.258810 | − | 0.0628061i | ||||
\(323\) | 732044. | 0.390419 | ||||||||
\(324\) | 1.07090e6 | + | 1.85486e6i | 0.566744 | + | 0.981630i | ||||
\(325\) | 291035. | − | 504088.i | 0.152840 | − | 0.264727i | ||||
\(326\) | −445267. | + | 771225.i | −0.232047 | + | 0.401917i | ||||
\(327\) | −1.91871e6 | − | 3.32330e6i | −0.992292 | − | 1.71870i | ||||
\(328\) | 2.48574e6 | 1.27576 | ||||||||
\(329\) | −678006. | + | 2.30969e6i | −0.345338 | + | 1.17642i | ||||
\(330\) | 881168. | 0.445424 | ||||||||
\(331\) | −391389. | − | 677905.i | −0.196353 | − | 0.340094i | 0.750990 | − | 0.660314i | \(-0.229577\pi\) |
−0.947343 | + | 0.320220i | \(0.896243\pi\) | |||||||
\(332\) | 779208. | − | 1.34963e6i | 0.387979 | − | 0.671999i | ||||
\(333\) | 2.56607e6 | − | 4.44457e6i | 1.26811 | − | 2.19644i | ||||
\(334\) | −728845. | − | 1.26240e6i | −0.357494 | − | 0.619198i | ||||
\(335\) | 1.66761e6 | 0.811863 | ||||||||
\(336\) | −458882. | − | 481193.i | −0.221744 | − | 0.232526i | ||||
\(337\) | −2.98847e6 | −1.43342 | −0.716711 | − | 0.697370i | \(-0.754354\pi\) | ||||
−0.716711 | + | 0.697370i | \(0.754354\pi\) | |||||||
\(338\) | −773963. | − | 1.34054e6i | −0.368492 | − | 0.638247i | ||||
\(339\) | −867630. | + | 1.50278e6i | −0.410048 | + | 0.710225i | ||||
\(340\) | 204896. | − | 354891.i | 0.0961252 | − | 0.166494i | ||||
\(341\) | 638195. | + | 1.10539e6i | 0.297213 | + | 0.514788i | ||||
\(342\) | −1.65621e6 | −0.765685 | ||||||||
\(343\) | 1.64639e6 | − | 1.42722e6i | 0.755610 | − | 0.655022i | ||||
\(344\) | −597052. | −0.272029 | ||||||||
\(345\) | 426727. | + | 739113.i | 0.193020 | + | 0.334321i | ||||
\(346\) | 47063.8 | − | 81516.9i | 0.0211347 | − | 0.0366064i | ||||
\(347\) | 307031. | − | 531794.i | 0.136886 | − | 0.237094i | −0.789430 | − | 0.613840i | \(-0.789624\pi\) |
0.926316 | + | 0.376747i | \(0.122957\pi\) | |||||||
\(348\) | −1.73300e6 | − | 3.00165e6i | −0.767098 | − | 1.32865i | ||||
\(349\) | −3.34125e6 | −1.46841 | −0.734203 | − | 0.678930i | \(-0.762444\pi\) | ||||
−0.734203 | + | 0.678930i | \(0.762444\pi\) | |||||||
\(350\) | −174494. | − | 182978.i | −0.0761395 | − | 0.0798415i | ||||
\(351\) | −7.54922e6 | −3.27065 | ||||||||
\(352\) | 1.21429e6 | + | 2.10320e6i | 0.522353 | + | 0.904742i | ||||
\(353\) | 1.81062e6 | − | 3.13608e6i | 0.773374 | − | 1.33952i | −0.162329 | − | 0.986737i | \(-0.551901\pi\) |
0.935704 | − | 0.352787i | \(-0.114766\pi\) | |||||||
\(354\) | 337804. | − | 585093.i | 0.143270 | − | 0.248151i | ||||
\(355\) | 387427. | + | 671044.i | 0.163162 | + | 0.282605i | ||||
\(356\) | 175966. | 0.0735876 | ||||||||
\(357\) | 749361. | − | 2.55276e6i | 0.311186 | − | 1.06008i | ||||
\(358\) | −1.85475e6 | −0.764854 | ||||||||
\(359\) | −1.79122e6 | − | 3.10248e6i | −0.733522 | − | 1.27050i | −0.955369 | − | 0.295415i | \(-0.904542\pi\) |
0.221847 | − | 0.975081i | \(-0.428791\pi\) | |||||||
\(360\) | −1.12990e6 | + | 1.95704e6i | −0.459497 | + | 0.795872i | ||||
\(361\) | 743804. | − | 1.28831e6i | 0.300393 | − | 0.520297i | ||||
\(362\) | −242201. | − | 419505.i | −0.0971415 | − | 0.168254i | ||||
\(363\) | 88708.6 | 0.0353345 | ||||||||
\(364\) | 2.61210e6 | − | 633884.i | 1.03332 | − | 0.250759i | ||||
\(365\) | −932863. | −0.366510 | ||||||||
\(366\) | −820802. | − | 1.42167e6i | −0.320284 | − | 0.554748i | ||||
\(367\) | −1.44015e6 | + | 2.49441e6i | −0.558138 | + | 0.966723i | 0.439514 | + | 0.898236i | \(0.355151\pi\) |
−0.997652 | + | 0.0684875i | \(0.978183\pi\) | |||||||
\(368\) | −112696. | + | 195195.i | −0.0433798 | + | 0.0751361i | ||||
\(369\) | 3.91838e6 | + | 6.78683e6i | 1.49810 | + | 2.59478i | ||||
\(370\) | 749995. | 0.284809 | ||||||||
\(371\) | −687626. | + | 166868.i | −0.259369 | + | 0.0629417i | ||||
\(372\) | −1.95429e6 | −0.732204 | ||||||||
\(373\) | 1.95904e6 | + | 3.39315e6i | 0.729071 | + | 1.26279i | 0.957276 | + | 0.289176i | \(0.0933812\pi\) |
−0.228205 | + | 0.973613i | \(0.573285\pi\) | |||||||
\(374\) | −465560. | + | 806374.i | −0.172106 | + | 0.298097i | ||||
\(375\) | 217748. | − | 377150.i | 0.0799605 | − | 0.138496i | ||||
\(376\) | 1.57199e6 | + | 2.72277e6i | 0.573431 | + | 0.993211i | ||||
\(377\) | 5.20220e6 | 1.88510 | ||||||||
\(378\) | −923650. | + | 3.14649e6i | −0.332489 | + | 1.13265i | ||||
\(379\) | −795965. | −0.284640 | −0.142320 | − | 0.989821i | \(-0.545456\pi\) | ||||
−0.142320 | + | 0.989821i | \(0.545456\pi\) | |||||||
\(380\) | 276675. | + | 479215.i | 0.0982904 | + | 0.170244i | ||||
\(381\) | 3.68410e6 | − | 6.38105e6i | 1.30023 | − | 2.25206i | ||||
\(382\) | −500779. | + | 867375.i | −0.175585 | + | 0.304122i | ||||
\(383\) | −1.01288e6 | − | 1.75435e6i | −0.352825 | − | 0.611111i | 0.633918 | − | 0.773400i | \(-0.281446\pi\) |
−0.986743 | + | 0.162289i | \(0.948112\pi\) | |||||||
\(384\) | −4.23056e6 | −1.46410 | ||||||||
\(385\) | −906458. | − | 950530.i | −0.311671 | − | 0.326824i | ||||
\(386\) | −2.26934e6 | −0.775230 | ||||||||
\(387\) | −941160. | − | 1.63014e6i | −0.319438 | − | 0.553282i | ||||
\(388\) | −1.66366e6 | + | 2.88154e6i | −0.561029 | + | 0.971730i | ||||
\(389\) | 1.30160e6 | − | 2.25443e6i | 0.436117 | − | 0.755376i | −0.561269 | − | 0.827633i | \(-0.689687\pi\) |
0.997386 | + | 0.0722571i | \(0.0230202\pi\) | |||||||
\(390\) | −1.01250e6 | − | 1.75369e6i | −0.337079 | − | 0.583838i | ||||
\(391\) | −901836. | −0.298322 | ||||||||
\(392\) | 135007. | − | 2.84266e6i | 0.0443752 | − | 0.934350i | ||||
\(393\) | 3.06573e6 | 1.00127 | ||||||||
\(394\) | 1.17474e6 | + | 2.03471e6i | 0.381243 | + | 0.660332i | ||||
\(395\) | −195768. | + | 339081.i | −0.0631320 | + | 0.109348i | ||||
\(396\) | −2.40813e6 | + | 4.17100e6i | −0.771688 | + | 1.33660i | ||||
\(397\) | 2.58387e6 | + | 4.47539e6i | 0.822800 | + | 1.42513i | 0.903589 | + | 0.428400i | \(0.140923\pi\) |
−0.0807894 | + | 0.996731i | \(0.525744\pi\) | |||||||
\(398\) | 301550. | 0.0954228 | ||||||||
\(399\) | 2.47928e6 | + | 2.59983e6i | 0.779640 | + | 0.817546i | ||||
\(400\) | 115011. | 0.0359410 | ||||||||
\(401\) | −675308. | − | 1.16967e6i | −0.209720 | − | 0.363247i | 0.741906 | − | 0.670504i | \(-0.233922\pi\) |
−0.951626 | + | 0.307257i | \(0.900589\pi\) | |||||||
\(402\) | 2.90076e6 | − | 5.02427e6i | 0.895256 | − | 1.55063i | ||||
\(403\) | 1.46662e6 | − | 2.54026e6i | 0.449837 | − | 0.779141i | ||||
\(404\) | −1.41292e6 | − | 2.44724e6i | −0.430688 | − | 0.745974i | ||||
\(405\) | −2.40517e6 | −0.728632 | ||||||||
\(406\) | 636491. | − | 2.16826e6i | 0.191636 | − | 0.652824i | ||||
\(407\) | 3.89606e6 | 1.16584 | ||||||||
\(408\) | −1.73743e6 | − | 3.00932e6i | −0.516723 | − | 0.894990i | ||||
\(409\) | 1.38902e6 | − | 2.40585e6i | 0.410581 | − | 0.711148i | −0.584372 | − | 0.811486i | \(-0.698659\pi\) |
0.994953 | + | 0.100338i | \(0.0319925\pi\) | |||||||
\(410\) | −572619. | + | 991805.i | −0.168231 | + | 0.291385i | ||||
\(411\) | 3.92823e6 | + | 6.80389e6i | 1.14708 | + | 1.98679i | ||||
\(412\) | −300555. | −0.0872330 | ||||||||
\(413\) | −978647. | + | 237491.i | −0.282326 | + | 0.0685129i | ||||
\(414\) | 2.04035e6 | 0.585066 | ||||||||
\(415\) | 875023. | + | 1.51558e6i | 0.249402 | + | 0.431976i | ||||
\(416\) | 2.79052e6 | − | 4.83332e6i | 0.790591 | − | 1.36934i | ||||
\(417\) | −3.29178e6 | + | 5.70153e6i | −0.927024 | + | 1.60565i | ||||
\(418\) | −628654. | − | 1.08886e6i | −0.175983 | − | 0.304812i | ||||
\(419\) | 1.67370e6 | 0.465739 | 0.232869 | − | 0.972508i | \(-0.425189\pi\) | ||||
0.232869 | + | 0.972508i | \(0.425189\pi\) | |||||||
\(420\) | 1.95433e6 | − | 474262.i | 0.540597 | − | 0.131188i | ||||
\(421\) | 3.23947e6 | 0.890776 | 0.445388 | − | 0.895338i | \(-0.353066\pi\) | ||||
0.445388 | + | 0.895338i | \(0.353066\pi\) | |||||||
\(422\) | 583327. | + | 1.01035e6i | 0.159452 | + | 0.276179i | ||||
\(423\) | −4.95601e6 | + | 8.58405e6i | −1.34673 | + | 2.33261i | ||||
\(424\) | −462090. | + | 800363.i | −0.124828 | + | 0.216208i | ||||
\(425\) | 230092. | + | 398530.i | 0.0617914 | + | 0.107026i | ||||
\(426\) | 2.69568e6 | 0.719687 | ||||||||
\(427\) | −689219. | + | 2.34788e6i | −0.182931 | + | 0.623170i | ||||
\(428\) | −1.65703e6 | −0.437242 | ||||||||
\(429\) | −5.25969e6 | − | 9.11006e6i | −1.37980 | − | 2.38989i | ||||
\(430\) | 137538. | − | 238223.i | 0.0358716 | − | 0.0621315i | ||||
\(431\) | −1.58160e6 | + | 2.73941e6i | −0.410112 | + | 0.710335i | −0.994902 | − | 0.100850i | \(-0.967844\pi\) |
0.584789 | + | 0.811185i | \(0.301177\pi\) | |||||||
\(432\) | −745825. | − | 1.29181e6i | −0.192277 | − | 0.333034i | ||||
\(433\) | −5.42491e6 | −1.39050 | −0.695252 | − | 0.718766i | \(-0.744707\pi\) | ||||
−0.695252 | + | 0.718766i | \(0.744707\pi\) | |||||||
\(434\) | −879331. | − | 922085.i | −0.224093 | − | 0.234988i | ||||
\(435\) | 3.89220e6 | 0.986216 | ||||||||
\(436\) | 1.53256e6 | + | 2.65448e6i | 0.386103 | + | 0.668749i | ||||
\(437\) | 608882. | − | 1.05461e6i | 0.152521 | − | 0.264174i | ||||
\(438\) | −1.62269e6 | + | 2.81058e6i | −0.404157 | + | 0.700021i | ||||
\(439\) | −253716. | − | 439449.i | −0.0628328 | − | 0.108830i | 0.832898 | − | 0.553427i | \(-0.186680\pi\) |
−0.895731 | + | 0.444597i | \(0.853347\pi\) | |||||||
\(440\) | −1.71552e6 | −0.422438 | ||||||||
\(441\) | 7.97415e6 | − | 4.11240e6i | 1.95249 | − | 1.00693i | ||||
\(442\) | 2.13979e6 | 0.520972 | ||||||||
\(443\) | 1.69198e6 | + | 2.93059e6i | 0.409624 | + | 0.709490i | 0.994848 | − | 0.101382i | \(-0.0323266\pi\) |
−0.585223 | + | 0.810872i | \(0.698993\pi\) | |||||||
\(444\) | −2.98265e6 | + | 5.16609e6i | −0.718033 | + | 1.24367i | ||||
\(445\) | −98802.1 | + | 171130.i | −0.0236519 | + | 0.0409663i | ||||
\(446\) | −851562. | − | 1.47495e6i | −0.202712 | − | 0.351107i | ||||
\(447\) | −714627. | −0.169165 | ||||||||
\(448\) | −1.14624e6 | − | 1.20197e6i | −0.269825 | − | 0.282944i | ||||
\(449\) | 2.00014e6 | 0.468215 | 0.234108 | − | 0.972211i | \(-0.424783\pi\) | ||||
0.234108 | + | 0.972211i | \(0.424783\pi\) | |||||||
\(450\) | −520570. | − | 901653.i | −0.121185 | − | 0.209898i | ||||
\(451\) | −2.97463e6 | + | 5.15221e6i | −0.688639 | + | 1.19276i | ||||
\(452\) | 693018. | − | 1.20034e6i | 0.159551 | − | 0.276350i | ||||
\(453\) | −3.65924e6 | − | 6.33799e6i | −0.837810 | − | 1.45113i | ||||
\(454\) | −384685. | −0.0875922 | ||||||||
\(455\) | −850183. | + | 2.89622e6i | −0.192524 | + | 0.655848i | ||||
\(456\) | 4.69217e6 | 1.05672 | ||||||||
\(457\) | 592334. | + | 1.02595e6i | 0.132671 | + | 0.229793i | 0.924705 | − | 0.380684i | \(-0.124311\pi\) |
−0.792034 | + | 0.610476i | \(0.790978\pi\) | |||||||
\(458\) | −1.68247e6 | + | 2.91412e6i | −0.374785 | + | 0.649147i | ||||
\(459\) | 2.98419e6 | − | 5.16878e6i | 0.661143 | − | 1.14513i | ||||
\(460\) | −340848. | − | 590366.i | −0.0751045 | − | 0.130085i | ||||
\(461\) | −8.48869e6 | −1.86032 | −0.930161 | − | 0.367152i | \(-0.880333\pi\) | ||||
−0.930161 | + | 0.367152i | \(0.880333\pi\) | |||||||
\(462\) | −4.44057e6 | + | 1.07760e6i | −0.967907 | + | 0.234885i | ||||
\(463\) | 4.81635e6 | 1.04416 | 0.522079 | − | 0.852897i | \(-0.325157\pi\) | ||||
0.522079 | + | 0.852897i | \(0.325157\pi\) | |||||||
\(464\) | 513952. | + | 890190.i | 0.110822 | + | 0.191950i | ||||
\(465\) | 1.09730e6 | − | 1.90058e6i | 0.235339 | − | 0.407619i | ||||
\(466\) | −220320. | + | 381606.i | −0.0469991 | + | 0.0814048i | ||||
\(467\) | 2.27367e6 | + | 3.93812e6i | 0.482431 | + | 0.835596i | 0.999797 | − | 0.0201689i | \(-0.00642040\pi\) |
−0.517365 | + | 0.855765i | \(0.673087\pi\) | |||||||
\(468\) | 1.10681e7 | 2.33593 | ||||||||
\(469\) | −8.40378e6 | + | 2.03937e6i | −1.76418 | + | 0.428118i | ||||
\(470\) | −1.44851e6 | −0.302466 | ||||||||
\(471\) | −3.65486e6 | − | 6.33040e6i | −0.759134 | − | 1.31486i | ||||
\(472\) | −657658. | + | 1.13910e6i | −0.135877 | + | 0.235346i | ||||
\(473\) | 714479. | − | 1.23751e6i | 0.146837 | − | 0.254330i | ||||
\(474\) | 681067. | + | 1.17964e6i | 0.139234 | + | 0.241160i | ||||
\(475\) | −621393. | −0.126367 | ||||||||
\(476\) | −598551. | + | 2.03901e6i | −0.121083 | + | 0.412480i | ||||
\(477\) | −2.91365e6 | −0.586329 | ||||||||
\(478\) | 793629. | + | 1.37461e6i | 0.158872 | + | 0.275175i | ||||
\(479\) | 4.37224e6 | − | 7.57295e6i | 0.870694 | − | 1.50809i | 0.00941398 | − | 0.999956i | \(-0.497003\pi\) |
0.861280 | − | 0.508131i | \(-0.169663\pi\) | |||||||
\(480\) | 2.08782e6 | − | 3.61621e6i | 0.413609 | − | 0.716392i | ||||
\(481\) | −4.47672e6 | − | 7.75390e6i | −0.882261 | − | 1.52812i | ||||
\(482\) | −80184.6 | −0.0157208 | ||||||||
\(483\) | −3.05434e6 | − | 3.20284e6i | −0.595729 | − | 0.624694i | ||||
\(484\) | −70855.8 | −0.0137487 | ||||||||
\(485\) | −1.86823e6 | − | 3.23587e6i | −0.360642 | − | 0.624650i | ||||
\(486\) | −1.11041e6 | + | 1.92330e6i | −0.213253 | + | 0.369365i | ||||
\(487\) | 4.52775e6 | − | 7.84230e6i | 0.865088 | − | 1.49838i | −0.00187155 | − | 0.999998i | \(-0.500596\pi\) |
0.866960 | − | 0.498378i | \(-0.166071\pi\) | |||||||
\(488\) | 1.59799e6 | + | 2.76780e6i | 0.303756 | + | 0.526121i | ||||
\(489\) | 7.95408e6 | 1.50424 | ||||||||
\(490\) | 1.10312e6 | + | 708707.i | 0.207554 | + | 0.133345i | ||||
\(491\) | −4.29340e6 | −0.803706 | −0.401853 | − | 0.915704i | \(-0.631634\pi\) | ||||
−0.401853 | + | 0.915704i | \(0.631634\pi\) | |||||||
\(492\) | −4.55448e6 | − | 7.88859e6i | −0.848255 | − | 1.46922i | ||||
\(493\) | −2.05642e6 | + | 3.56183e6i | −0.381061 | + | 0.660018i | ||||
\(494\) | −1.44469e6 | + | 2.50228e6i | −0.266354 | + | 0.461338i | ||||
\(495\) | −2.70425e6 | − | 4.68389e6i | −0.496059 | − | 0.859199i | ||||
\(496\) | 579579. | 0.105781 | ||||||||
\(497\) | −2.77304e6 | − | 2.90787e6i | −0.503577 | − | 0.528061i | ||||
\(498\) | 6.08832e6 | 1.10008 | ||||||||
\(499\) | 1.82917e6 | + | 3.16822e6i | 0.328855 | + | 0.569593i | 0.982285 | − | 0.187394i | \(-0.0600041\pi\) |
−0.653430 | + | 0.756987i | \(0.726671\pi\) | |||||||
\(500\) | −173926. | + | 301248.i | −0.0311128 | + | 0.0538889i | ||||
\(501\) | −6.50990e6 | + | 1.12755e7i | −1.15872 | + | 2.00697i | ||||
\(502\) | 48273.1 | + | 83611.5i | 0.00854960 | + | 0.0148083i | ||||
\(503\) | −248395. | −0.0437746 | −0.0218873 | − | 0.999760i | \(-0.506968\pi\) | ||||
−0.0218873 | + | 0.999760i | \(0.506968\pi\) | |||||||
\(504\) | 3.30070e6 | − | 1.12441e7i | 0.578801 | − | 1.97173i | ||||
\(505\) | 3.17331e6 | 0.553713 | ||||||||
\(506\) | 774465. | + | 1.34141e6i | 0.134470 | + | 0.232909i | ||||
\(507\) | −6.91289e6 | + | 1.19735e7i | −1.19437 | + | 2.06871i | ||||
\(508\) | −2.94267e6 | + | 5.09686e6i | −0.505921 | + | 0.876281i | ||||
\(509\) | −4.06027e6 | − | 7.03259e6i | −0.694640 | − | 1.20315i | −0.970302 | − | 0.241898i | \(-0.922230\pi\) |
0.275661 | − | 0.961255i | \(-0.411103\pi\) | |||||||
\(510\) | 1.60095e6 | 0.272554 | ||||||||
\(511\) | 4.70108e6 | − | 1.14082e6i | 0.796426 | − | 0.193271i | ||||
\(512\) | 2.09985e6 | 0.354008 | ||||||||
\(513\) | 4.02961e6 | + | 6.97949e6i | 0.676036 | + | 1.17093i | ||||
\(514\) | −399594. | + | 692117.i | −0.0667131 | + | 0.115551i | ||||
\(515\) | 168756. | − | 292294.i | 0.0280377 | − | 0.0485627i | ||||
\(516\) | 1.09395e6 | + | 1.89477e6i | 0.180872 | + | 0.313280i | ||||
\(517\) | −7.52468e6 | −1.23812 | ||||||||
\(518\) | −3.77953e6 | + | 917189.i | −0.618890 | + | 0.150188i | ||||
\(519\) | −840731. | −0.137006 | ||||||||
\(520\) | 1.97119e6 | + | 3.41421e6i | 0.319684 | + | 0.553709i | ||||
\(521\) | −3.51230e6 | + | 6.08349e6i | −0.566889 | + | 0.981880i | 0.429982 | + | 0.902837i | \(0.358520\pi\) |
−0.996871 | + | 0.0790430i | \(0.974814\pi\) | |||||||
\(522\) | 4.65254e6 | − | 8.05844e6i | 0.747333 | − | 1.29442i | ||||
\(523\) | 201663. | + | 349290.i | 0.0322382 | + | 0.0558382i | 0.881694 | − | 0.471821i | \(-0.156403\pi\) |
−0.849456 | + | 0.527659i | \(0.823070\pi\) | |||||||
\(524\) | −2.44875e6 | −0.389598 | ||||||||
\(525\) | −636093. | + | 2.16690e6i | −0.100722 | + | 0.343116i | ||||
\(526\) | 3.18522e6 | 0.501968 | ||||||||
\(527\) | 1.15951e6 | + | 2.00832e6i | 0.181864 | + | 0.314997i | ||||
\(528\) | 1.03926e6 | − | 1.80006e6i | 0.162234 | − | 0.280997i | ||||
\(529\) | 2.46806e6 | − | 4.27481e6i | 0.383458 | − | 0.664168i | ||||
\(530\) | −212895. | − | 368746.i | −0.0329213 | − | 0.0570213i | ||||
\(531\) | −4.14679e6 | −0.638227 | ||||||||
\(532\) | −1.98033e6 | − | 2.07661e6i | −0.303359 | − | 0.318109i | ||||
\(533\) | 1.36718e7 | 2.08453 | ||||||||
\(534\) | 343727. | + | 595353.i | 0.0521628 | + | 0.0903486i | ||||
\(535\) | 930395. | − | 1.61149e6i | 0.140534 | − | 0.243413i | ||||
\(536\) | −5.64740e6 | + | 9.78158e6i | −0.849056 | + | 1.47061i | ||||
\(537\) | 8.28315e6 | + | 1.43468e7i | 1.23954 | + | 2.14694i | ||||
\(538\) | −1.54079e6 | −0.229503 | ||||||||
\(539\) | 5.73044e6 | + | 3.68158e6i | 0.849603 | + | 0.545836i | ||||
\(540\) | 4.51149e6 | 0.665788 | ||||||||
\(541\) | −643040. | − | 1.11378e6i | −0.0944593 | − | 0.163608i | 0.814924 | − | 0.579568i | \(-0.196779\pi\) |
−0.909383 | + | 0.415960i | \(0.863446\pi\) | |||||||
\(542\) | 2.30260e6 | − | 3.98822e6i | 0.336683 | − | 0.583151i | ||||
\(543\) | −2.16330e6 | + | 3.74694e6i | −0.314859 | + | 0.545352i | ||||
\(544\) | 2.20618e6 | + | 3.82121e6i | 0.319627 | + | 0.553610i | ||||
\(545\) | −3.44203e6 | −0.496391 | ||||||||
\(546\) | 7.24702e6 | + | 7.59938e6i | 1.04035 | + | 1.09093i | ||||
\(547\) | −7.76839e6 | −1.11010 | −0.555051 | − | 0.831816i | \(-0.687301\pi\) | ||||
−0.555051 | + | 0.831816i | \(0.687301\pi\) | |||||||
\(548\) | −3.13767e6 | − | 5.43460e6i | −0.446329 | − | 0.773065i | ||||
\(549\) | −5.03797e6 | + | 8.72602e6i | −0.713386 | + | 1.23562i | ||||
\(550\) | 395189. | − | 684488.i | 0.0557055 | − | 0.0964848i | ||||
\(551\) | −2.77682e6 | − | 4.80960e6i | −0.389645 | − | 0.674885i | ||||
\(552\) | −5.78048e6 | −0.807451 | ||||||||
\(553\) | 571885. | − | 1.94818e6i | 0.0795236 | − | 0.270904i | ||||
\(554\) | −2.73952e6 | −0.379228 | ||||||||
\(555\) | −3.34941e6 | − | 5.80134e6i | −0.461568 | − | 0.799459i | ||||
\(556\) | 2.62931e6 | − | 4.55409e6i | 0.360707 | − | 0.624762i | ||||
\(557\) | 3.33475e6 | − | 5.77595e6i | 0.455433 | − | 0.788834i | −0.543280 | − | 0.839552i | \(-0.682818\pi\) |
0.998713 | + | 0.0507181i | \(0.0161510\pi\) | |||||||
\(558\) | −2.62332e6 | − | 4.54372e6i | −0.356669 | − | 0.617769i | ||||
\(559\) | −3.28386e6 | −0.444482 | ||||||||
\(560\) | −579589. | + | 140651.i | −0.0780999 | + | 0.0189527i | ||||
\(561\) | 8.31659e6 | 1.11568 | ||||||||
\(562\) | 2.28729e6 | + | 3.96171e6i | 0.305479 | + | 0.529105i | ||||
\(563\) | 853267. | − | 1.47790e6i | 0.113452 | − | 0.196505i | −0.803708 | − | 0.595024i | \(-0.797142\pi\) |
0.917160 | + | 0.398519i | \(0.130476\pi\) | |||||||
\(564\) | 5.76055e6 | − | 9.97757e6i | 0.762547 | − | 1.32077i | ||||
\(565\) | 778235. | + | 1.34794e6i | 0.102563 | + | 0.177644i | ||||
\(566\) | 5.40183e6 | 0.708761 | ||||||||
\(567\) | 1.21206e7 | − | 2.94135e6i | 1.58332 | − | 0.384228i | ||||
\(568\) | −5.24812e6 | −0.682548 | ||||||||
\(569\) | 1.10864e6 | + | 1.92022e6i | 0.143552 | + | 0.248639i | 0.928832 | − | 0.370502i | \(-0.120814\pi\) |
−0.785280 | + | 0.619141i | \(0.787481\pi\) | |||||||
\(570\) | −1.08090e6 | + | 1.87217e6i | −0.139347 | + | 0.241356i | ||||
\(571\) | 3.18782e6 | − | 5.52146e6i | 0.409169 | − | 0.708702i | −0.585628 | − | 0.810580i | \(-0.699152\pi\) |
0.994797 | + | 0.101878i | \(0.0324853\pi\) | |||||||
\(572\) | 4.20117e6 | + | 7.27665e6i | 0.536884 | + | 0.929910i | ||||
\(573\) | 8.94573e6 | 1.13823 | ||||||||
\(574\) | 1.67275e6 | − | 5.69838e6i | 0.211911 | − | 0.721891i | ||||
\(575\) | 765520. | 0.0965578 | ||||||||
\(576\) | −3.41960e6 | − | 5.92292e6i | −0.429456 | − | 0.743840i | ||||
\(577\) | 1.45598e6 | − | 2.52184e6i | 0.182061 | − | 0.315339i | −0.760521 | − | 0.649313i | \(-0.775056\pi\) |
0.942582 | + | 0.333974i | \(0.108390\pi\) | |||||||
\(578\) | 1.36948e6 | − | 2.37200e6i | 0.170504 | − | 0.295322i | ||||
\(579\) | 1.01346e7 | + | 1.75537e7i | 1.25635 | + | 2.17607i | ||||
\(580\) | −3.10889e6 | −0.383738 | ||||||||
\(581\) | −6.26305e6 | − | 6.56756e6i | −0.769743 | − | 0.807168i | ||||
\(582\) | −1.29989e7 | −1.59075 | ||||||||
\(583\) | −1.10595e6 | − | 1.91555e6i | −0.134760 | − | 0.233412i | ||||
\(584\) | 3.15916e6 | − | 5.47183e6i | 0.383301 | − | 0.663896i | ||||
\(585\) | −6.21456e6 | + | 1.07639e7i | −0.750794 | + | 1.30041i | ||||
\(586\) | 973169. | + | 1.68558e6i | 0.117070 | + | 0.202770i | ||||
\(587\) | 1.61871e7 | 1.93899 | 0.969494 | − | 0.245116i | \(-0.0788259\pi\) | ||||
0.969494 | + | 0.245116i | \(0.0788259\pi\) | |||||||
\(588\) | −9.26866e6 | + | 4.78000e6i | −1.10554 | + | 0.570144i | ||||
\(589\) | −3.13140e6 | −0.371921 | ||||||||
\(590\) | −302999. | − | 524809.i | −0.0358353 | − | 0.0620685i | ||||
\(591\) | 1.04926e7 | − | 1.81737e7i | 1.23570 | − | 2.14030i | ||||
\(592\) | 884555. | − | 1.53209e6i | 0.103734 | − | 0.179672i | ||||
\(593\) | 4.17033e6 | + | 7.22322e6i | 0.487005 | + | 0.843517i | 0.999888 | − | 0.0149411i | \(-0.00475608\pi\) |
−0.512884 | + | 0.858458i | \(0.671423\pi\) | |||||||
\(594\) | −1.02509e7 | −1.19205 | ||||||||
\(595\) | −1.64690e6 | − | 1.72697e6i | −0.190710 | − | 0.199983i | ||||
\(596\) | 570807. | 0.0658224 | ||||||||
\(597\) | −1.34670e6 | − | 2.33255e6i | −0.154644 | − | 0.267852i | ||||
\(598\) | 1.77978e6 | − | 3.08267e6i | 0.203523 | − | 0.352512i | ||||
\(599\) | −7.04980e6 | + | 1.22106e7i | −0.802805 | + | 1.39050i | 0.114958 | + | 0.993370i | \(0.463327\pi\) |
−0.917763 | + | 0.397128i | \(0.870007\pi\) | |||||||
\(600\) | 1.47481e6 | + | 2.55445e6i | 0.167247 | + | 0.289681i | ||||
\(601\) | −6.75584e6 | −0.762945 | −0.381472 | − | 0.924380i | \(-0.624583\pi\) | ||||
−0.381472 | + | 0.924380i | \(0.624583\pi\) | |||||||
\(602\) | −401781. | + | 1.36870e6i | −0.0451854 | + | 0.153928i | ||||
\(603\) | −3.56090e7 | −3.98810 | ||||||||
\(604\) | 2.92281e6 | + | 5.06246e6i | 0.325993 | + | 0.564637i | ||||
\(605\) | 39784.3 | − | 68908.4i | 0.00441899 | − | 0.00765392i | ||||
\(606\) | 5.51989e6 | − | 9.56073e6i | 0.610589 | − | 1.05757i | ||||
\(607\) | −6.01038e6 | − | 1.04103e7i | −0.662110 | − | 1.14681i | −0.980060 | − | 0.198701i | \(-0.936328\pi\) |
0.317950 | − | 0.948108i | \(-0.397006\pi\) | |||||||
\(608\) | −5.95808e6 | −0.653653 | ||||||||
\(609\) | −1.96144e7 | + | 4.75988e6i | −2.14305 | + | 0.520059i | ||||
\(610\) | −1.47246e6 | −0.160221 | ||||||||
\(611\) | 8.64614e6 | + | 1.49756e7i | 0.936956 | + | 1.62286i | ||||
\(612\) | −4.37521e6 | + | 7.57809e6i | −0.472194 | + | 0.817865i | ||||
\(613\) | 729703. | − | 1.26388e6i | 0.0784323 | − | 0.135849i | −0.824141 | − | 0.566384i | \(-0.808342\pi\) |
0.902574 | + | 0.430535i | \(0.141675\pi\) | |||||||
\(614\) | 3.00031e6 | + | 5.19669e6i | 0.321178 | + | 0.556296i | ||||
\(615\) | 1.02290e7 | 1.09055 | ||||||||
\(616\) | 8.64519e6 | − | 2.09795e6i | 0.917958 | − | 0.222763i | ||||
\(617\) | −6.88916e6 | −0.728540 | −0.364270 | − | 0.931293i | \(-0.618681\pi\) | ||||
−0.364270 | + | 0.931293i | \(0.618681\pi\) | |||||||
\(618\) | −587094. | − | 1.01688e6i | −0.0618353 | − | 0.107102i | ||||
\(619\) | 5.85438e6 | − | 1.01401e7i | 0.614121 | − | 1.06369i | −0.376417 | − | 0.926451i | \(-0.622844\pi\) |
0.990538 | − | 0.137239i | \(-0.0438228\pi\) | |||||||
\(620\) | −876468. | + | 1.51809e6i | −0.0915707 | + | 0.158605i | ||||
\(621\) | −4.96425e6 | − | 8.59833e6i | −0.516564 | − | 0.894715i | ||||
\(622\) | 6.56255e6 | 0.680137 | ||||||||
\(623\) | 288624. | − | 983223.i | 0.0297929 | − | 0.101492i | ||||
\(624\) | −4.77661e6 | −0.491087 | ||||||||
\(625\) | −195312. | − | 338291.i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −4.28057e6 | + | 7.41416e6i | −0.436582 | + | 0.756182i | ||||
\(627\) | −5.61502e6 | + | 9.72550e6i | −0.570404 | + | 0.987968i | ||||
\(628\) | 2.91931e6 | + | 5.05640e6i | 0.295380 | + | 0.511614i | ||||
\(629\) | 7.07856e6 | 0.713375 | ||||||||
\(630\) | 3.72602e6 | + | 3.90718e6i | 0.374019 | + | 0.392204i | ||||
\(631\) | 2.08769e6 | 0.208734 | 0.104367 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(632\) | −1.32595e6 | − | 2.29661e6i | −0.132048 | − | 0.228715i | ||||
\(633\) | 5.21017e6 | − | 9.02427e6i | 0.516824 | − | 0.895165i | ||||
\(634\) | 2.35926e6 | − | 4.08636e6i | 0.233106 | − | 0.403751i | ||||
\(635\) | −3.30452e6 | − | 5.72359e6i | −0.325217 | − | 0.563293i | ||||
\(636\) | 3.38665e6 | 0.331992 | ||||||||
\(637\) | 742553. | − | 1.56350e7i | 0.0725068 | − | 1.52668i | ||||
\(638\) | 7.06394e6 | 0.687061 | ||||||||
\(639\) | −8.27285e6 | − | 1.43290e7i | −0.801499 | − | 1.38824i | ||||
\(640\) | −1.89734e6 | + | 3.28628e6i | −0.183102 | + | 0.317143i | ||||
\(641\) | −6.28598e6 | + | 1.08876e7i | −0.604266 | + | 1.04662i | 0.387901 | + | 0.921701i | \(0.373200\pi\) |
−0.992167 | + | 0.124918i | \(0.960133\pi\) | |||||||
\(642\) | −3.23679e6 | − | 5.60629e6i | −0.309940 | − | 0.536831i | ||||
\(643\) | −5.47387e6 | −0.522116 | −0.261058 | − | 0.965323i | \(-0.584071\pi\) | ||||
−0.261058 | + | 0.965323i | \(0.584071\pi\) | |||||||
\(644\) | 2.43965e6 | + | 2.55826e6i | 0.231799 | + | 0.243069i | ||||
\(645\) | −2.45693e6 | −0.232537 | ||||||||
\(646\) | −1.14217e6 | − | 1.97830e6i | −0.107684 | − | 0.186514i | ||||
\(647\) | −16516.5 | + | 28607.5i | −0.00155116 | + | 0.00268670i | −0.866800 | − | 0.498656i | \(-0.833827\pi\) |
0.865249 | + | 0.501343i | \(0.167160\pi\) | |||||||
\(648\) | 8.14516e6 | − | 1.41078e7i | 0.762012 | − | 1.31984i | ||||
\(649\) | −1.57401e6 | − | 2.72627e6i | −0.146688 | − | 0.254072i | ||||
\(650\) | −1.81635e6 | −0.168623 | ||||||||
\(651\) | −3.20548e6 | + | 1.09197e7i | −0.296442 | + | 1.00986i | ||||
\(652\) | −6.35331e6 | −0.585303 | ||||||||
\(653\) | −3.39385e6 | − | 5.87832e6i | −0.311465 | − | 0.539473i | 0.667215 | − | 0.744866i | \(-0.267486\pi\) |
−0.978680 | + | 0.205392i | \(0.934153\pi\) | |||||||
\(654\) | −5.98732e6 | + | 1.03703e7i | −0.547379 | + | 0.948089i | ||||
\(655\) | 1.37493e6 | − | 2.38145e6i | 0.125221 | − | 0.216889i | ||||
\(656\) | 1.35071e6 | + | 2.33950e6i | 0.122547 | + | 0.212258i | ||||
\(657\) | 1.99197e7 | 1.80040 | ||||||||
\(658\) | 7.29962e6 | − | 1.77142e6i | 0.657258 | − | 0.159499i | ||||
\(659\) | 1.30322e7 | 1.16898 | 0.584488 | − | 0.811403i | \(-0.301296\pi\) | ||||
0.584488 | + | 0.811403i | \(0.301296\pi\) | |||||||
\(660\) | 3.14325e6 | + | 5.44426e6i | 0.280879 | + | 0.486496i | ||||
\(661\) | 7.90405e6 | − | 1.36902e7i | 0.703632 | − | 1.21873i | −0.263551 | − | 0.964646i | \(-0.584894\pi\) |
0.967183 | − | 0.254081i | \(-0.0817731\pi\) | |||||||
\(662\) | −1.22133e6 | + | 2.11540e6i | −0.108315 | + | 0.187607i | ||||
\(663\) | −9.55608e6 | − | 1.65516e7i | −0.844299 | − | 1.46237i | ||||
\(664\) | −1.18531e7 | −1.04331 | ||||||||
\(665\) | 3.13145e6 | − | 759919.i | 0.274595 | − | 0.0666366i | ||||
\(666\) | −1.60149e7 | −1.39906 | ||||||||
\(667\) | 3.42088e6 | + | 5.92514e6i | 0.297731 | + | 0.515685i | ||||
\(668\) | 5.19978e6 | − | 9.00628e6i | 0.450862 | − | 0.780916i | ||||
\(669\) | −7.60600e6 | + | 1.31740e7i | −0.657039 | + | 1.13802i | ||||
\(670\) | −2.60189e6 | − | 4.50660e6i | −0.223925 | − | 0.387849i | ||||
\(671\) | −7.64912e6 | −0.655851 | ||||||||
\(672\) | −6.09902e6 | + | 2.07768e7i | −0.520999 | + | 1.77483i | ||||
\(673\) | 1.94847e7 | 1.65827 | 0.829137 | − | 0.559045i | \(-0.188832\pi\) | ||||
0.829137 | + | 0.559045i | \(0.188832\pi\) | |||||||
\(674\) | 4.66276e6 | + | 8.07614e6i | 0.395361 | + | 0.684784i | ||||
\(675\) | −2.53312e6 | + | 4.38750e6i | −0.213992 | + | 0.370645i | ||||
\(676\) | 5.52166e6 | − | 9.56380e6i | 0.464733 | − | 0.804941i | ||||
\(677\) | −3.98541e6 | − | 6.90293e6i | −0.334196 | − | 0.578844i | 0.649134 | − | 0.760674i | \(-0.275131\pi\) |
−0.983330 | + | 0.181830i | \(0.941798\pi\) | |||||||
\(678\) | 5.41487e6 | 0.452391 | ||||||||
\(679\) | 1.33720e7 | + | 1.40222e7i | 1.11307 | + | 1.16719i | ||||
\(680\) | −3.11684e6 | −0.258489 | ||||||||
\(681\) | 1.71797e6 | + | 2.97560e6i | 0.141954 | + | 0.245871i | ||||
\(682\) | 1.99149e6 | − | 3.44936e6i | 0.163952 | − | 0.283973i | ||||
\(683\) | 4.96510e6 | − | 8.59980e6i | 0.407264 | − | 0.705402i | −0.587318 | − | 0.809356i | \(-0.699816\pi\) |
0.994582 | + | 0.103954i | \(0.0331495\pi\) | |||||||
\(684\) | −5.90793e6 | − | 1.02328e7i | −0.482831 | − | 0.836287i | ||||
\(685\) | 7.04698e6 | 0.573821 | ||||||||
\(686\) | −6.42575e6 | − | 2.22244e6i | −0.521331 | − | 0.180310i | ||||
\(687\) | 3.00549e7 | 2.42954 | ||||||||
\(688\) | −324429. | − | 561927.i | −0.0261305 | − | 0.0452594i | ||||
\(689\) | −2.54155e6 | + | 4.40209e6i | −0.203962 | + | 0.353273i | ||||
\(690\) | 1.33160e6 | − | 2.30640e6i | 0.106476 | − | 0.184422i | ||||
\(691\) | −3.19613e6 | − | 5.53586e6i | −0.254642 | − | 0.441053i | 0.710156 | − | 0.704044i | \(-0.248624\pi\) |
−0.964798 | + | 0.262991i | \(0.915291\pi\) | |||||||
\(692\) | 671532. | 0.0533091 | ||||||||
\(693\) | 1.93559e7 | + | 2.02969e7i | 1.53101 | + | 1.60545i | ||||
\(694\) | −1.91618e6 | −0.151021 | ||||||||
\(695\) | 2.95262e6 | + | 5.11408e6i | 0.231870 | + | 0.401611i | ||||
\(696\) | −1.31810e7 | + | 2.28302e7i | −1.03140 | + | 1.78643i | ||||
\(697\) | −5.40446e6 | + | 9.36080e6i | −0.421376 | + | 0.729845i | ||||
\(698\) | 5.21319e6 | + | 9.02951e6i | 0.405009 | + | 0.701497i | ||||
\(699\) | 3.93572e6 | 0.304671 | ||||||||
\(700\) | 508078. | − | 1.73081e6i | 0.0391909 | − | 0.133507i | ||||
\(701\) | −5.78581e6 | −0.444702 | −0.222351 | − | 0.974967i | \(-0.571373\pi\) | ||||
−0.222351 | + | 0.974967i | \(0.571373\pi\) | |||||||
\(702\) | 1.17787e7 | + | 2.04013e7i | 0.902097 | + | 1.56248i | ||||
\(703\) | −4.77915e6 | + | 8.27773e6i | −0.364722 | + | 0.631717i | ||||
\(704\) | 2.59598e6 | − | 4.49637e6i | 0.197410 | − | 0.341925i | ||||
\(705\) | 6.46890e6 | + | 1.12045e7i | 0.490182 | + | 0.849021i | ||||
\(706\) | −1.13001e7 | −0.853235 | ||||||||
\(707\) | −1.59916e7 | + | 3.88073e6i | −1.20322 | + | 0.291988i | ||||
\(708\) | 4.81997e6 | 0.361377 | ||||||||
\(709\) | 1.21294e7 | + | 2.10087e7i | 0.906198 | + | 1.56958i | 0.819301 | + | 0.573364i | \(0.194362\pi\) |
0.0868970 | + | 0.996217i | \(0.472305\pi\) | |||||||
\(710\) | 1.20897e6 | − | 2.09399e6i | 0.0900053 | − | 0.155894i | ||||
\(711\) | 4.18030e6 | − | 7.24049e6i | 0.310122 | − | 0.537148i | ||||
\(712\) | −669191. | − | 1.15907e6i | −0.0494709 | − | 0.0856861i | ||||
\(713\) | 3.85770e6 | 0.284188 | ||||||||
\(714\) | −8.06785e6 | + | 1.95785e6i | −0.592260 | + | 0.143725i | ||||
\(715\) | −9.43554e6 | −0.690243 | ||||||||
\(716\) | −6.61615e6 | − | 1.14595e7i | −0.482306 | − | 0.835379i | ||||
\(717\) | 7.08854e6 | − | 1.22777e7i | 0.514943 | − | 0.891907i | ||||
\(718\) | −5.58950e6 | + | 9.68130e6i | −0.404634 | + | 0.700846i | ||||
\(719\) | −3.35317e6 | − | 5.80786e6i | −0.241898 | − | 0.418980i | 0.719357 | − | 0.694641i | \(-0.244437\pi\) |
−0.961255 | + | 0.275661i | \(0.911103\pi\) | |||||||
\(720\) | −2.45587e6 | −0.176553 | ||||||||
\(721\) | −492977. | + | 1.67937e6i | −0.0353174 | + | 0.120312i | ||||
\(722\) | −4.64208e6 | −0.331413 | ||||||||
\(723\) | 358097. | + | 620242.i | 0.0254774 | + | 0.0441281i | ||||
\(724\) | 1.72793e6 | − | 2.99286e6i | 0.122512 | − | 0.212197i | ||||
\(725\) | 1.74559e6 | − | 3.02345e6i | 0.123338 | − | 0.213628i | ||||
\(726\) | −138407. | − | 239729.i | −0.00974581 | − | 0.0168802i | ||||
\(727\) | −1.44972e7 | −1.01730 | −0.508649 | − | 0.860974i | \(-0.669855\pi\) | ||||
−0.508649 | + | 0.860974i | \(0.669855\pi\) | |||||||
\(728\) | −1.41090e7 | − | 1.47950e7i | −0.986659 | − | 1.03463i | ||||
\(729\) | −3.54221e6 | −0.246863 | ||||||||
\(730\) | 1.45550e6 | + | 2.52100e6i | 0.101089 | + | 0.175092i | ||||
\(731\) | 1.29810e6 | − | 2.24838e6i | 0.0898495 | − | 0.155624i | ||||
\(732\) | 5.85582e6 | − | 1.01426e7i | 0.403934 | − | 0.699634i | ||||
\(733\) | −5.36265e6 | − | 9.28837e6i | −0.368654 | − | 0.638528i | 0.620701 | − | 0.784047i | \(-0.286848\pi\) |
−0.989355 | + | 0.145519i | \(0.953515\pi\) | |||||||
\(734\) | 8.98795e6 | 0.615773 | ||||||||
\(735\) | 555566. | − | 1.16978e7i | 0.0379330 | − | 0.798705i | ||||
\(736\) | 7.34001e6 | 0.499461 | ||||||||
\(737\) | −1.35162e7 | − | 2.34108e7i | −0.916616 | − | 1.58762i | ||||
\(738\) | 1.22273e7 | − | 2.11783e7i | 0.826399 | − | 1.43136i | ||||
\(739\) | 1.77352e6 | − | 3.07182e6i | 0.119461 | − | 0.206912i | −0.800093 | − | 0.599875i | \(-0.795217\pi\) |
0.919554 | + | 0.392964i | \(0.128550\pi\) | |||||||
\(740\) | 2.67533e6 | + | 4.63381e6i | 0.179597 | + | 0.311071i | ||||
\(741\) | 2.58075e7 | 1.72663 | ||||||||
\(742\) | 1.52382e6 | + | 1.59791e6i | 0.101607 | + | 0.106547i | ||||
\(743\) | −8.10764e6 | −0.538794 | −0.269397 | − | 0.963029i | \(-0.586824\pi\) | ||||
−0.269397 | + | 0.963029i | \(0.586824\pi\) | |||||||
\(744\) | 7.43207e6 | + | 1.28727e7i | 0.492240 | + | 0.852585i | ||||
\(745\) | −320498. | + | 555119.i | −0.0211561 | + | 0.0366434i | ||||
\(746\) | 6.11317e6 | − | 1.05883e7i | 0.402179 | − | 0.696594i | ||||
\(747\) | −1.86846e7 | − | 3.23627e7i | −1.22513 | − | 2.12199i | ||||
\(748\) | −6.64287e6 | −0.434112 | ||||||||
\(749\) | −2.71790e6 | + | 9.25877e6i | −0.177023 | + | 0.603043i | ||||
\(750\) | −1.35896e6 | −0.0882175 | ||||||||
\(751\) | 1.21987e7 | + | 2.11288e7i | 0.789250 | + | 1.36702i | 0.926427 | + | 0.376474i | \(0.122864\pi\) |
−0.137177 | + | 0.990547i | \(0.543803\pi\) | |||||||
\(752\) | −1.70839e6 | + | 2.95902e6i | −0.110165 | + | 0.190811i | ||||
\(753\) | 431166. | − | 746802.i | 0.0277113 | − | 0.0479975i | ||||
\(754\) | −8.11673e6 | − | 1.40586e7i | −0.519939 | − | 0.900562i | ||||
\(755\) | −6.56443e6 | −0.419112 | ||||||||
\(756\) | −2.27353e7 | + | 5.51723e6i | −1.44676 | + | 0.351088i | ||||
\(757\) | −9.35579e6 | −0.593391 | −0.296695 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296695 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(758\) | 1.24190e6 | + | 2.15104e6i | 0.0785082 | + | 0.135980i | ||||
\(759\) | 6.91738e6 | − | 1.19813e7i | 0.435850 | − | 0.754915i | ||||
\(760\) | 2.10436e6 | − | 3.64486e6i | 0.132156 | − | 0.228900i | ||||
\(761\) | 8.68869e6 | + | 1.50493e7i | 0.543867 | + | 0.942005i | 0.998677 | + | 0.0514170i | \(0.0163738\pi\) |
−0.454810 | + | 0.890588i | \(0.650293\pi\) | |||||||
\(762\) | −2.29925e7 | −1.43449 | ||||||||
\(763\) | 1.73458e7 | − | 4.20936e6i | 1.07866 | − | 0.261761i | ||||
\(764\) | −7.14539e6 | −0.442886 | ||||||||
\(765\) | −4.91321e6 | − | 8.50993e6i | −0.303537 | − | 0.525742i | ||||
\(766\) | −3.16068e6 | + | 5.47446e6i | −0.194630 | + | 0.337108i | ||||
\(767\) | −3.61720e6 | + | 6.26517e6i | −0.222016 | + | 0.384543i | ||||
\(768\) | 1.23140e7 | + | 2.13285e7i | 0.753348 | + | 1.30484i | ||||
\(769\) | 4.58080e6 | 0.279335 | 0.139667 | − | 0.990198i | \(-0.455397\pi\) | ||||
0.139667 | + | 0.990198i | \(0.455397\pi\) | |||||||
\(770\) | −1.15444e6 | + | 3.93270e6i | −0.0701690 | + | 0.239037i | ||||
\(771\) | 7.13820e6 | 0.432467 | ||||||||
\(772\) | −8.09503e6 | − | 1.40210e7i | −0.488850 | − | 0.846713i | ||||
\(773\) | −1.18714e7 | + | 2.05619e7i | −0.714585 | + | 1.23770i | 0.248534 | + | 0.968623i | \(0.420051\pi\) |
−0.963119 | + | 0.269075i | \(0.913282\pi\) | |||||||
\(774\) | −2.93689e6 | + | 5.08684e6i | −0.176212 | + | 0.305208i | ||||
\(775\) | −984243. | − | 1.70476e6i | −0.0588638 | − | 0.101955i | ||||
\(776\) | 2.53072e7 | 1.50866 | ||||||||
\(777\) | 2.39737e7 | + | 2.51393e7i | 1.42456 | + | 1.49383i | ||||
\(778\) | −8.12326e6 | −0.481151 | ||||||||
\(779\) | −7.29773e6 | − | 1.26400e7i | −0.430868 | − | 0.746285i | ||||
\(780\) | 7.22342e6 | − | 1.25113e7i | 0.425115 | − | 0.736321i | ||||
\(781\) | 6.28031e6 | − | 1.08778e7i | 0.368429 | − | 0.638138i | ||||
\(782\) | 1.40709e6 | + | 2.43715e6i | 0.0822819 | + | 0.142516i | ||||
\(783\) | −4.52791e7 | −2.63933 | ||||||||
\(784\) | 2.74878e6 | − | 1.41759e6i | 0.159717 | − | 0.0823684i | ||||
\(785\) | −6.55657e6 | −0.379754 | ||||||||
\(786\) | −4.78331e6 | − | 8.28494e6i | −0.276167 | − | 0.478336i | ||||
\(787\) | −7.41205e6 | + | 1.28381e7i | −0.426581 | + | 0.738860i | −0.996567 | − | 0.0827946i | \(-0.973615\pi\) |
0.569986 | + | 0.821655i | \(0.306949\pi\) | |||||||
\(788\) | −8.38093e6 | + | 1.45162e7i | −0.480813 | + | 0.832793i | ||||
\(789\) | −1.42249e7 | − | 2.46383e7i | −0.813499 | − | 1.40902i | ||||
\(790\) | 1.22179e6 | 0.0696512 | ||||||||
\(791\) | −5.57028e6 | − | 5.84111e6i | −0.316545 | − | 0.331936i | ||||
\(792\) | 3.66319e7 | 2.07514 | ||||||||
\(793\) | 8.78914e6 | + | 1.52232e7i | 0.496322 | + | 0.859654i | ||||
\(794\) | 8.06296e6 | − | 1.39655e7i | 0.453882 | − | 0.786147i | ||||
\(795\) | −1.90154e6 | + | 3.29357e6i | −0.106706 | + | 0.184820i | ||||
\(796\) | 1.07567e6 | + | 1.86312e6i | 0.0601724 | + | 0.104222i | ||||
\(797\) | −1.29629e7 | −0.722866 | −0.361433 | − | 0.932398i | \(-0.617712\pi\) | ||||
−0.361433 | + | 0.932398i | \(0.617712\pi\) | |||||||
\(798\) | 3.15755e6 | − | 1.07565e7i | 0.175527 | − | 0.597947i | ||||
\(799\) | −1.36712e7 | −0.757601 | ||||||||
\(800\) | −1.87271e6 | − | 3.24362e6i | −0.103453 | − | 0.179187i | ||||
\(801\) | 2.10975e6 | − | 3.65420e6i | 0.116185 | − | 0.201238i | ||||
\(802\) | −2.10730e6 | + | 3.64995e6i | −0.115688 | + | 0.200378i | ||||
\(803\) | 7.56100e6 | + | 1.30960e7i | 0.413800 | + | 0.716722i | ||||
\(804\) | 4.13897e7 | 2.25815 | ||||||||
\(805\) | −3.85777e6 | + | 936176.i | −0.209820 | + | 0.0509176i | ||||
\(806\) | −9.15318e6 | −0.496288 | ||||||||
\(807\) | 6.88105e6 | + | 1.19183e7i | 0.371938 | + | 0.644216i | ||||
\(808\) | −1.07465e7 | + | 1.86135e7i | −0.579079 | + | 1.00300i | ||||
\(809\) | −1.50010e7 | + | 2.59826e7i | −0.805843 | + | 1.39576i | 0.109878 | + | 0.993945i | \(0.464954\pi\) |
−0.915721 | + | 0.401815i | \(0.868379\pi\) | |||||||
\(810\) | 3.75266e6 | + | 6.49981e6i | 0.200968 | + | 0.348087i | ||||
\(811\) | −9.00717e6 | −0.480880 | −0.240440 | − | 0.970664i | \(-0.577292\pi\) | ||||
−0.240440 | + | 0.970664i | \(0.577292\pi\) | |||||||
\(812\) | 1.56670e7 | − | 3.80195e6i | 0.833863 | − | 0.202356i | ||||
\(813\) | −4.11328e7 | −2.18254 | ||||||||
\(814\) | −6.07882e6 | − | 1.05288e7i | −0.321557 | − | 0.556953i | ||||
\(815\) | 3.56727e6 | − | 6.17870e6i | 0.188123 | − | 0.325839i | ||||
\(816\) | 1.88819e6 | − | 3.27044e6i | 0.0992703 | − | 0.171941i | ||||
\(817\) | 1.75285e6 | + | 3.03603e6i | 0.0918734 | + | 0.159129i | ||||
\(818\) | −8.66885e6 | −0.452979 | ||||||||
\(819\) | 1.81542e7 | − | 6.18439e7i | 0.945731 | − | 3.22171i | ||||
\(820\) | −8.17044e6 | −0.424337 | ||||||||
\(821\) | −1.55118e7 | − | 2.68672e7i | −0.803163 | − | 1.39112i | −0.917524 | − | 0.397679i | \(-0.869816\pi\) |
0.114362 | − | 0.993439i | \(-0.463518\pi\) | |||||||
\(822\) | 1.22580e7 | − | 2.12315e7i | 0.632763 | − | 1.09598i | ||||
\(823\) | −5.91942e6 | + | 1.02527e7i | −0.304635 | + | 0.527643i | −0.977180 | − | 0.212413i | \(-0.931868\pi\) |
0.672545 | + | 0.740056i | \(0.265201\pi\) | |||||||
\(824\) | 1.14299e6 | + | 1.97972e6i | 0.0586443 | + | 0.101575i | ||||
\(825\) | −7.05952e6 | −0.361110 | ||||||||
\(826\) | 2.16874e6 | + | 2.27418e6i | 0.110600 | + | 0.115978i | ||||
\(827\) | 3.17753e7 | 1.61557 | 0.807785 | − | 0.589478i | \(-0.200666\pi\) | ||||
0.807785 | + | 0.589478i | \(0.200666\pi\) | |||||||
\(828\) | 7.27822e6 | + | 1.26063e7i | 0.368935 | + | 0.639014i | ||||
\(829\) | −6.56550e6 | + | 1.13718e7i | −0.331804 | + | 0.574702i | −0.982866 | − | 0.184323i | \(-0.940991\pi\) |
0.651062 | + | 0.759025i | \(0.274324\pi\) | |||||||
\(830\) | 2.73051e6 | − | 4.72938e6i | 0.137578 | − | 0.238292i | ||||
\(831\) | 1.22344e7 | + | 2.11907e7i | 0.614585 | + | 1.06449i | ||||
\(832\) | −1.19315e7 | −0.597568 | ||||||||
\(833\) | 1.04114e7 | + | 6.68888e6i | 0.519870 | + | 0.333996i | ||||
\(834\) | 2.05440e7 | 1.02275 | ||||||||
\(835\) | 5.83917e6 | + | 1.01137e7i | 0.289824 | + | 0.501990i | ||||
\(836\) | 4.48499e6 | − | 7.76823e6i | 0.221945 | − | 0.384420i | ||||
\(837\) | −1.27652e7 | + | 2.21100e7i | −0.629818 | + | 1.09088i | ||||
\(838\) | −2.61139e6 | − | 4.52306e6i | −0.128458 | − | 0.222496i | ||||
\(839\) | 1.51638e7 | 0.743707 | 0.371853 | − | 0.928291i | \(-0.378722\pi\) | ||||
0.371853 | + | 0.928291i | \(0.378722\pi\) | |||||||
\(840\) | −1.05561e7 | − | 1.10693e7i | −0.516185 | − | 0.541282i | ||||
\(841\) | 1.06909e7 | 0.521224 | ||||||||
\(842\) | −5.05438e6 | − | 8.75444e6i | −0.245690 | − | 0.425547i | ||||
\(843\) | 2.04297e7 | − | 3.53853e7i | 0.990132 | − | 1.71496i | ||||
\(844\) | −4.16161e6 | + | 7.20812e6i | −0.201097 | + | 0.348310i | ||||
\(845\) | 6.20064e6 | + | 1.07398e7i | 0.298741 | + | 0.517434i | ||||
\(846\) | 3.09304e7 | 1.48580 | ||||||||
\(847\) | −116219. | + | 395911.i | −0.00556634 | + | 0.0189622i | ||||
\(848\) | −1.00437e6 | −0.0479627 | ||||||||
\(849\) | −2.41241e7 | − | 4.17841e7i | −1.14863 | − | 1.98949i | ||||
\(850\) | 718000. | − | 1.24361e6i | 0.0340861 | − | 0.0590389i | ||||
\(851\) | 5.88764e6 | − | 1.01977e7i | 0.278687 | − | 0.482700i | ||||
\(852\) | 9.61585e6 | + | 1.66551e7i | 0.453825 | + | 0.786048i | ||||
\(853\) | 1.27022e7 | 0.597733 | 0.298866 | − | 0.954295i | \(-0.403392\pi\) | ||||
0.298866 | + | 0.954295i | \(0.403392\pi\) | |||||||
\(854\) | 7.42035e6 | − | 1.80072e6i | 0.348160 | − | 0.0844891i | ||||
\(855\) | 1.32688e7 | 0.620749 | ||||||||
\(856\) | 6.30160e6 | + | 1.09147e7i | 0.293945 | + | 0.509128i | ||||
\(857\) | −1.26910e6 | + | 2.19814e6i | −0.0590260 | + | 0.102236i | −0.894028 | − | 0.448010i | \(-0.852133\pi\) |
0.835002 | + | 0.550246i | \(0.185466\pi\) | |||||||
\(858\) | −1.64129e7 | + | 2.84279e7i | −0.761143 | + | 1.31834i | ||||
\(859\) | 913028. | + | 1.58141e6i | 0.0422184 | + | 0.0731243i | 0.886362 | − | 0.462992i | \(-0.153224\pi\) |
−0.844144 | + | 0.536116i | \(0.819891\pi\) | |||||||
\(860\) | 1.96247e6 | 0.0904807 | ||||||||
\(861\) | −5.15484e7 | + | 1.25094e7i | −2.36977 | + | 0.575080i | ||||
\(862\) | 9.87075e6 | 0.452462 | ||||||||
\(863\) | −1.89628e7 | − | 3.28446e7i | −0.866714 | − | 1.50119i | −0.865335 | − | 0.501194i | \(-0.832894\pi\) |
−0.00137974 | − | 0.999999i | \(-0.500439\pi\) | |||||||
\(864\) | −2.42883e7 | + | 4.20685e7i | −1.10691 | + | 1.91722i | ||||
\(865\) | −377054. | + | 653076.i | −0.0171342 | + | 0.0296772i | ||||
\(866\) | 8.46421e6 | + | 1.46604e7i | 0.383523 | + | 0.664281i | ||||
\(867\) | −2.44638e7 | −1.10529 | ||||||||
\(868\) | 2.56037e6 | − | 8.72212e6i | 0.115346 | − | 0.392937i | ||||
\(869\) | 6.34693e6 | 0.285111 | ||||||||
\(870\) | −6.07280e6 | − | 1.05184e7i | −0.272014 | − | 0.471142i | ||||
\(871\) | −3.10614e7 | + | 5.37999e7i | −1.38731 | + | 2.40290i | ||||
\(872\) | 1.16565e7 | − | 2.01897e7i | 0.519132 | − | 0.899163i | ||||
\(873\) | 3.98929e7 | + | 6.90965e7i | 1.77158 | + | 3.06846i | ||||
\(874\) | −3.80003e6 | −0.168271 | ||||||||
\(875\) | 1.39797e6 | + | 1.46593e6i | 0.0617272 | + | 0.0647283i | ||||
\(876\) | −2.31534e7 | −1.01942 | ||||||||
\(877\) | 8.02684e6 | + | 1.39029e7i | 0.352408 | + | 0.610388i | 0.986671 | − | 0.162729i | \(-0.0520297\pi\) |
−0.634263 | + | 0.773117i | \(0.718696\pi\) | |||||||
\(878\) | −791720. | + | 1.37130e6i | −0.0346606 | + | 0.0600338i | ||||
\(879\) | 8.69216e6 | − | 1.50553e7i | 0.379451 | − | 0.657228i | ||||
\(880\) | −932184. | − | 1.61459e6i | −0.0405784 | − | 0.0702839i | ||||
\(881\) | −2.93698e6 | −0.127486 | −0.0637428 | − | 0.997966i | \(-0.520304\pi\) | ||||
−0.0637428 | + | 0.997966i | \(0.520304\pi\) | |||||||
\(882\) | −2.35551e7 | − | 1.51332e7i | −1.01956 | − | 0.655029i | ||||
\(883\) | 5.42066e6 | 0.233965 | 0.116982 | − | 0.993134i | \(-0.462678\pi\) | ||||
0.116982 | + | 0.993134i | \(0.462678\pi\) | |||||||
\(884\) | 7.63291e6 | + | 1.32206e7i | 0.328518 | + | 0.569010i | ||||
\(885\) | −2.70633e6 | + | 4.68750e6i | −0.116151 | + | 0.201179i | ||||
\(886\) | 5.27982e6 | − | 9.14491e6i | 0.225961 | − | 0.391377i | ||||
\(887\) | −1.96850e6 | − | 3.40955e6i | −0.0840092 | − | 0.145508i | 0.820959 | − | 0.570987i | \(-0.193439\pi\) |
−0.904969 | + | 0.425478i | \(0.860106\pi\) | |||||||
\(888\) | 4.53713e7 | 1.93085 | ||||||||
\(889\) | 2.36524e7 | + | 2.48023e7i | 1.00374 | + | 1.05254i | ||||
\(890\) | 616624. | 0.0260943 | ||||||||
\(891\) | 1.94943e7 | + | 3.37651e7i | 0.822645 | + | 1.42486i | ||||
\(892\) | 6.07528e6 | − | 1.05227e7i | 0.255655 | − | 0.442807i | ||||
\(893\) | 9.23024e6 | − | 1.59873e7i | 0.387333 | − | 0.670880i | ||||
\(894\) | 1.11500e6 | + | 1.93123e6i | 0.0466584 | + | 0.0808146i | ||||
\(895\) | 1.48594e7 | 0.620075 | ||||||||
\(896\) | 5.54257e6 | − | 1.88812e7i | 0.230643 | − | 0.785706i | ||||
\(897\) | −3.17933e7 | −1.31933 | ||||||||
\(898\) | −3.12072e6 | − | 5.40525e6i | −0.129141 | − | 0.223679i | ||||
\(899\) | 8.79658e6 | − | 1.52361e7i | 0.363007 | − | 0.628746i | ||||
\(900\) | 3.71389e6 | − | 6.43264e6i | 0.152835 | − | 0.264718i | ||||
\(901\) | −2.00934e6 | − | 3.48028e6i | −0.0824596 | − | 0.142824i | ||||
\(902\) | 1.85646e7 | 0.759749 | ||||||||
\(903\) | 1.23815e7 | − | 3.00464e6i | 0.505304 | − | 0.122623i | ||||
\(904\) | −1.05420e7 | −0.429045 | ||||||||
\(905\) | 1.94040e6 | + | 3.36088e6i | 0.0787537 | + | 0.136405i | ||||
\(906\) | −1.14187e7 | + | 1.97777e7i | −0.462162 | + | 0.800488i | ||||
\(907\) | −976709. | + | 1.69171e6i | −0.0394228 | + | 0.0682822i | −0.885064 | − | 0.465470i | \(-0.845885\pi\) |
0.845641 | + | 0.533752i | \(0.179219\pi\) | |||||||
\(908\) | −1.37222e6 | − | 2.37676e6i | −0.0552344 | − | 0.0956689i | ||||
\(909\) | −6.77607e7 | −2.72000 | ||||||||
\(910\) | 9.15333e6 | − | 2.22126e6i | 0.366417 | − | 0.0889195i | ||||
\(911\) | 3.17289e7 | 1.26666 | 0.633329 | − | 0.773882i | \(-0.281688\pi\) | ||||
0.633329 | + | 0.773882i | \(0.281688\pi\) | |||||||
\(912\) | 2.54965e6 | + | 4.41612e6i | 0.101506 | + | 0.175814i | ||||
\(913\) | 1.41844e7 | − | 2.45681e7i | 0.563163 | − | 0.975426i | ||||
\(914\) | 1.84838e6 | − | 3.20148e6i | 0.0731855 | − | 0.126761i | ||||
\(915\) | 6.57589e6 | + | 1.13898e7i | 0.259658 | + | 0.449741i | ||||
\(916\) | −2.40063e7 | −0.945338 | ||||||||
\(917\) | −4.01650e6 | + | 1.36825e7i | −0.157734 | + | 0.537333i | ||||
\(918\) | −1.86243e7 | −0.729415 | ||||||||
\(919\) | 245575. | + | 425348.i | 0.00959169 | + | 0.0166133i | 0.870781 | − | 0.491670i | \(-0.163613\pi\) |
−0.861190 | + | 0.508284i | \(0.830280\pi\) | |||||||
\(920\) | −2.59245e6 | + | 4.49026e6i | −0.100981 | + | 0.174905i | ||||
\(921\) | 2.67982e7 | − | 4.64159e7i | 1.04101 | − | 1.80309i | ||||
\(922\) | 1.32445e7 | + | 2.29401e7i | 0.513106 | + | 0.888726i | ||||
\(923\) | −2.88653e7 | −1.11525 | ||||||||
\(924\) | −2.24981e7 | − | 2.35919e7i | −0.866892 | − | 0.909041i | ||||
\(925\) | −6.00861e6 | −0.230898 | ||||||||
\(926\) | −7.51471e6 | − | 1.30159e7i | −0.287995 | − | 0.498822i | ||||
\(927\) | −3.60350e6 | + | 6.24145e6i | −0.137729 | + | 0.238554i | ||||
\(928\) | 1.67371e7 | − | 2.89896e7i | 0.637986 | − | 1.10502i | ||||
\(929\) | −1.38975e7 | − | 2.40712e7i | −0.528320 | − | 0.915077i | −0.999455 | − | 0.0330157i | \(-0.989489\pi\) |
0.471135 | − | 0.882061i | \(-0.343844\pi\) | |||||||
\(930\) | −6.84825e6 | −0.259641 | ||||||||
\(931\) | −1.48514e7 | + | 7.65908e6i | −0.561554 | + | 0.289603i | ||||
\(932\) | −3.14365e6 | −0.118548 | ||||||||
\(933\) | −2.93077e7 | − | 5.07625e7i | −1.10225 | − | 1.90914i | ||||
\(934\) | 7.09499e6 | − | 1.22889e7i | 0.266124 | − | 0.460941i | ||||
\(935\) | 3.72985e6 | − | 6.46030e6i | 0.139528 | − | 0.241670i | ||||
\(936\) | −4.20915e7 | − | 7.29046e7i | −1.57038 | − | 2.71998i | ||||
\(937\) | 2.96127e7 | 1.10187 | 0.550934 | − | 0.834549i | \(-0.314272\pi\) | ||||
0.550934 | + | 0.834549i | \(0.314272\pi\) | |||||||
\(938\) | 1.86232e7 | + | 1.95287e7i | 0.691111 | + | 0.724713i | ||||
\(939\) | 7.64665e7 | 2.83013 | ||||||||
\(940\) | −5.16702e6 | − | 8.94955e6i | −0.190731 | − | 0.330355i | ||||
\(941\) | −2.46773e7 | + | 4.27423e7i | −0.908497 | + | 1.57356i | −0.0923449 | + | 0.995727i | \(0.529436\pi\) |
−0.816152 | + | 0.577837i | \(0.803897\pi\) | |||||||
\(942\) | −1.14050e7 | + | 1.97540e7i | −0.418762 | + | 0.725317i | ||||
\(943\) | 8.99039e6 | + | 1.55718e7i | 0.329230 | + | 0.570243i | ||||
\(944\) | −1.42944e6 | −0.0522080 | ||||||||
\(945\) | 7.39986e6 | − | 2.52082e7i | 0.269553 | − | 0.918254i | ||||
\(946\) | −4.45906e6 | −0.162000 | ||||||||
\(947\) | 5.84586e6 | + | 1.01253e7i | 0.211823 | + | 0.366889i | 0.952285 | − | 0.305210i | \(-0.0987265\pi\) |
−0.740462 | + | 0.672098i | \(0.765393\pi\) | |||||||
\(948\) | −4.85892e6 | + | 8.41589e6i | −0.175598 | + | 0.304144i | ||||
\(949\) | 1.73758e7 | − | 3.00957e7i | 0.626294 | − | 1.08477i | ||||
\(950\) | 969528. | + | 1.67927e6i | 0.0348539 | + | 0.0603687i | ||||
\(951\) | −4.21450e7 | −1.51110 | ||||||||
\(952\) | 1.57070e7 | − | 3.81167e6i | 0.561696 | − | 0.136308i | ||||
\(953\) | 5.11241e7 | 1.82345 | 0.911725 | − | 0.410802i | \(-0.134751\pi\) | ||||
0.911725 | + | 0.410802i | \(0.134751\pi\) | |||||||
\(954\) | 4.54602e6 | + | 7.87394e6i | 0.161719 | + | 0.280105i | ||||
\(955\) | 4.01201e6 | − | 6.94901e6i | 0.142349 | − | 0.246555i | ||||
\(956\) | −5.66196e6 | + | 9.80681e6i | −0.200365 | + | 0.347043i | ||||
\(957\) | −3.15469e7 | − | 5.46408e7i | −1.11347 | − | 1.92858i | ||||
\(958\) | −2.72872e7 | −0.960604 | ||||||||
\(959\) | −3.55126e7 | + | 8.61795e6i | −1.24691 | + | 0.302592i | ||||
\(960\) | −8.92697e6 | −0.312627 | ||||||||
\(961\) | 9.35466e6 | + | 1.62027e7i | 0.326753 | + | 0.565953i | ||||
\(962\) | −1.39696e7 | + | 2.41960e7i | −0.486683 | + | 0.842960i | ||||
\(963\) | −1.98670e7 | + | 3.44106e7i | −0.690345 | + | 1.19571i | ||||
\(964\) | −286029. | − | 495418.i | −0.00991330 | − | 0.0171703i | ||||
\(965\) | 1.81809e7 | 0.628487 | ||||||||
\(966\) | −3.88992e6 | + | 1.32514e7i | −0.134121 | + | 0.456896i | ||||
\(967\) | 3.09492e7 | 1.06435 | 0.532173 | − | 0.846636i | \(-0.321376\pi\) | ||||
0.532173 | + | 0.846636i | \(0.321376\pi\) | |||||||
\(968\) | 269461. | + | 466720.i | 0.00924288 | + | 0.0160091i | ||||
\(969\) | −1.02017e7 | + | 1.76698e7i | −0.349029 | + | 0.604536i | ||||
\(970\) | −5.82981e6 | + | 1.00975e7i | −0.198941 | + | 0.344577i | ||||
\(971\) | −2.34720e7 | − | 4.06546e7i | −0.798917 | − | 1.38376i | −0.920322 | − | 0.391161i | \(-0.872073\pi\) |
0.121405 | − | 0.992603i | \(-0.461260\pi\) | |||||||
\(972\) | −1.58440e7 | −0.537897 | ||||||||
\(973\) | −2.11336e7 | − | 2.21611e7i | −0.715635 | − | 0.750429i | ||||
\(974\) | −2.82577e7 | −0.954420 | ||||||||
\(975\) | 8.11165e6 | + | 1.40498e7i | 0.273274 | + | 0.473324i | ||||
\(976\) | −1.73665e6 | + | 3.00796e6i | −0.0583561 | + | 0.101076i | ||||
\(977\) | −1.69606e7 | + | 2.93767e7i | −0.568467 | + | 0.984614i | 0.428250 | + | 0.903660i | \(0.359130\pi\) |
−0.996718 | + | 0.0809543i | \(0.974203\pi\) | |||||||
\(978\) | −1.24103e7 | − | 2.14954e7i | −0.414894 | − | 0.718617i | ||||
\(979\) | 3.20322e6 | 0.106815 | ||||||||
\(980\) | −443757. | + | 9.34361e6i | −0.0147598 | + | 0.310777i | ||||
\(981\) | 7.34988e7 | 2.43841 | ||||||||
\(982\) | 6.69877e6 | + | 1.16026e7i | 0.221675 | + | 0.383952i | ||||
\(983\) | −7.36307e6 | + | 1.27532e7i | −0.243038 | + | 0.420955i | −0.961578 | − | 0.274531i | \(-0.911477\pi\) |
0.718540 | + | 0.695486i | \(0.244811\pi\) | |||||||
\(984\) | −3.46409e7 | + | 5.99998e7i | −1.14052 | + | 1.97543i | ||||
\(985\) | −9.41149e6 | − | 1.63012e7i | −0.309078 | − | 0.535339i | ||||
\(986\) | 1.28341e7 | 0.420411 | ||||||||
\(987\) | −4.63017e7 | − | 4.85529e7i | −1.51288 | − | 1.58643i | ||||
\(988\) | −2.06137e7 | −0.671836 | ||||||||
\(989\) | −2.15941e6 | − | 3.74021e6i | −0.0702012 | − | 0.121592i | ||||
\(990\) | −8.43860e6 | + | 1.46161e7i | −0.273642 | + | 0.473961i | ||||
\(991\) | −411387. | + | 712543.i | −0.0133066 | + | 0.0230477i | −0.872602 | − | 0.488432i | \(-0.837569\pi\) |
0.859295 | + | 0.511480i | \(0.170902\pi\) | |||||||
\(992\) | −9.43717e6 | − | 1.63457e7i | −0.304483 | − | 0.527380i | ||||
\(993\) | 2.18174e7 | 0.702148 | ||||||||
\(994\) | −3.53168e6 | + | 1.20310e7i | −0.113374 | + | 0.386219i | ||||
\(995\) | −2.41588e6 | −0.0773603 | ||||||||
\(996\) | 2.17179e7 | + | 3.76164e7i | 0.693695 | + | 1.20152i | ||||
\(997\) | −5.50332e6 | + | 9.53203e6i | −0.175342 | + | 0.303702i | −0.940280 | − | 0.340403i | \(-0.889437\pi\) |
0.764937 | + | 0.644105i | \(0.222770\pi\) | |||||||
\(998\) | 5.70794e6 | − | 9.88644e6i | 0.181406 | − | 0.314205i | ||||
\(999\) | 3.89646e7 | + | 6.74887e7i | 1.23526 | + | 2.13953i |
(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 | 35.6.e.a.11.2 | ✓ | 12 | |
7.2 | even | 3 | inner | 35.6.e.a.16.2 | yes | 12 | |
7.3 | odd | 6 | 245.6.a.h.1.5 | 6 | |||
7.4 | even | 3 | 245.6.a.i.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.e.a.11.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
35.6.e.a.16.2 | yes | 12 | 7.2 | even | 3 | inner | |
245.6.a.h.1.5 | 6 | 7.3 | odd | 6 | |||
245.6.a.i.1.5 | 6 | 7.4 | even | 3 |