Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,7,Mod(19,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.d (of order \(2\), degree \(1\), 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: | \(4.60108167240\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} - 10x^{8} - 1775x^{6} - 1000x^{4} + 160000x^{2} + 1000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.11 | ||
Root | \(0.826519 + 3.05235i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.19 |
Dual form | 20.7.d.d.19.12 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.42116 | − | 2.98770i | 0.927645 | − | 0.373462i | ||||
\(3\) | −6.08848 | −0.225499 | −0.112750 | − | 0.993623i | \(-0.535966\pi\) | ||||
−0.112750 | + | 0.993623i | \(0.535966\pi\) | |||||||
\(4\) | 46.1473 | − | 44.3444i | 0.721052 | − | 0.692881i | ||||
\(5\) | 26.7958 | − | 122.094i | 0.214366 | − | 0.976753i | ||||
\(6\) | −45.1836 | + | 18.1905i | −0.209184 | + | 0.0842155i | ||||
\(7\) | 422.345 | 1.23133 | 0.615663 | − | 0.788010i | \(-0.288888\pi\) | ||||
0.615663 | + | 0.788010i | \(0.288888\pi\) | |||||||
\(8\) | 209.979 | − | 466.961i | 0.410116 | − | 0.912033i | ||||
\(9\) | −691.930 | −0.949150 | ||||||||
\(10\) | −165.925 | − | 986.138i | −0.165925 | − | 0.986138i | ||||
\(11\) | 1743.93i | 1.31024i | 0.755526 | + | 0.655119i | \(0.227382\pi\) | ||||
−0.755526 | + | 0.655119i | \(0.772618\pi\) | |||||||
\(12\) | −280.967 | + | 269.990i | −0.162597 | + | 0.156244i | ||||
\(13\) | − | 898.704i | − | 0.409060i | −0.978860 | − | 0.204530i | \(-0.934433\pi\) | ||
0.978860 | − | 0.204530i | \(-0.0655666\pi\) | |||||||
\(14\) | 3134.29 | − | 1261.84i | 1.14223 | − | 0.459854i | ||||
\(15\) | −163.146 | + | 743.368i | −0.0483395 | + | 0.220257i | ||||
\(16\) | 163.152 | − | 4092.75i | 0.0398321 | − | 0.999206i | ||||
\(17\) | 5542.94i | 1.12822i | 0.825700 | + | 0.564110i | \(0.190781\pi\) | ||||
−0.825700 | + | 0.564110i | \(0.809219\pi\) | |||||||
\(18\) | −5134.93 | + | 2067.28i | −0.880475 | + | 0.354472i | ||||
\(19\) | 8906.74i | 1.29855i | 0.760554 | + | 0.649274i | \(0.224927\pi\) | ||||
−0.760554 | + | 0.649274i | \(0.775073\pi\) | |||||||
\(20\) | −4177.64 | − | 6822.56i | −0.522205 | − | 0.852820i | ||||
\(21\) | −2571.44 | −0.277663 | ||||||||
\(22\) | 5210.33 | + | 12942.0i | 0.489324 | + | 1.21544i | ||||
\(23\) | −3740.11 | −0.307398 | −0.153699 | − | 0.988118i | \(-0.549119\pi\) | ||||
−0.153699 | + | 0.988118i | \(0.549119\pi\) | |||||||
\(24\) | −1278.46 | + | 2843.09i | −0.0924809 | + | 0.205663i | ||||
\(25\) | −14189.0 | − | 6543.22i | −0.908094 | − | 0.418766i | ||||
\(26\) | −2685.06 | − | 6669.43i | −0.152768 | − | 0.379462i | ||||
\(27\) | 8651.31 | 0.439532 | ||||||||
\(28\) | 19490.1 | − | 18728.6i | 0.887850 | − | 0.853162i | ||||
\(29\) | 31180.3 | 1.27846 | 0.639229 | − | 0.769016i | \(-0.279253\pi\) | ||||
0.639229 | + | 0.769016i | \(0.279253\pi\) | |||||||
\(30\) | 1010.23 | + | 6004.09i | 0.0374159 | + | 0.222374i | ||||
\(31\) | − | 22647.9i | − | 0.760227i | −0.924940 | − | 0.380113i | \(-0.875885\pi\) | ||
0.924940 | − | 0.380113i | \(-0.124115\pi\) | |||||||
\(32\) | −11017.1 | − | 30860.4i | −0.336216 | − | 0.941785i | ||||
\(33\) | − | 10617.9i | − | 0.295458i | ||||||
\(34\) | 16560.6 | + | 41135.1i | 0.421347 | + | 1.04659i | ||||
\(35\) | 11317.1 | − | 51565.8i | 0.263955 | − | 1.20270i | ||||
\(36\) | −31930.7 | + | 30683.2i | −0.684387 | + | 0.657648i | ||||
\(37\) | − | 14997.5i | − | 0.296082i | −0.988981 | − | 0.148041i | \(-0.952703\pi\) | ||
0.988981 | − | 0.148041i | \(-0.0472968\pi\) | |||||||
\(38\) | 26610.7 | + | 66098.4i | 0.484959 | + | 1.20459i | ||||
\(39\) | 5471.75i | 0.0922427i | ||||||||
\(40\) | −51386.7 | − | 38149.8i | −0.802917 | − | 0.596091i | ||||
\(41\) | 6598.75 | 0.0957436 | 0.0478718 | − | 0.998853i | \(-0.484756\pi\) | ||||
0.0478718 | + | 0.998853i | \(0.484756\pi\) | |||||||
\(42\) | −19083.1 | + | 7682.68i | −0.257573 | + | 0.103697i | ||||
\(43\) | −81078.0 | −1.01976 | −0.509880 | − | 0.860246i | \(-0.670310\pi\) | ||||
−0.509880 | + | 0.860246i | \(0.670310\pi\) | |||||||
\(44\) | 77333.4 | + | 80477.6i | 0.907839 | + | 0.944750i | ||||
\(45\) | −18540.8 | + | 84480.7i | −0.203466 | + | 0.927085i | ||||
\(46\) | −27756.0 | + | 11174.3i | −0.285156 | + | 0.114802i | ||||
\(47\) | −30231.0 | −0.291178 | −0.145589 | − | 0.989345i | \(-0.546508\pi\) | ||||
−0.145589 | + | 0.989345i | \(0.546508\pi\) | |||||||
\(48\) | −993.349 | + | 24918.6i | −0.00898211 | + | 0.225320i | ||||
\(49\) | 60726.1 | 0.516164 | ||||||||
\(50\) | −124848. | − | 6165.93i | −0.998783 | − | 0.0493274i | ||||
\(51\) | − | 33748.1i | − | 0.254413i | ||||||
\(52\) | −39852.5 | − | 41472.8i | −0.283430 | − | 0.294953i | ||||
\(53\) | − | 17256.7i | − | 0.115913i | −0.998319 | − | 0.0579563i | \(-0.981542\pi\) | ||
0.998319 | − | 0.0579563i | \(-0.0184584\pi\) | |||||||
\(54\) | 64202.8 | − | 25847.5i | 0.407730 | − | 0.164149i | ||||
\(55\) | 212923. | + | 46729.9i | 1.27978 | + | 0.280871i | ||||
\(56\) | 88683.7 | − | 197219.i | 0.504986 | − | 1.12301i | ||||
\(57\) | − | 54228.6i | − | 0.292822i | ||||||
\(58\) | 231394. | − | 93157.4i | 1.18596 | − | 0.477456i | ||||
\(59\) | 294323.i | 1.43307i | 0.697550 | + | 0.716536i | \(0.254273\pi\) | ||||
−0.697550 | + | 0.716536i | \(0.745727\pi\) | |||||||
\(60\) | 25435.5 | + | 41539.1i | 0.117757 | + | 0.192310i | ||||
\(61\) | −211992. | −0.933963 | −0.466982 | − | 0.884267i | \(-0.654659\pi\) | ||||
−0.466982 | + | 0.884267i | \(0.654659\pi\) | |||||||
\(62\) | −67665.1 | − | 168074.i | −0.283916 | − | 0.705221i | ||||
\(63\) | −292233. | −1.16871 | ||||||||
\(64\) | −173961. | − | 196104.i | −0.663610 | − | 0.748079i | ||||
\(65\) | −109727. | − | 24081.5i | −0.399550 | − | 0.0876886i | ||||
\(66\) | −31723.0 | − | 78797.0i | −0.110342 | − | 0.274080i | ||||
\(67\) | 452884. | 1.50578 | 0.752891 | − | 0.658145i | \(-0.228659\pi\) | ||||
0.752891 | + | 0.658145i | \(0.228659\pi\) | |||||||
\(68\) | 245798. | + | 255792.i | 0.781722 | + | 0.813505i | ||||
\(69\) | 22771.6 | 0.0693181 | ||||||||
\(70\) | −70077.4 | − | 416490.i | −0.204307 | − | 1.21426i | ||||
\(71\) | 246386.i | 0.688401i | 0.938896 | + | 0.344201i | \(0.111850\pi\) | ||||
−0.938896 | + | 0.344201i | \(0.888150\pi\) | |||||||
\(72\) | −145291. | + | 323105.i | −0.389261 | + | 0.865657i | ||||
\(73\) | − | 476862.i | − | 1.22581i | −0.790155 | − | 0.612907i | \(-0.790000\pi\) | ||
0.790155 | − | 0.612907i | \(-0.210000\pi\) | |||||||
\(74\) | −44807.9 | − | 111299.i | −0.110576 | − | 0.274659i | ||||
\(75\) | 86389.3 | + | 39838.3i | 0.204775 | + | 0.0944315i | ||||
\(76\) | 394964. | + | 411022.i | 0.899740 | + | 0.936321i | ||||
\(77\) | 736539.i | 1.61333i | ||||||||
\(78\) | 16347.9 | + | 40606.7i | 0.0344492 | + | 0.0855686i | ||||
\(79\) | − | 680467.i | − | 1.38015i | −0.723738 | − | 0.690075i | \(-0.757578\pi\) | ||
0.723738 | − | 0.690075i | \(-0.242422\pi\) | |||||||
\(80\) | −495329. | − | 129588.i | −0.967440 | − | 0.253102i | ||||
\(81\) | 451744. | 0.850036 | ||||||||
\(82\) | 48970.4 | − | 19715.1i | 0.0888161 | − | 0.0357566i | ||||
\(83\) | −1.03860e6 | −1.81641 | −0.908207 | − | 0.418521i | \(-0.862549\pi\) | ||||
−0.908207 | + | 0.418521i | \(0.862549\pi\) | |||||||
\(84\) | −118665. | + | 114029.i | −0.200210 | + | 0.192388i | ||||
\(85\) | 676761. | + | 148528.i | 1.10199 | + | 0.241852i | ||||
\(86\) | −601693. | + | 242237.i | −0.945975 | + | 0.380842i | ||||
\(87\) | −189841. | −0.288292 | ||||||||
\(88\) | 814346. | + | 366189.i | 1.19498 | + | 0.537349i | ||||
\(89\) | −937027. | −1.32918 | −0.664588 | − | 0.747210i | \(-0.731393\pi\) | ||||
−0.664588 | + | 0.747210i | \(0.731393\pi\) | |||||||
\(90\) | 114808. | + | 682339.i | 0.157487 | + | 0.935993i | ||||
\(91\) | − | 379563.i | − | 0.503686i | ||||||
\(92\) | −172596. | + | 165853.i | −0.221650 | + | 0.212990i | ||||
\(93\) | 137891.i | 0.171431i | ||||||||
\(94\) | −224349. | + | 90321.0i | −0.270110 | + | 0.108744i | ||||
\(95\) | 1.08746e6 | + | 238663.i | 1.26836 | + | 0.278365i | ||||
\(96\) | 67077.6 | + | 187893.i | 0.0758165 | + | 0.212372i | ||||
\(97\) | − | 957172.i | − | 1.04876i | −0.851485 | − | 0.524379i | \(-0.824298\pi\) | ||
0.851485 | − | 0.524379i | \(-0.175702\pi\) | |||||||
\(98\) | 450659. | − | 181431.i | 0.478817 | − | 0.192768i | ||||
\(99\) | − | 1.20668e6i | − | 1.24361i | ||||||
\(100\) | −944938. | + | 327249.i | −0.944938 | + | 0.327249i | ||||
\(101\) | 561162. | 0.544658 | 0.272329 | − | 0.962204i | \(-0.412206\pi\) | ||||
0.272329 | + | 0.962204i | \(0.412206\pi\) | |||||||
\(102\) | −100829. | − | 250450.i | −0.0950136 | − | 0.236005i | ||||
\(103\) | −649255. | −0.594161 | −0.297080 | − | 0.954852i | \(-0.596013\pi\) | ||||
−0.297080 | + | 0.954852i | \(0.596013\pi\) | |||||||
\(104\) | −419660. | − | 188709.i | −0.373076 | − | 0.167762i | ||||
\(105\) | −68903.7 | + | 313958.i | −0.0595216 | + | 0.271209i | ||||
\(106\) | −51557.9 | − | 128065.i | −0.0432890 | − | 0.107526i | ||||
\(107\) | 1.01005e6 | 0.824501 | 0.412251 | − | 0.911070i | \(-0.364743\pi\) | ||||
0.412251 | + | 0.911070i | \(0.364743\pi\) | |||||||
\(108\) | 399235. | − | 383637.i | 0.316926 | − | 0.304543i | ||||
\(109\) | 202984. | 0.156741 | 0.0783703 | − | 0.996924i | \(-0.475028\pi\) | ||||
0.0783703 | + | 0.996924i | \(0.475028\pi\) | |||||||
\(110\) | 1.71975e6 | − | 289360.i | 1.29208 | − | 0.217401i | ||||
\(111\) | 91311.8i | 0.0667664i | ||||||||
\(112\) | 68906.4 | − | 1.72855e6i | 0.0490462 | − | 1.23035i | ||||
\(113\) | − | 1.50469e6i | − | 1.04283i | −0.853305 | − | 0.521413i | \(-0.825405\pi\) | ||
0.853305 | − | 0.521413i | \(-0.174595\pi\) | |||||||
\(114\) | −162019. | − | 402439.i | −0.109358 | − | 0.271635i | ||||
\(115\) | −100219. | + | 456646.i | −0.0658958 | + | 0.300252i | ||||
\(116\) | 1.43889e6 | − | 1.38267e6i | 0.921835 | − | 0.885820i | ||||
\(117\) | 621841.i | 0.388259i | ||||||||
\(118\) | 879347. | + | 2.18422e6i | 0.535198 | + | 1.32938i | ||||
\(119\) | 2.34103e6i | 1.38921i | ||||||||
\(120\) | 312867. | + | 232275.i | 0.181057 | + | 0.134418i | ||||
\(121\) | −1.26972e6 | −0.716725 | ||||||||
\(122\) | −1.57323e6 | + | 633368.i | −0.866387 | + | 0.348800i | ||||
\(123\) | −40176.4 | −0.0215901 | ||||||||
\(124\) | −1.00431e6 | − | 1.04514e6i | −0.526747 | − | 0.548163i | ||||
\(125\) | −1.17909e6 | + | 1.55706e6i | −0.603696 | + | 0.797215i | ||||
\(126\) | −2.16871e6 | + | 873104.i | −1.08415 | + | 0.436470i | ||||
\(127\) | −1.14744e6 | −0.560168 | −0.280084 | − | 0.959975i | \(-0.590362\pi\) | ||||
−0.280084 | + | 0.959975i | \(0.590362\pi\) | |||||||
\(128\) | −1.87690e6 | − | 935578.i | −0.894974 | − | 0.446118i | ||||
\(129\) | 493642. | 0.229955 | ||||||||
\(130\) | −886247. | + | 149117.i | −0.403390 | + | 0.0678731i | ||||
\(131\) | 2.85296e6i | 1.26906i | 0.772899 | + | 0.634529i | \(0.218806\pi\) | ||||
−0.772899 | + | 0.634529i | \(0.781194\pi\) | |||||||
\(132\) | −470843. | − | 489987.i | −0.204717 | − | 0.213041i | ||||
\(133\) | 3.76172e6i | 1.59894i | ||||||||
\(134\) | 3.36092e6 | − | 1.35308e6i | 1.39683 | − | 0.562353i | ||||
\(135\) | 231819. | − | 1.05627e6i | 0.0942209 | − | 0.429315i | ||||
\(136\) | 2.58834e6 | + | 1.16390e6i | 1.02897 | + | 0.462701i | ||||
\(137\) | − | 1.39333e6i | − | 0.541866i | −0.962598 | − | 0.270933i | \(-0.912668\pi\) | ||
0.962598 | − | 0.270933i | \(-0.0873321\pi\) | |||||||
\(138\) | 168992. | − | 68034.7i | 0.0643026 | − | 0.0258877i | ||||
\(139\) | 489730.i | 0.182353i | 0.995835 | + | 0.0911764i | \(0.0290627\pi\) | ||||
−0.995835 | + | 0.0911764i | \(0.970937\pi\) | |||||||
\(140\) | −1.76440e6 | − | 2.88147e6i | −0.643004 | − | 1.05010i | ||||
\(141\) | 184061. | 0.0656605 | ||||||||
\(142\) | 736128. | + | 1.82847e6i | 0.257092 | + | 0.638592i | ||||
\(143\) | 1.56727e6 | 0.535966 | ||||||||
\(144\) | −112890. | + | 2.83190e6i | −0.0378066 | + | 0.948397i | ||||
\(145\) | 835501. | − | 3.80694e6i | 0.274058 | − | 1.24874i | ||||
\(146\) | −1.42472e6 | − | 3.53887e6i | −0.457795 | − | 1.13712i | ||||
\(147\) | −369730. | −0.116395 | ||||||||
\(148\) | −665053. | − | 692093.i | −0.205150 | − | 0.213491i | ||||
\(149\) | 1.02592e6 | 0.310138 | 0.155069 | − | 0.987904i | \(-0.450440\pi\) | ||||
0.155069 | + | 0.987904i | \(0.450440\pi\) | |||||||
\(150\) | 760134. | + | 37541.2i | 0.225225 | + | 0.0111233i | ||||
\(151\) | − | 4.68243e6i | − | 1.36000i | −0.733210 | − | 0.680002i | \(-0.761979\pi\) | ||
0.733210 | − | 0.680002i | \(-0.238021\pi\) | |||||||
\(152\) | 4.15910e6 | + | 1.87023e6i | 1.18432 | + | 0.532555i | ||||
\(153\) | − | 3.83533e6i | − | 1.07085i | ||||||
\(154\) | 2.20055e6 | + | 5.46597e6i | 0.602518 | + | 1.49660i | ||||
\(155\) | −2.76518e6 | − | 606869.i | −0.742554 | − | 0.162967i | ||||
\(156\) | 242641. | + | 252507.i | 0.0639132 | + | 0.0665118i | ||||
\(157\) | 3.46076e6i | 0.894278i | 0.894464 | + | 0.447139i | \(0.147557\pi\) | ||||
−0.894464 | + | 0.447139i | \(0.852443\pi\) | |||||||
\(158\) | −2.03303e6 | − | 5.04986e6i | −0.515433 | − | 1.28029i | ||||
\(159\) | 105067.i | 0.0261382i | ||||||||
\(160\) | −4.06309e6 | + | 518197.i | −0.991965 | + | 0.126513i | ||||
\(161\) | −1.57962e6 | −0.378507 | ||||||||
\(162\) | 3.35246e6 | − | 1.34967e6i | 0.788532 | − | 0.317456i | ||||
\(163\) | 5.02544e6 | 1.16041 | 0.580205 | − | 0.814471i | \(-0.302972\pi\) | ||||
0.580205 | + | 0.814471i | \(0.302972\pi\) | |||||||
\(164\) | 304514. | − | 292617.i | 0.0690361 | − | 0.0663389i | ||||
\(165\) | −1.29638e6 | − | 284514.i | −0.288590 | − | 0.0633362i | ||||
\(166\) | −7.70764e6 | + | 3.10303e6i | −1.68499 | + | 0.678362i | ||||
\(167\) | 1.81735e6 | 0.390201 | 0.195101 | − | 0.980783i | \(-0.437497\pi\) | ||||
0.195101 | + | 0.980783i | \(0.437497\pi\) | |||||||
\(168\) | −539949. | + | 1.20076e6i | −0.113874 | + | 0.253238i | ||||
\(169\) | 4.01914e6 | 0.832670 | ||||||||
\(170\) | 5.46611e6 | − | 919711.i | 1.11258 | − | 0.187199i | ||||
\(171\) | − | 6.16285e6i | − | 1.23252i | ||||||
\(172\) | −3.74153e6 | + | 3.59535e6i | −0.735300 | + | 0.706572i | ||||
\(173\) | 2.12346e6i | 0.410115i | 0.978750 | + | 0.205058i | \(0.0657382\pi\) | ||||
−0.978750 | + | 0.205058i | \(0.934262\pi\) | |||||||
\(174\) | −1.40884e6 | + | 567187.i | −0.267432 | + | 0.107666i | ||||
\(175\) | −5.99264e6 | − | 2.76349e6i | −1.11816 | − | 0.515637i | ||||
\(176\) | 7.13746e6 | + | 284525.i | 1.30920 | + | 0.0521895i | ||||
\(177\) | − | 1.79198e6i | − | 0.323157i | ||||||
\(178\) | −6.95383e6 | + | 2.79955e6i | −1.23300 | + | 0.496397i | ||||
\(179\) | 1.28491e6i | 0.224034i | 0.993706 | + | 0.112017i | \(0.0357312\pi\) | ||||
−0.993706 | + | 0.112017i | \(0.964269\pi\) | |||||||
\(180\) | 2.89063e6 | + | 4.72074e6i | 0.495650 | + | 0.809454i | ||||
\(181\) | 1.89832e6 | 0.320136 | 0.160068 | − | 0.987106i | \(-0.448829\pi\) | ||||
0.160068 | + | 0.987106i | \(0.448829\pi\) | |||||||
\(182\) | −1.13402e6 | − | 2.81680e6i | −0.188108 | − | 0.467242i | ||||
\(183\) | 1.29071e6 | 0.210608 | ||||||||
\(184\) | −785346. | + | 1.74649e6i | −0.126069 | + | 0.280357i | ||||
\(185\) | −1.83110e6 | − | 401869.i | −0.289199 | − | 0.0634700i | ||||
\(186\) | 411978. | + | 1.02332e6i | 0.0640229 | + | 0.159027i | ||||
\(187\) | −9.66649e6 | −1.47824 | ||||||||
\(188\) | −1.39508e6 | + | 1.34057e6i | −0.209955 | + | 0.201752i | ||||
\(189\) | 3.65384e6 | 0.541207 | ||||||||
\(190\) | 8.78328e6 | − | 1.47785e6i | 1.28055 | − | 0.215461i | ||||
\(191\) | 1.10365e7i | 1.58391i | 0.610581 | + | 0.791954i | \(0.290936\pi\) | ||||
−0.610581 | + | 0.791954i | \(0.709064\pi\) | |||||||
\(192\) | 1.05916e6 | + | 1.19398e6i | 0.149644 | + | 0.168691i | ||||
\(193\) | 9.60496e6i | 1.33605i | 0.744137 | + | 0.668027i | \(0.232861\pi\) | ||||
−0.744137 | + | 0.668027i | \(0.767139\pi\) | |||||||
\(194\) | −2.85974e6 | − | 7.10333e6i | −0.391671 | − | 0.972875i | ||||
\(195\) | 668068. | + | 146620.i | 0.0900984 | + | 0.0197737i | ||||
\(196\) | 2.80235e6 | − | 2.69286e6i | 0.372181 | − | 0.357640i | ||||
\(197\) | − | 3.52707e6i | − | 0.461334i | −0.973033 | − | 0.230667i | \(-0.925909\pi\) | ||
0.973033 | − | 0.230667i | \(-0.0740908\pi\) | |||||||
\(198\) | −3.60518e6 | − | 8.95494e6i | −0.464442 | − | 1.15363i | ||||
\(199\) | − | 1.68919e6i | − | 0.214347i | −0.994240 | − | 0.107174i | \(-0.965820\pi\) | ||
0.994240 | − | 0.107174i | \(-0.0341801\pi\) | |||||||
\(200\) | −6.03482e6 | + | 5.25176e6i | −0.754352 | + | 0.656470i | ||||
\(201\) | −2.75738e6 | −0.339553 | ||||||||
\(202\) | 4.16448e6 | − | 1.67658e6i | 0.505250 | − | 0.203409i | ||||
\(203\) | 1.31688e7 | 1.57420 | ||||||||
\(204\) | −1.49654e6 | − | 1.55739e6i | −0.176278 | − | 0.183445i | ||||
\(205\) | 176819. | − | 805668.i | 0.0205242 | − | 0.0935179i | ||||
\(206\) | −4.81823e6 | + | 1.93978e6i | −0.551170 | + | 0.221897i | ||||
\(207\) | 2.58790e6 | 0.291767 | ||||||||
\(208\) | −3.67817e6 | − | 146625.i | −0.408735 | − | 0.0162937i | ||||
\(209\) | −1.55327e7 | −1.70141 | ||||||||
\(210\) | 426665. | + | 2.53580e6i | 0.0460712 | + | 0.273814i | ||||
\(211\) | 5.46799e6i | 0.582077i | 0.956711 | + | 0.291038i | \(0.0940007\pi\) | ||||
−0.956711 | + | 0.291038i | \(0.905999\pi\) | |||||||
\(212\) | −765239. | − | 796352.i | −0.0803136 | − | 0.0835790i | ||||
\(213\) | − | 1.50012e6i | − | 0.155234i | ||||||
\(214\) | 7.49574e6 | − | 3.01772e6i | 0.764845 | − | 0.307920i | ||||
\(215\) | −2.17255e6 | + | 9.89915e6i | −0.218602 | + | 0.996053i | ||||
\(216\) | 1.81660e6 | − | 4.03983e6i | 0.180259 | − | 0.400868i | ||||
\(217\) | − | 9.56523e6i | − | 0.936087i | ||||||
\(218\) | 1.50637e6 | − | 606453.i | 0.145400 | − | 0.0585367i | ||||
\(219\) | 2.90337e6i | 0.276420i | ||||||||
\(220\) | 1.18981e7 | − | 7.28549e6i | 1.11740 | − | 0.684212i | ||||
\(221\) | 4.98147e6 | 0.461509 | ||||||||
\(222\) | 272812. | + | 677640.i | 0.0249347 | + | 0.0619355i | ||||
\(223\) | 6.77154e6 | 0.610622 | 0.305311 | − | 0.952253i | \(-0.401240\pi\) | ||||
0.305311 | + | 0.952253i | \(0.401240\pi\) | |||||||
\(224\) | −4.65302e6 | − | 1.30337e7i | −0.413991 | − | 1.15964i | ||||
\(225\) | 9.81778e6 | + | 4.52745e6i | 0.861918 | + | 0.397472i | ||||
\(226\) | −4.49556e6 | − | 1.11665e7i | −0.389456 | − | 0.967372i | ||||
\(227\) | −5.17157e6 | −0.442125 | −0.221062 | − | 0.975260i | \(-0.570952\pi\) | ||||
−0.221062 | + | 0.975260i | \(0.570952\pi\) | |||||||
\(228\) | −2.40473e6 | − | 2.50250e6i | −0.202891 | − | 0.211140i | ||||
\(229\) | −1.14858e7 | −0.956432 | −0.478216 | − | 0.878242i | \(-0.658716\pi\) | ||||
−0.478216 | + | 0.878242i | \(0.658716\pi\) | |||||||
\(230\) | 620577. | + | 3.68827e6i | 0.0510049 | + | 0.303137i | ||||
\(231\) | − | 4.48440e6i | − | 0.363805i | ||||||
\(232\) | 6.54722e6 | − | 1.45600e7i | 0.524316 | − | 1.16600i | ||||
\(233\) | − | 611879.i | − | 0.0483724i | −0.999707 | − | 0.0241862i | \(-0.992301\pi\) | ||
0.999707 | − | 0.0241862i | \(-0.00769946\pi\) | |||||||
\(234\) | 1.85787e6 | + | 4.61478e6i | 0.145000 | + | 0.360167i | ||||
\(235\) | −810063. | + | 3.69103e6i | −0.0624188 | + | 0.284409i | ||||
\(236\) | 1.30516e7 | + | 1.35822e7i | 0.992948 | + | 1.03332i | ||||
\(237\) | 4.14301e6i | 0.311223i | ||||||||
\(238\) | 6.99430e6 | + | 1.73732e7i | 0.518816 | + | 1.28869i | ||||
\(239\) | − | 1.88564e7i | − | 1.38123i | −0.723225 | − | 0.690613i | \(-0.757341\pi\) | ||
0.723225 | − | 0.690613i | \(-0.242659\pi\) | |||||||
\(240\) | 3.01580e6 | + | 788997.i | 0.218157 | + | 0.0570744i | ||||
\(241\) | 1.19579e7 | 0.854285 | 0.427143 | − | 0.904184i | \(-0.359520\pi\) | ||||
0.427143 | + | 0.904184i | \(0.359520\pi\) | |||||||
\(242\) | −9.42281e6 | + | 3.79354e6i | −0.664866 | + | 0.267670i | ||||
\(243\) | −9.05724e6 | −0.631215 | ||||||||
\(244\) | −9.78286e6 | + | 9.40065e6i | −0.673436 | + | 0.647125i | ||||
\(245\) | 1.62720e6 | − | 7.41431e6i | 0.110648 | − | 0.504165i | ||||
\(246\) | −298155. | + | 120035.i | −0.0200280 | + | 0.00806310i | ||||
\(247\) | 8.00453e6 | 0.531184 | ||||||||
\(248\) | −1.05757e7 | − | 4.75559e6i | −0.693352 | − | 0.311781i | ||||
\(249\) | 6.32351e6 | 0.409600 | ||||||||
\(250\) | −4.09822e6 | + | 1.50780e7i | −0.262286 | + | 0.964990i | ||||
\(251\) | − | 4.43941e6i | − | 0.280740i | −0.990099 | − | 0.140370i | \(-0.955171\pi\) | ||
0.990099 | − | 0.140370i | \(-0.0448292\pi\) | |||||||
\(252\) | −1.34858e7 | + | 1.29589e7i | −0.842703 | + | 0.809779i | ||||
\(253\) | − | 6.52249e6i | − | 0.402765i | ||||||
\(254\) | −8.51533e6 | + | 3.42820e6i | −0.519637 | + | 0.209202i | ||||
\(255\) | −4.12045e6 | − | 904308.i | −0.248499 | − | 0.0545376i | ||||
\(256\) | −1.67240e7 | − | 1.33548e6i | −0.996827 | − | 0.0796009i | ||||
\(257\) | 3.02099e7i | 1.77971i | 0.456240 | + | 0.889857i | \(0.349196\pi\) | ||||
−0.456240 | + | 0.889857i | \(0.650804\pi\) | |||||||
\(258\) | 3.66340e6 | − | 1.47485e6i | 0.213317 | − | 0.0858796i | ||||
\(259\) | − | 6.33410e6i | − | 0.364574i | ||||||
\(260\) | −6.13147e6 | + | 3.75446e6i | −0.348854 | + | 0.213613i | ||||
\(261\) | −2.15746e7 | −1.21345 | ||||||||
\(262\) | 8.52378e6 | + | 2.11723e7i | 0.473946 | + | 1.17724i | ||||
\(263\) | −2.91425e7 | −1.60199 | −0.800994 | − | 0.598673i | \(-0.795695\pi\) | ||||
−0.800994 | + | 0.598673i | \(0.795695\pi\) | |||||||
\(264\) | −4.95813e6 | − | 2.22953e6i | −0.269468 | − | 0.121172i | ||||
\(265\) | −2.10695e6 | − | 462407.i | −0.113218 | − | 0.0248478i | ||||
\(266\) | 1.12389e7 | + | 2.79163e7i | 0.597142 | + | 1.48325i | ||||
\(267\) | 5.70508e6 | 0.299728 | ||||||||
\(268\) | 2.08994e7 | − | 2.00828e7i | 1.08575 | − | 1.04333i | ||||
\(269\) | 2.25831e7 | 1.16018 | 0.580091 | − | 0.814552i | \(-0.303017\pi\) | ||||
0.580091 | + | 0.814552i | \(0.303017\pi\) | |||||||
\(270\) | −1.43547e6 | − | 8.53139e6i | −0.0729292 | − | 0.433440i | ||||
\(271\) | − | 7.50243e6i | − | 0.376959i | −0.982077 | − | 0.188479i | \(-0.939644\pi\) | ||
0.982077 | − | 0.188479i | \(-0.0603559\pi\) | |||||||
\(272\) | 2.26859e7 | + | 904343.i | 1.12732 | + | 0.0449393i | ||||
\(273\) | 2.31096e6i | 0.113581i | ||||||||
\(274\) | −4.16284e6 | − | 1.03401e7i | −0.202366 | − | 0.502659i | ||||
\(275\) | 1.14109e7 | − | 2.47445e7i | 0.548683 | − | 1.18982i | ||||
\(276\) | 1.05085e6 | − | 1.00979e6i | 0.0499820 | − | 0.0480292i | ||||
\(277\) | − | 2.36803e7i | − | 1.11416i | −0.830459 | − | 0.557080i | \(-0.811922\pi\) | ||
0.830459 | − | 0.557080i | \(-0.188078\pi\) | |||||||
\(278\) | 1.46317e6 | + | 3.63437e6i | 0.0681019 | + | 0.169159i | ||||
\(279\) | 1.56708e7i | 0.721569i | ||||||||
\(280\) | −2.17029e7 | − | 1.61124e7i | −0.988652 | − | 0.733983i | ||||
\(281\) | 2.22984e7 | 1.00498 | 0.502488 | − | 0.864584i | \(-0.332418\pi\) | ||||
0.502488 | + | 0.864584i | \(0.332418\pi\) | |||||||
\(282\) | 1.36595e6 | − | 549918.i | 0.0609097 | − | 0.0245217i | ||||
\(283\) | −2.01491e6 | −0.0888988 | −0.0444494 | − | 0.999012i | \(-0.514153\pi\) | ||||
−0.0444494 | + | 0.999012i | \(0.514153\pi\) | |||||||
\(284\) | 1.09258e7 | + | 1.13701e7i | 0.476980 | + | 0.496373i | ||||
\(285\) | −6.62099e6 | − | 1.45310e6i | −0.286015 | − | 0.0627711i | ||||
\(286\) | 1.16310e7 | − | 4.68254e6i | 0.497186 | − | 0.200163i | ||||
\(287\) | 2.78695e6 | 0.117892 | ||||||||
\(288\) | 7.62308e6 | + | 2.13533e7i | 0.319119 | + | 0.893895i | ||||
\(289\) | −6.58667e6 | −0.272880 | ||||||||
\(290\) | −5.17358e6 | − | 3.07481e7i | −0.212128 | − | 1.26074i | ||||
\(291\) | 5.82773e6i | 0.236494i | ||||||||
\(292\) | −2.11462e7 | − | 2.20059e7i | −0.849343 | − | 0.883875i | ||||
\(293\) | − | 3.19886e7i | − | 1.27172i | −0.771804 | − | 0.635861i | \(-0.780645\pi\) | ||
0.771804 | − | 0.635861i | \(-0.219355\pi\) | |||||||
\(294\) | −2.74383e6 | + | 1.10464e6i | −0.107973 | + | 0.0434690i | ||||
\(295\) | 3.59351e7 | + | 7.88661e6i | 1.39976 | + | 0.307202i | ||||
\(296\) | −7.00323e6 | − | 3.14916e6i | −0.270037 | − | 0.121428i | ||||
\(297\) | 1.50873e7i | 0.575892i | ||||||||
\(298\) | 7.61353e6 | − | 3.06514e6i | 0.287698 | − | 0.115825i | ||||
\(299\) | 3.36126e6i | 0.125744i | ||||||||
\(300\) | 5.75324e6 | − | 1.99245e6i | 0.213083 | − | 0.0737945i | ||||
\(301\) | −3.42429e7 | −1.25566 | ||||||||
\(302\) | −1.39897e7 | − | 3.47491e7i | −0.507910 | − | 1.26160i | ||||
\(303\) | −3.41663e6 | −0.122820 | ||||||||
\(304\) | 3.64531e7 | + | 1.45315e6i | 1.29752 | + | 0.0517239i | ||||
\(305\) | −5.68049e6 | + | 2.58830e7i | −0.200210 | + | 0.912252i | ||||
\(306\) | −1.14588e7 | − | 2.84626e7i | −0.399922 | − | 0.993369i | ||||
\(307\) | 1.45346e7 | 0.502328 | 0.251164 | − | 0.967945i | \(-0.419187\pi\) | ||||
0.251164 | + | 0.967945i | \(0.419187\pi\) | |||||||
\(308\) | 3.26613e7 | + | 3.39893e7i | 1.11785 | + | 1.16330i | ||||
\(309\) | 3.95298e6 | 0.133983 | ||||||||
\(310\) | −2.23340e7 | + | 3.75785e6i | −0.749689 | + | 0.126140i | ||||
\(311\) | 5.75145e6i | 0.191204i | 0.995420 | + | 0.0956018i | \(0.0304776\pi\) | ||||
−0.995420 | + | 0.0956018i | \(0.969522\pi\) | |||||||
\(312\) | 2.55509e6 | + | 1.14895e6i | 0.0841285 | + | 0.0378302i | ||||
\(313\) | 8.24901e6i | 0.269010i | 0.990913 | + | 0.134505i | \(0.0429444\pi\) | ||||
−0.990913 | + | 0.134505i | \(0.957056\pi\) | |||||||
\(314\) | 1.03397e7 | + | 2.56829e7i | 0.333979 | + | 0.829573i | ||||
\(315\) | −7.83062e6 | + | 3.56800e7i | −0.250533 | + | 1.14154i | ||||
\(316\) | −3.01749e7 | − | 3.14018e7i | −0.956279 | − | 0.995159i | ||||
\(317\) | − | 2.38162e7i | − | 0.747643i | −0.927501 | − | 0.373821i | \(-0.878047\pi\) | ||
0.927501 | − | 0.373821i | \(-0.121953\pi\) | |||||||
\(318\) | 313909. | + | 779721.i | 0.00976164 | + | 0.0242470i | ||||
\(319\) | 5.43762e7i | 1.67509i | ||||||||
\(320\) | −2.86046e7 | + | 1.59849e7i | −0.872944 | + | 0.487821i | ||||
\(321\) | −6.14967e6 | −0.185925 | ||||||||
\(322\) | −1.17226e7 | + | 4.71942e6i | −0.351121 | + | 0.141358i | ||||
\(323\) | −4.93696e7 | −1.46505 | ||||||||
\(324\) | 2.08468e7 | − | 2.00323e7i | 0.612920 | − | 0.588974i | ||||
\(325\) | −5.88042e6 | + | 1.27517e7i | −0.171300 | + | 0.371465i | ||||
\(326\) | 3.72946e7 | − | 1.50145e7i | 1.07645 | − | 0.433369i | ||||
\(327\) | −1.23586e6 | −0.0353449 | ||||||||
\(328\) | 1.38560e6 | − | 3.08136e6i | 0.0392660 | − | 0.0873214i | ||||
\(329\) | −1.27679e7 | −0.358535 | ||||||||
\(330\) | −1.04707e7 | + | 1.76177e6i | −0.291363 | + | 0.0490237i | ||||
\(331\) | − | 467508.i | − | 0.0128915i | −0.999979 | − | 0.00644577i | \(-0.997948\pi\) | ||
0.999979 | − | 0.00644577i | \(-0.00205177\pi\) | |||||||
\(332\) | −4.79287e7 | + | 4.60562e7i | −1.30973 | + | 1.25856i | ||||
\(333\) | 1.03772e7i | 0.281026i | ||||||||
\(334\) | 1.34868e7 | − | 5.42968e6i | 0.361968 | − | 0.145725i | ||||
\(335\) | 1.21354e7 | − | 5.52945e7i | 0.322789 | − | 1.47078i | ||||
\(336\) | −419536. | + | 1.05243e7i | −0.0110599 | + | 0.277443i | ||||
\(337\) | 2.14399e7i | 0.560186i | 0.959973 | + | 0.280093i | \(0.0903653\pi\) | ||||
−0.959973 | + | 0.280093i | \(0.909635\pi\) | |||||||
\(338\) | 2.98267e7 | − | 1.20080e7i | 0.772423 | − | 0.310971i | ||||
\(339\) | 9.16128e6i | 0.235156i | ||||||||
\(340\) | 3.78171e7 | − | 2.31564e7i | 0.962169 | − | 0.589162i | ||||
\(341\) | 3.94963e7 | 0.996078 | ||||||||
\(342\) | −1.84127e7 | − | 4.57355e7i | −0.460299 | − | 1.14334i | ||||
\(343\) | −2.40411e7 | −0.595760 | ||||||||
\(344\) | −1.70247e7 | + | 3.78603e7i | −0.418219 | + | 0.930055i | ||||
\(345\) | 610183. | − | 2.78028e6i | 0.0148595 | − | 0.0677067i | ||||
\(346\) | 6.34425e6 | + | 1.57585e7i | 0.153162 | + | 0.380441i | ||||
\(347\) | 2.74539e7 | 0.657077 | 0.328538 | − | 0.944491i | \(-0.393444\pi\) | ||||
0.328538 | + | 0.944491i | \(0.393444\pi\) | |||||||
\(348\) | −8.76065e6 | + | 8.41838e6i | −0.207873 | + | 0.199752i | ||||
\(349\) | 5.59712e7 | 1.31670 | 0.658352 | − | 0.752710i | \(-0.271254\pi\) | ||||
0.658352 | + | 0.752710i | \(0.271254\pi\) | |||||||
\(350\) | −5.27288e7 | − | 2.60415e6i | −1.22983 | − | 0.0607382i | ||||
\(351\) | − | 7.77497e6i | − | 0.179795i | ||||||
\(352\) | 5.38183e7 | − | 1.92131e7i | 1.23396 | − | 0.440523i | ||||
\(353\) | 2.18485e7i | 0.496704i | 0.968670 | + | 0.248352i | \(0.0798889\pi\) | ||||
−0.968670 | + | 0.248352i | \(0.920111\pi\) | |||||||
\(354\) | −5.35389e6 | − | 1.32986e7i | −0.120687 | − | 0.299775i | ||||
\(355\) | 3.00823e7 | + | 6.60211e6i | 0.672398 | + | 0.147570i | ||||
\(356\) | −4.32413e7 | + | 4.15519e7i | −0.958404 | + | 0.920960i | ||||
\(357\) | − | 1.42533e7i | − | 0.313265i | ||||||
\(358\) | 3.83893e6 | + | 9.53554e6i | 0.0836683 | + | 0.207824i | ||||
\(359\) | − | 5.17942e7i | − | 1.11943i | −0.828685 | − | 0.559716i | \(-0.810910\pi\) | ||
0.828685 | − | 0.559716i | \(-0.189090\pi\) | |||||||
\(360\) | 3.55560e7 | + | 2.63970e7i | 0.762088 | + | 0.565780i | ||||
\(361\) | −3.22842e7 | −0.686228 | ||||||||
\(362\) | 1.40878e7 | − | 5.67162e6i | 0.296973 | − | 0.119559i | ||||
\(363\) | 7.73068e6 | 0.161621 | ||||||||
\(364\) | −1.68315e7 | − | 1.75158e7i | −0.348994 | − | 0.363184i | ||||
\(365\) | −5.82221e7 | − | 1.27779e7i | −1.19732 | − | 0.262773i | ||||
\(366\) | 9.57857e6 | − | 3.85625e6i | 0.195370 | − | 0.0786542i | ||||
\(367\) | −6.56443e7 | −1.32800 | −0.664001 | − | 0.747732i | \(-0.731143\pi\) | ||||
−0.664001 | + | 0.747732i | \(0.731143\pi\) | |||||||
\(368\) | −610207. | + | 1.53073e7i | −0.0122443 | + | 0.307154i | ||||
\(369\) | −4.56587e6 | −0.0908750 | ||||||||
\(370\) | −1.47896e7 | + | 2.48845e6i | −0.291978 | + | 0.0491273i | ||||
\(371\) | − | 7.28829e6i | − | 0.142726i | ||||||
\(372\) | 6.11471e6 | + | 6.36332e6i | 0.118781 | + | 0.123610i | ||||
\(373\) | − | 8.58466e7i | − | 1.65423i | −0.562031 | − | 0.827116i | \(-0.689980\pi\) | ||
0.562031 | − | 0.827116i | \(-0.310020\pi\) | |||||||
\(374\) | −7.17366e7 | + | 2.88806e7i | −1.37128 | + | 0.552066i | ||||
\(375\) | 7.17889e6 | − | 9.48014e6i | 0.136133 | − | 0.179771i | ||||
\(376\) | −6.34788e6 | + | 1.41167e7i | −0.119417 | + | 0.265564i | ||||
\(377\) | − | 2.80219e7i | − | 0.522966i | ||||||
\(378\) | 2.71157e7 | − | 1.09166e7i | 0.502049 | − | 0.202120i | ||||
\(379\) | − | 4.15395e7i | − | 0.763034i | −0.924362 | − | 0.381517i | \(-0.875402\pi\) | ||
0.924362 | − | 0.381517i | \(-0.124598\pi\) | |||||||
\(380\) | 6.07668e7 | − | 3.72091e7i | 1.10743 | − | 0.678108i | ||||
\(381\) | 6.98616e6 | 0.126318 | ||||||||
\(382\) | 3.29736e7 | + | 8.19034e7i | 0.591530 | + | 1.46930i | ||||
\(383\) | 4.94031e7 | 0.879343 | 0.439671 | − | 0.898159i | \(-0.355095\pi\) | ||||
0.439671 | + | 0.898159i | \(0.355095\pi\) | |||||||
\(384\) | 1.14275e7 | + | 5.69625e6i | 0.201816 | + | 0.100599i | ||||
\(385\) | 8.99271e7 | + | 1.97361e7i | 1.57583 | + | 0.345844i | ||||
\(386\) | 2.86967e7 | + | 7.12800e7i | 0.498965 | + | 1.23938i | ||||
\(387\) | 5.61003e7 | 0.967905 | ||||||||
\(388\) | −4.24452e7 | − | 4.41709e7i | −0.726664 | − | 0.756208i | ||||
\(389\) | −2.48999e7 | −0.423008 | −0.211504 | − | 0.977377i | \(-0.567836\pi\) | ||||
−0.211504 | + | 0.977377i | \(0.567836\pi\) | |||||||
\(390\) | 5.39590e6 | − | 907897.i | 0.0909641 | − | 0.0153053i | ||||
\(391\) | − | 2.07312e7i | − | 0.346813i | ||||||
\(392\) | 1.27512e7 | − | 2.83567e7i | 0.211687 | − | 0.470759i | ||||
\(393\) | − | 1.73702e7i | − | 0.286172i | ||||||
\(394\) | −1.05378e7 | − | 2.61750e7i | −0.172291 | − | 0.427955i | ||||
\(395\) | −8.30811e7 | − | 1.82337e7i | −1.34807 | − | 0.295857i | ||||
\(396\) | −5.35093e7 | − | 5.56849e7i | −0.861676 | − | 0.896710i | ||||
\(397\) | 1.03578e8i | 1.65537i | 0.561190 | + | 0.827687i | \(0.310344\pi\) | ||||
−0.561190 | + | 0.827687i | \(0.689656\pi\) | |||||||
\(398\) | −5.04678e6 | − | 1.25357e7i | −0.0800507 | − | 0.198838i | ||||
\(399\) | − | 2.29032e7i | − | 0.360559i | ||||||
\(400\) | −2.90947e7 | + | 5.70044e7i | −0.454605 | + | 0.890693i | ||||
\(401\) | 8.14381e7 | 1.26297 | 0.631487 | − | 0.775386i | \(-0.282445\pi\) | ||||
0.631487 | + | 0.775386i | \(0.282445\pi\) | |||||||
\(402\) | −2.04629e7 | + | 8.23820e6i | −0.314985 | + | 0.126810i | ||||
\(403\) | −2.03538e7 | −0.310978 | ||||||||
\(404\) | 2.58961e7 | − | 2.48844e7i | 0.392727 | − | 0.377383i | ||||
\(405\) | 1.21048e7 | − | 5.51553e7i | 0.182219 | − | 0.830275i | ||||
\(406\) | 9.77282e7 | − | 3.93445e7i | 1.46030 | − | 0.587904i | ||||
\(407\) | 2.61545e7 | 0.387938 | ||||||||
\(408\) | −1.57591e7 | − | 7.08641e6i | −0.232033 | − | 0.104339i | ||||
\(409\) | −9.56658e7 | −1.39826 | −0.699128 | − | 0.714996i | \(-0.746428\pi\) | ||||
−0.699128 | + | 0.714996i | \(0.746428\pi\) | |||||||
\(410\) | −1.09489e6 | − | 6.50728e6i | −0.0158862 | − | 0.0944165i | ||||
\(411\) | 8.48325e6i | 0.122190i | ||||||||
\(412\) | −2.99614e7 | + | 2.87908e7i | −0.428421 | + | 0.411683i | ||||
\(413\) | 1.24306e8i | 1.76458i | ||||||||
\(414\) | 1.92052e7 | − | 7.73186e6i | 0.270656 | − | 0.108964i | ||||
\(415\) | −2.78302e7 | + | 1.26807e8i | −0.389378 | + | 1.77419i | ||||
\(416\) | −2.77344e7 | + | 9.90113e6i | −0.385246 | + | 0.137532i | ||||
\(417\) | − | 2.98171e6i | − | 0.0411205i | ||||||
\(418\) | −1.15271e8 | + | 4.64071e7i | −1.57830 | + | 0.635412i | ||||
\(419\) | 2.42825e6i | 0.0330105i | 0.999864 | + | 0.0165053i | \(0.00525402\pi\) | ||||
−0.999864 | + | 0.0165053i | \(0.994746\pi\) | |||||||
\(420\) | 1.07425e7 | + | 1.75438e7i | 0.144997 | + | 0.236797i | ||||
\(421\) | −5.13368e7 | −0.687991 | −0.343995 | − | 0.938971i | \(-0.611780\pi\) | ||||
−0.343995 | + | 0.938971i | \(0.611780\pi\) | |||||||
\(422\) | 1.63367e7 | + | 4.05788e7i | 0.217384 | + | 0.539961i | ||||
\(423\) | 2.09177e7 | 0.276372 | ||||||||
\(424\) | −8.05822e6 | − | 3.62355e6i | −0.105716 | − | 0.0475376i | ||||
\(425\) | 3.62687e7 | − | 7.86487e7i | 0.472460 | − | 1.02453i | ||||
\(426\) | −4.48190e6 | − | 1.11326e7i | −0.0579740 | − | 0.144002i | ||||
\(427\) | −8.95337e7 | −1.15001 | ||||||||
\(428\) | 4.66111e7 | − | 4.47900e7i | 0.594508 | − | 0.571281i | ||||
\(429\) | −9.54233e6 | −0.120860 | ||||||||
\(430\) | 1.34528e7 | + | 7.99541e7i | 0.169203 | + | 1.00562i | ||||
\(431\) | 8.99001e7i | 1.12287i | 0.827522 | + | 0.561434i | \(0.189750\pi\) | ||||
−0.827522 | + | 0.561434i | \(0.810250\pi\) | |||||||
\(432\) | 1.41148e6 | − | 3.54077e7i | 0.0175075 | − | 0.439183i | ||||
\(433\) | 3.62806e7i | 0.446900i | 0.974715 | + | 0.223450i | \(0.0717320\pi\) | ||||
−0.974715 | + | 0.223450i | \(0.928268\pi\) | |||||||
\(434\) | −2.85780e7 | − | 7.09851e7i | −0.349593 | − | 0.868357i | ||||
\(435\) | −5.08694e6 | + | 2.31785e7i | −0.0618000 | + | 0.281590i | ||||
\(436\) | 9.36715e6 | − | 9.00118e6i | 0.113018 | − | 0.108603i | ||||
\(437\) | − | 3.33122e7i | − | 0.399171i | ||||||
\(438\) | 8.67439e6 | + | 2.15464e7i | 0.103232 | + | 0.256420i | ||||
\(439\) | 2.02544e7i | 0.239401i | 0.992810 | + | 0.119701i | \(0.0381935\pi\) | ||||
−0.992810 | + | 0.119701i | \(0.961806\pi\) | |||||||
\(440\) | 6.65305e7 | − | 8.96146e7i | 0.781022 | − | 1.05201i | ||||
\(441\) | −4.20183e7 | −0.489917 | ||||||||
\(442\) | 3.69683e7 | − | 1.48831e7i | 0.428117 | − | 0.172356i | ||||
\(443\) | 1.42522e8 | 1.63935 | 0.819676 | − | 0.572828i | \(-0.194154\pi\) | ||||
0.819676 | + | 0.572828i | \(0.194154\pi\) | |||||||
\(444\) | 4.04916e6 | + | 4.21379e6i | 0.0462612 | + | 0.0481420i | ||||
\(445\) | −2.51084e7 | + | 1.14406e8i | −0.284930 | + | 1.29828i | ||||
\(446\) | 5.02527e7 | − | 2.02313e7i | 0.566441 | − | 0.228044i | ||||
\(447\) | −6.24631e6 | −0.0699360 | ||||||||
\(448\) | −7.34717e7 | − | 8.28236e7i | −0.817120 | − | 0.921129i | ||||
\(449\) | −8.30869e7 | −0.917896 | −0.458948 | − | 0.888463i | \(-0.651774\pi\) | ||||
−0.458948 | + | 0.888463i | \(0.651774\pi\) | |||||||
\(450\) | 8.63860e7 | + | 4.26639e6i | 0.947995 | + | 0.0468191i | ||||
\(451\) | 1.15077e7i | 0.125447i | ||||||||
\(452\) | −6.67245e7 | − | 6.94374e7i | −0.722554 | − | 0.751931i | ||||
\(453\) | 2.85089e7i | 0.306680i | ||||||||
\(454\) | −3.83790e7 | + | 1.54511e7i | −0.410135 | + | 0.165117i | ||||
\(455\) | −4.63424e7 | − | 1.01707e7i | −0.491977 | − | 0.107973i | ||||
\(456\) | −2.53226e7 | − | 1.13869e7i | −0.267063 | − | 0.120091i | ||||
\(457\) | − | 1.72794e8i | − | 1.81043i | −0.424956 | − | 0.905214i | \(-0.639711\pi\) | ||
0.424956 | − | 0.905214i | \(-0.360289\pi\) | |||||||
\(458\) | −8.52378e7 | + | 3.43160e7i | −0.887229 | + | 0.357191i | ||||
\(459\) | 4.79537e7i | 0.495889i | ||||||||
\(460\) | 1.56248e7 | + | 2.55172e7i | 0.160525 | + | 0.262155i | ||||
\(461\) | 1.94634e7 | 0.198663 | 0.0993315 | − | 0.995054i | \(-0.468330\pi\) | ||||
0.0993315 | + | 0.995054i | \(0.468330\pi\) | |||||||
\(462\) | −1.33980e7 | − | 3.32795e7i | −0.135867 | − | 0.337482i | ||||
\(463\) | 1.61739e8 | 1.62957 | 0.814785 | − | 0.579763i | \(-0.196855\pi\) | ||||
0.814785 | + | 0.579763i | \(0.196855\pi\) | |||||||
\(464\) | 5.08714e6 | − | 1.27613e8i | 0.0509236 | − | 1.27744i | ||||
\(465\) | 1.68357e7 | + | 3.69491e6i | 0.167446 | + | 0.0367490i | ||||
\(466\) | −1.82811e6 | − | 4.54085e6i | −0.0180653 | − | 0.0448725i | ||||
\(467\) | −5.34609e7 | −0.524911 | −0.262455 | − | 0.964944i | \(-0.584532\pi\) | ||||
−0.262455 | + | 0.964944i | \(0.584532\pi\) | |||||||
\(468\) | 2.75751e7 | + | 2.86963e7i | 0.269017 | + | 0.279955i | ||||
\(469\) | 1.91273e8 | 1.85411 | ||||||||
\(470\) | 5.01606e6 | + | 2.98119e7i | 0.0483136 | + | 0.287142i | ||||
\(471\) | − | 2.10708e7i | − | 0.201659i | ||||||
\(472\) | 1.37437e8 | + | 6.18017e7i | 1.30701 | + | 0.587725i | ||||
\(473\) | − | 1.41394e8i | − | 1.33613i | ||||||
\(474\) | 1.23781e7 | + | 3.07460e7i | 0.116230 | + | 0.288704i | ||||
\(475\) | 5.82788e7 | − | 1.26378e8i | 0.543788 | − | 1.17920i | ||||
\(476\) | 1.03812e8 | + | 1.08032e8i | 0.962555 | + | 1.00169i | ||||
\(477\) | 1.19404e7i | 0.110018i | ||||||||
\(478\) | −5.63371e7 | − | 1.39936e8i | −0.515835 | − | 1.28129i | ||||
\(479\) | − | 5.20964e7i | − | 0.474024i | −0.971507 | − | 0.237012i | \(-0.923832\pi\) | ||
0.971507 | − | 0.237012i | \(-0.0761682\pi\) | |||||||
\(480\) | 2.47381e7 | − | 3.15503e6i | 0.223688 | − | 0.0285286i | ||||
\(481\) | −1.34783e7 | −0.121115 | ||||||||
\(482\) | 8.87413e7 | − | 3.57265e7i | 0.792474 | − | 0.319043i | ||||
\(483\) | 9.61748e6 | 0.0853532 | ||||||||
\(484\) | −5.85943e7 | + | 5.63050e7i | −0.516796 | + | 0.496605i | ||||
\(485\) | −1.16865e8 | − | 2.56482e7i | −1.02438 | − | 0.224818i | ||||
\(486\) | −6.72153e7 | + | 2.70603e7i | −0.585544 | + | 0.235735i | ||||
\(487\) | −4.49422e7 | −0.389105 | −0.194553 | − | 0.980892i | \(-0.562326\pi\) | ||||
−0.194553 | + | 0.980892i | \(0.562326\pi\) | |||||||
\(488\) | −4.45139e7 | + | 9.89920e7i | −0.383033 | + | 0.851806i | ||||
\(489\) | −3.05973e7 | −0.261672 | ||||||||
\(490\) | −1.00760e7 | − | 5.98844e7i | −0.0856442 | − | 0.509009i | ||||
\(491\) | 2.58692e7i | 0.218543i | 0.994012 | + | 0.109272i | \(0.0348519\pi\) | ||||
−0.994012 | + | 0.109272i | \(0.965148\pi\) | |||||||
\(492\) | −1.85403e6 | + | 1.78160e6i | −0.0155676 | + | 0.0149594i | ||||
\(493\) | 1.72831e8i | 1.44238i | ||||||||
\(494\) | 5.94029e7 | − | 2.39151e7i | 0.492750 | − | 0.198377i | ||||
\(495\) | −1.47328e8 | − | 3.23338e7i | −1.21470 | − | 0.266589i | ||||
\(496\) | −9.26922e7 | − | 3.69506e6i | −0.759623 | − | 0.0302814i | ||||
\(497\) | 1.04060e8i | 0.847646i | ||||||||
\(498\) | 4.69278e7 | − | 1.88927e7i | 0.379964 | − | 0.152970i | ||||
\(499\) | 2.14540e7i | 0.172666i | 0.996266 | + | 0.0863329i | \(0.0275149\pi\) | ||||
−0.996266 | + | 0.0863329i | \(0.972485\pi\) | |||||||
\(500\) | 1.46349e7 | + | 1.24140e8i | 0.117079 | + | 0.993123i | ||||
\(501\) | −1.10649e7 | −0.0879901 | ||||||||
\(502\) | −1.32636e7 | − | 3.29456e7i | −0.104846 | − | 0.260427i | ||||
\(503\) | −1.02143e8 | −0.802607 | −0.401303 | − | 0.915945i | \(-0.631443\pi\) | ||||
−0.401303 | + | 0.915945i | \(0.631443\pi\) | |||||||
\(504\) | −6.13629e7 | + | 1.36462e8i | −0.479308 | + | 1.06591i | ||||
\(505\) | 1.50368e7 | − | 6.85146e7i | 0.116756 | − | 0.531997i | ||||
\(506\) | −1.94872e7 | − | 4.84044e7i | −0.150417 | − | 0.373623i | ||||
\(507\) | −2.44705e7 | −0.187767 | ||||||||
\(508\) | −5.29512e7 | + | 5.08825e7i | −0.403910 | + | 0.388130i | ||||
\(509\) | 1.68263e8 | 1.27595 | 0.637976 | − | 0.770056i | \(-0.279772\pi\) | ||||
0.637976 | + | 0.770056i | \(0.279772\pi\) | |||||||
\(510\) | −3.32803e7 | + | 5.59964e6i | −0.250886 | + | 0.0422134i | ||||
\(511\) | − | 2.01400e8i | − | 1.50938i | ||||||
\(512\) | −1.28101e8 | + | 4.00554e7i | −0.954430 | + | 0.298436i | ||||
\(513\) | 7.70550e7i | 0.570754i | ||||||||
\(514\) | 9.02581e7 | + | 2.24193e8i | 0.664656 | + | 1.65094i | ||||
\(515\) | −1.73973e7 | + | 7.92703e7i | −0.127368 | + | 0.580348i | ||||
\(516\) | 2.27803e7 | − | 2.18903e7i | 0.165810 | − | 0.159332i | ||||
\(517\) | − | 5.27206e7i | − | 0.381513i | ||||||
\(518\) | −1.89244e7 | − | 4.70064e7i | −0.136155 | − | 0.338195i | ||||
\(519\) | − | 1.29287e7i | − | 0.0924807i | ||||||
\(520\) | −3.42854e7 | + | 4.61814e7i | −0.243837 | + | 0.328441i | ||||
\(521\) | 7.03931e7 | 0.497756 | 0.248878 | − | 0.968535i | \(-0.419938\pi\) | ||||
0.248878 | + | 0.968535i | \(0.419938\pi\) | |||||||
\(522\) | −1.60109e8 | + | 6.44584e7i | −1.12565 | + | 0.453177i | ||||
\(523\) | 1.32429e7 | 0.0925719 | 0.0462859 | − | 0.998928i | \(-0.485261\pi\) | ||||
0.0462859 | + | 0.998928i | \(0.485261\pi\) | |||||||
\(524\) | 1.26513e8 | + | 1.31656e8i | 0.879307 | + | 0.915058i | ||||
\(525\) | 3.64861e7 | + | 1.68255e7i | 0.252144 | + | 0.116276i | ||||
\(526\) | −2.16271e8 | + | 8.70689e7i | −1.48608 | + | 0.598282i | ||||
\(527\) | 1.25536e8 | 0.857703 | ||||||||
\(528\) | −4.34563e7 | − | 1.73233e6i | −0.295224 | − | 0.0117687i | ||||
\(529\) | −1.34047e8 | −0.905506 | ||||||||
\(530\) | −1.70175e7 | + | 2.86331e6i | −0.114306 | + | 0.0192327i | ||||
\(531\) | − | 2.03651e8i | − | 1.36020i | ||||||
\(532\) | 1.66811e8 | + | 1.73593e8i | 1.10787 | + | 1.15292i | ||||
\(533\) | − | 5.93032e6i | − | 0.0391649i | ||||||
\(534\) | 4.23383e7 | − | 1.70450e7i | 0.278042 | − | 0.111937i | ||||
\(535\) | 2.70651e7 | − | 1.23321e8i | 0.176745 | − | 0.805334i | ||||
\(536\) | 9.50962e7 | − | 2.11479e8i | 0.617545 | − | 1.37332i | ||||
\(537\) | − | 7.82317e6i | − | 0.0505196i | ||||||
\(538\) | 1.67593e8 | − | 6.74713e7i | 1.07624 | − | 0.433284i | ||||
\(539\) | 1.05902e8i | 0.676297i | ||||||||
\(540\) | −3.61420e7 | − | 5.90241e7i | −0.229526 | − | 0.374842i | ||||
\(541\) | 8.75392e6 | 0.0552855 | 0.0276427 | − | 0.999618i | \(-0.491200\pi\) | ||||
0.0276427 | + | 0.999618i | \(0.491200\pi\) | |||||||
\(542\) | −2.24150e7 | − | 5.56767e7i | −0.140780 | − | 0.349684i | ||||
\(543\) | −1.15579e7 | −0.0721905 | ||||||||
\(544\) | 1.71058e8 | − | 6.10673e7i | 1.06254 | − | 0.379325i | ||||
\(545\) | 5.43910e6 | − | 2.47831e7i | 0.0335999 | − | 0.153097i | ||||
\(546\) | 6.90446e6 | + | 1.71500e7i | 0.0424182 | + | 0.105363i | ||||
\(547\) | −1.27352e8 | −0.778114 | −0.389057 | − | 0.921214i | \(-0.627199\pi\) | ||||
−0.389057 | + | 0.921214i | \(0.627199\pi\) | |||||||
\(548\) | −6.17862e7 | − | 6.42983e7i | −0.375448 | − | 0.390713i | ||||
\(549\) | 1.46684e8 | 0.886471 | ||||||||
\(550\) | 1.07529e7 | − | 2.17726e8i | 0.0646307 | − | 1.30864i | ||||
\(551\) | 2.77715e8i | 1.66014i | ||||||||
\(552\) | 4.78157e6 | − | 1.06335e7i | 0.0284284 | − | 0.0632204i | ||||
\(553\) | − | 2.87392e8i | − | 1.69941i | ||||||
\(554\) | −7.07495e7 | − | 1.75735e8i | −0.416096 | − | 1.03354i | ||||
\(555\) | 1.11486e7 | + | 2.44677e6i | 0.0652143 | + | 0.0143125i | ||||
\(556\) | 2.17168e7 | + | 2.25997e7i | 0.126349 | + | 0.131486i | ||||
\(557\) | 2.82592e8i | 1.63529i | 0.575723 | + | 0.817645i | \(0.304721\pi\) | ||||
−0.575723 | + | 0.817645i | \(0.695279\pi\) | |||||||
\(558\) | 4.68196e7 | + | 1.16295e8i | 0.269479 | + | 0.669360i | ||||
\(559\) | 7.28652e7i | 0.417143i | ||||||||
\(560\) | −2.09200e8 | − | 5.47310e7i | −1.19123 | − | 0.311651i | ||||
\(561\) | 5.88543e7 | 0.333342 | ||||||||
\(562\) | 1.65480e8 | − | 6.66210e7i | 0.932261 | − | 0.375320i | ||||
\(563\) | −2.23747e7 | −0.125381 | −0.0626905 | − | 0.998033i | \(-0.519968\pi\) | ||||
−0.0626905 | + | 0.998033i | \(0.519968\pi\) | |||||||
\(564\) | 8.49392e6 | − | 8.16207e6i | 0.0473446 | − | 0.0454949i | ||||
\(565\) | −1.83714e8 | − | 4.03193e7i | −1.01858 | − | 0.223547i | ||||
\(566\) | −1.49530e7 | + | 6.01993e6i | −0.0824665 | + | 0.0332003i | ||||
\(567\) | 1.90792e8 | 1.04667 | ||||||||
\(568\) | 1.15053e8 | + | 5.17360e7i | 0.627845 | + | 0.282324i | ||||
\(569\) | −2.06789e8 | −1.12251 | −0.561256 | − | 0.827642i | \(-0.689682\pi\) | ||||
−0.561256 | + | 0.827642i | \(0.689682\pi\) | |||||||
\(570\) | −5.34769e7 | + | 8.99785e6i | −0.288763 | + | 0.0485864i | ||||
\(571\) | 1.67454e8i | 0.899473i | 0.893161 | + | 0.449737i | \(0.148482\pi\) | ||||
−0.893161 | + | 0.449737i | \(0.851518\pi\) | |||||||
\(572\) | 7.23256e7 | − | 6.94998e7i | 0.386459 | − | 0.371360i | ||||
\(573\) | − | 6.71954e7i | − | 0.357170i | ||||||
\(574\) | 2.06824e7 | − | 8.32655e6i | 0.109362 | − | 0.0440280i | ||||
\(575\) | 5.30684e7 | + | 2.44724e7i | 0.279146 | + | 0.128728i | ||||
\(576\) | 1.20369e8 | + | 1.35691e8i | 0.629865 | + | 0.710039i | ||||
\(577\) | − | 1.29395e8i | − | 0.673583i | −0.941579 | − | 0.336792i | \(-0.890658\pi\) | ||
0.941579 | − | 0.336792i | \(-0.109342\pi\) | |||||||
\(578\) | −4.88807e7 | + | 1.96790e7i | −0.253136 | + | 0.101910i | ||||
\(579\) | − | 5.84797e7i | − | 0.301279i | ||||||
\(580\) | −1.30260e8 | − | 2.12730e8i | −0.667617 | − | 1.09030i | ||||
\(581\) | −4.38648e8 | −2.23660 | ||||||||
\(582\) | 1.74115e7 | + | 4.32485e7i | 0.0883216 | + | 0.219383i | ||||
\(583\) | 3.00945e7 | 0.151873 | ||||||||
\(584\) | −2.22676e8 | − | 1.00131e8i | −1.11798 | − | 0.502725i | ||||
\(585\) | 7.59231e7 | + | 1.66627e7i | 0.379233 | + | 0.0832296i | ||||
\(586\) | −9.55722e7 | − | 2.37393e8i | −0.474940 | − | 1.17971i | ||||
\(587\) | 1.84946e8 | 0.914386 | 0.457193 | − | 0.889367i | \(-0.348855\pi\) | ||||
0.457193 | + | 0.889367i | \(0.348855\pi\) | |||||||
\(588\) | −1.70621e7 | + | 1.63955e7i | −0.0839266 | + | 0.0806476i | ||||
\(589\) | 2.01719e8 | 0.987191 | ||||||||
\(590\) | 2.90243e8 | − | 4.88354e7i | 1.41321 | − | 0.237782i | ||||
\(591\) | 2.14745e7i | 0.104031i | ||||||||
\(592\) | −6.13808e7 | − | 2.44687e6i | −0.295847 | − | 0.0117936i | ||||
\(593\) | 1.51763e8i | 0.727784i | 0.931441 | + | 0.363892i | \(0.118552\pi\) | ||||
−0.931441 | + | 0.363892i | \(0.881448\pi\) | |||||||
\(594\) | 4.50762e7 | + | 1.11965e8i | 0.215074 | + | 0.534224i | ||||
\(595\) | 2.85827e8 | + | 6.27298e7i | 1.35691 | + | 0.297799i | ||||
\(596\) | 4.73436e7 | − | 4.54939e7i | 0.223626 | − | 0.214889i | ||||
\(597\) | 1.02846e7i | 0.0483352i | ||||||||
\(598\) | 1.00424e7 | + | 2.49444e7i | 0.0469607 | + | 0.116646i | ||||
\(599\) | 2.67870e8i | 1.24636i | 0.782079 | + | 0.623180i | \(0.214159\pi\) | ||||
−0.782079 | + | 0.623180i | \(0.785841\pi\) | |||||||
\(600\) | 3.67429e7 | − | 3.19752e7i | 0.170106 | − | 0.148034i | ||||
\(601\) | 2.92898e8 | 1.34925 | 0.674626 | − | 0.738160i | \(-0.264305\pi\) | ||||
0.674626 | + | 0.738160i | \(0.264305\pi\) | |||||||
\(602\) | −2.54122e8 | + | 1.02307e8i | −1.16480 | + | 0.468940i | ||||
\(603\) | −3.13364e8 | −1.42921 | ||||||||
\(604\) | −2.07639e8 | − | 2.16082e8i | −0.942322 | − | 0.980634i | ||||
\(605\) | −3.40232e7 | + | 1.55026e8i | −0.153642 | + | 0.700063i | ||||
\(606\) | −2.53553e7 | + | 1.02078e7i | −0.113934 | + | 0.0458687i | ||||
\(607\) | −2.54116e8 | −1.13623 | −0.568115 | − | 0.822949i | \(-0.692327\pi\) | ||||
−0.568115 | + | 0.822949i | \(0.692327\pi\) | |||||||
\(608\) | 2.74866e8 | − | 9.81267e7i | 1.22295 | − | 0.436592i | ||||
\(609\) | −8.01783e7 | −0.354981 | ||||||||
\(610\) | 3.51747e7 | + | 2.09053e8i | 0.154967 | + | 0.921017i | ||||
\(611\) | 2.71687e7i | 0.119109i | ||||||||
\(612\) | −1.70075e8 | − | 1.76990e8i | −0.741972 | − | 0.772139i | ||||
\(613\) | 3.65576e7i | 0.158707i | 0.996847 | + | 0.0793534i | \(0.0252856\pi\) | ||||
−0.996847 | + | 0.0793534i | \(0.974714\pi\) | |||||||
\(614\) | 1.07864e8 | − | 4.34249e7i | 0.465982 | − | 0.187601i | ||||
\(615\) | −1.07656e6 | + | 4.90530e6i | −0.00462819 | + | 0.0210882i | ||||
\(616\) | 3.43935e8 | + | 1.54658e8i | 1.47141 | + | 0.661652i | ||||
\(617\) | − | 1.37267e8i | − | 0.584400i | −0.956357 | − | 0.292200i | \(-0.905613\pi\) | ||
0.956357 | − | 0.292200i | \(-0.0943872\pi\) | |||||||
\(618\) | 2.93357e7 | − | 1.18103e7i | 0.124289 | − | 0.0500375i | ||||
\(619\) | − | 2.41038e8i | − | 1.01628i | −0.861275 | − | 0.508140i | \(-0.830333\pi\) | ||
0.861275 | − | 0.508140i | \(-0.169667\pi\) | |||||||
\(620\) | −1.54517e8 | + | 9.46148e7i | −0.648337 | + | 0.396994i | ||||
\(621\) | −3.23569e7 | −0.135111 | ||||||||
\(622\) | 1.71836e7 | + | 4.26825e7i | 0.0714073 | + | 0.177369i | ||||
\(623\) | −3.95749e8 | −1.63665 | ||||||||
\(624\) | 2.23945e7 | + | 892727.i | 0.0921695 | + | 0.00367422i | ||||
\(625\) | 1.58513e8 | + | 1.85683e8i | 0.649270 | + | 0.760558i | ||||
\(626\) | 2.46455e7 | + | 6.12172e7i | 0.100465 | + | 0.249546i | ||||
\(627\) | 9.45707e7 | 0.383667 | ||||||||
\(628\) | 1.53465e8 | + | 1.59705e8i | 0.619628 | + | 0.644821i | ||||
\(629\) | 8.31301e7 | 0.334046 | ||||||||
\(630\) | 4.84887e7 | + | 2.88182e8i | 0.193918 | + | 1.15251i | ||||
\(631\) | − | 2.23847e8i | − | 0.890968i | −0.895290 | − | 0.445484i | \(-0.853032\pi\) | ||
0.895290 | − | 0.445484i | \(-0.146968\pi\) | |||||||
\(632\) | −3.17752e8 | − | 1.42884e8i | −1.25874 | − | 0.566021i | ||||
\(633\) | − | 3.32918e7i | − | 0.131258i | ||||||
\(634\) | −7.11555e7 | − | 1.76744e8i | −0.279216 | − | 0.693547i | ||||
\(635\) | −3.07465e7 | + | 1.40096e8i | −0.120081 | + | 0.547146i | ||||
\(636\) | 4.65914e6 | + | 4.84857e6i | 0.0181107 | + | 0.0188470i | ||||
\(637\) | − | 5.45748e7i | − | 0.211142i | ||||||
\(638\) | 1.62460e8 | + | 4.03535e8i | 0.625581 | + | 1.55389i | ||||
\(639\) | − | 1.70482e8i | − | 0.653396i | ||||||
\(640\) | −1.64522e8 | + | 2.04089e8i | −0.627600 | + | 0.778536i | ||||
\(641\) | 5.85061e7 | 0.222140 | 0.111070 | − | 0.993813i | \(-0.464572\pi\) | ||||
0.111070 | + | 0.993813i | \(0.464572\pi\) | |||||||
\(642\) | −4.56377e7 | + | 1.83734e7i | −0.172472 | + | 0.0694358i | ||||
\(643\) | −2.24198e7 | −0.0843331 | −0.0421666 | − | 0.999111i | \(-0.513426\pi\) | ||||
−0.0421666 | + | 0.999111i | \(0.513426\pi\) | |||||||
\(644\) | −7.28951e7 | + | 7.00472e7i | −0.272923 | + | 0.262260i | ||||
\(645\) | 1.32275e7 | − | 6.02708e7i | 0.0492946 | − | 0.224609i | ||||
\(646\) | −3.66380e8 | + | 1.47501e8i | −1.35905 | + | 0.547140i | ||||
\(647\) | 1.77477e8 | 0.655283 | 0.327641 | − | 0.944802i | \(-0.393746\pi\) | ||||
0.327641 | + | 0.944802i | \(0.393746\pi\) | |||||||
\(648\) | 9.48569e7 | − | 2.10947e8i | 0.348613 | − | 0.775261i | ||||
\(649\) | −5.13278e8 | −1.87767 | ||||||||
\(650\) | −5.54135e6 | + | 1.12201e8i | −0.0201779 | + | 0.408562i | ||||
\(651\) | 5.82378e7i | 0.211087i | ||||||||
\(652\) | 2.31911e8 | − | 2.22850e8i | 0.836716 | − | 0.804026i | ||||
\(653\) | − | 3.43085e8i | − | 1.23215i | −0.787689 | − | 0.616073i | \(-0.788723\pi\) | ||
0.787689 | − | 0.616073i | \(-0.211277\pi\) | |||||||
\(654\) | −9.17153e6 | + | 3.69238e6i | −0.0327875 | + | 0.0132000i | ||||
\(655\) | 3.48330e8 | + | 7.64473e7i | 1.23956 | + | 0.272043i | ||||
\(656\) | 1.07660e6 | − | 2.70070e7i | 0.00381366 | − | 0.0956676i | ||||
\(657\) | 3.29955e8i | 1.16348i | ||||||||
\(658\) | −9.47527e7 | + | 3.81466e7i | −0.332594 | + | 0.133899i | ||||
\(659\) | − | 2.57705e8i | − | 0.900465i | −0.892911 | − | 0.450233i | \(-0.851341\pi\) | ||
0.892911 | − | 0.450233i | \(-0.148659\pi\) | |||||||
\(660\) | −7.24411e7 | + | 4.43576e7i | −0.251973 | + | 0.154290i | ||||
\(661\) | 1.58848e8 | 0.550018 | 0.275009 | − | 0.961442i | \(-0.411319\pi\) | ||||
0.275009 | + | 0.961442i | \(0.411319\pi\) | |||||||
\(662\) | −1.39677e6 | − | 3.46945e6i | −0.00481450 | − | 0.0119588i | ||||
\(663\) | −3.03296e7 | −0.104070 | ||||||||
\(664\) | −2.18085e8 | + | 4.84987e8i | −0.744940 | + | 1.65663i | ||||
\(665\) | 4.59284e8 | + | 1.00798e8i | 1.56177 | + | 0.342758i | ||||
\(666\) | 3.10039e7 | + | 7.70109e7i | 0.104953 | + | 0.260693i | ||||
\(667\) | −1.16618e8 | −0.392996 | ||||||||
\(668\) | 8.38657e7 | − | 8.05891e7i | 0.281355 | − | 0.270363i | ||||
\(669\) | −4.12284e7 | −0.137695 | ||||||||
\(670\) | −7.51445e7 | − | 4.46606e8i | −0.249846 | − | 1.48491i | ||||
\(671\) | − | 3.69699e8i | − | 1.22371i | ||||||
\(672\) | 2.83299e7 | + | 7.93557e7i | 0.0933548 | + | 0.261499i | ||||
\(673\) | 2.76715e8i | 0.907793i | 0.891054 | + | 0.453897i | \(0.149966\pi\) | ||||
−0.891054 | + | 0.453897i | \(0.850034\pi\) | |||||||
\(674\) | 6.40558e7 | + | 1.59109e8i | 0.209208 | + | 0.519654i | ||||
\(675\) | −1.22753e8 | − | 5.66074e7i | −0.399137 | − | 0.184061i | ||||
\(676\) | 1.85473e8 | − | 1.78226e8i | 0.600398 | − | 0.576941i | ||||
\(677\) | − | 4.19801e8i | − | 1.35294i | −0.736472 | − | 0.676468i | \(-0.763510\pi\) | ||
0.736472 | − | 0.676468i | \(-0.236490\pi\) | |||||||
\(678\) | 2.73711e7 | + | 6.79873e7i | 0.0878220 | + | 0.218142i | ||||
\(679\) | − | 4.04257e8i | − | 1.29136i | ||||||
\(680\) | 2.11462e8 | − | 2.84833e8i | 0.672522 | − | 0.905867i | ||||
\(681\) | 3.14870e7 | 0.0996988 | ||||||||
\(682\) | 2.93109e8 | − | 1.18003e8i | 0.924008 | − | 0.371998i | ||||
\(683\) | −9.99621e7 | −0.313742 | −0.156871 | − | 0.987619i | \(-0.550141\pi\) | ||||
−0.156871 | + | 0.987619i | \(0.550141\pi\) | |||||||
\(684\) | −2.73288e8 | − | 2.84399e8i | −0.853988 | − | 0.888709i | ||||
\(685\) | −1.70117e8 | − | 3.73353e7i | −0.529269 | − | 0.116158i | ||||
\(686\) | −1.78413e8 | + | 7.18275e7i | −0.552654 | + | 0.222494i | ||||
\(687\) | 6.99310e7 | 0.215675 | ||||||||
\(688\) | −1.32280e7 | + | 3.31832e8i | −0.0406191 | + | 1.01895i | ||||
\(689\) | −1.55087e7 | −0.0474152 | ||||||||
\(690\) | −3.77837e6 | − | 2.24560e7i | −0.0115016 | − | 0.0683572i | ||||
\(691\) | 2.78223e8i | 0.843254i | 0.906769 | + | 0.421627i | \(0.138541\pi\) | ||||
−0.906769 | + | 0.421627i | \(0.861459\pi\) | |||||||
\(692\) | 9.41635e7 | + | 9.79920e7i | 0.284161 | + | 0.295714i | ||||
\(693\) | − | 5.09633e8i | − | 1.53129i | ||||||
\(694\) | 2.03740e8 | − | 8.20241e7i | 0.609534 | − | 0.245393i | ||||
\(695\) | 5.97932e7 | + | 1.31227e7i | 0.178114 | + | 0.0390903i | ||||
\(696\) | −3.98627e7 | + | 8.86483e7i | −0.118233 | + | 0.262932i | ||||
\(697\) | 3.65765e7i | 0.108020i | ||||||||
\(698\) | 4.15372e8 | − | 1.67225e8i | 1.22144 | − | 0.491739i | ||||
\(699\) | 3.72542e6i | 0.0109080i | ||||||||
\(700\) | −3.99090e8 | + | 1.38212e8i | −1.16353 | + | 0.402950i | ||||
\(701\) | 1.43797e8 | 0.417443 | 0.208721 | − | 0.977975i | \(-0.433070\pi\) | ||||
0.208721 | + | 0.977975i | \(0.433070\pi\) | |||||||
\(702\) | −2.32293e7 | − | 5.76993e7i | −0.0671466 | − | 0.166786i | ||||
\(703\) | 1.33579e8 | 0.384477 | ||||||||
\(704\) | 3.41992e8 | − | 3.03376e8i | 0.980161 | − | 0.869487i | ||||
\(705\) | 4.93206e6 | − | 2.24728e7i | 0.0140754 | − | 0.0641341i | ||||
\(706\) | 6.52767e7 | + | 1.62141e8i | 0.185500 | + | 0.460765i | ||||
\(707\) | 2.37004e8 | 0.670652 | ||||||||
\(708\) | −7.94642e7 | − | 8.26951e7i | −0.223909 | − | 0.233013i | ||||
\(709\) | 3.30939e8 | 0.928558 | 0.464279 | − | 0.885689i | \(-0.346314\pi\) | ||||
0.464279 | + | 0.885689i | \(0.346314\pi\) | |||||||
\(710\) | 2.42971e8 | − | 4.08815e7i | 0.678859 | − | 0.114223i | ||||
\(711\) | 4.70836e8i | 1.30997i | ||||||||
\(712\) | −1.96756e8 | + | 4.37555e8i | −0.545116 | + | 1.21225i | ||||
\(713\) | 8.47058e7i | 0.233692i | ||||||||
\(714\) | −4.25847e7 | − | 1.05776e8i | −0.116993 | − | 0.290599i | ||||
\(715\) | 4.19964e7 | − | 1.91355e8i | 0.114893 | − | 0.523506i | ||||
\(716\) | 5.69786e7 | + | 5.92953e7i | 0.155229 | + | 0.161540i | ||||
\(717\) | 1.14807e8i | 0.311466i | ||||||||
\(718\) | −1.54745e8 | − | 3.84373e8i | −0.418065 | − | 1.03844i | ||||
\(719\) | 3.88053e8i | 1.04401i | 0.852943 | + | 0.522004i | \(0.174815\pi\) | ||||
−0.852943 | + | 0.522004i | \(0.825185\pi\) | |||||||
\(720\) | 3.42733e8 | + | 8.96661e7i | 0.918245 | + | 0.240232i | ||||
\(721\) | −2.74210e8 | −0.731605 | ||||||||
\(722\) | −2.39586e8 | + | 9.64555e7i | −0.636577 | + | 0.256280i | ||||
\(723\) | −7.28053e7 | −0.192641 | ||||||||
\(724\) | 8.76026e7 | − | 8.41800e7i | 0.230835 | − | 0.221816i | ||||
\(725\) | −4.42417e8 | − | 2.04020e8i | −1.16096 | − | 0.535375i | ||||
\(726\) | 5.73706e7 | − | 2.30969e7i | 0.149927 | − | 0.0603593i | ||||
\(727\) | −6.94954e8 | −1.80864 | −0.904322 | − | 0.426852i | \(-0.859623\pi\) | ||||
−0.904322 | + | 0.426852i | \(0.859623\pi\) | |||||||
\(728\) | −1.77241e8 | − | 7.97004e7i | −0.459378 | − | 0.206570i | ||||
\(729\) | −2.74176e8 | −0.707697 | ||||||||
\(730\) | −4.70252e8 | + | 7.91232e7i | −1.20882 | + | 0.203393i | ||||
\(731\) | − | 4.49411e8i | − | 1.15051i | ||||||
\(732\) | 5.95628e7 | − | 5.72357e7i | 0.151859 | − | 0.145926i | ||||
\(733\) | 6.03758e8i | 1.53303i | 0.642226 | + | 0.766515i | \(0.278011\pi\) | ||||
−0.642226 | + | 0.766515i | \(0.721989\pi\) | |||||||
\(734\) | −4.87157e8 | + | 1.96125e8i | −1.23191 | + | 0.495958i | ||||
\(735\) | −9.90721e6 | + | 4.51419e7i | −0.0249511 | + | 0.113689i | ||||
\(736\) | 4.12053e7 | + | 1.15421e8i | 0.103352 | + | 0.289503i | ||||
\(737\) | 7.89796e8i | 1.97293i | ||||||||
\(738\) | −3.38841e7 | + | 1.36414e7i | −0.0842998 | + | 0.0339384i | ||||
\(739\) | 7.73026e8i | 1.91540i | 0.287760 | + | 0.957702i | \(0.407089\pi\) | ||||
−0.287760 | + | 0.957702i | \(0.592911\pi\) | |||||||
\(740\) | −1.02321e8 | + | 6.26539e7i | −0.252505 | + | 0.154616i | ||||
\(741\) | −4.87355e7 | −0.119782 | ||||||||
\(742\) | −2.17752e7 | − | 5.40876e7i | −0.0533028 | − | 0.132399i | ||||
\(743\) | 6.42826e7 | 0.156721 | 0.0783605 | − | 0.996925i | \(-0.475031\pi\) | ||||
0.0783605 | + | 0.996925i | \(0.475031\pi\) | |||||||
\(744\) | 6.43900e7 | + | 2.89544e7i | 0.156351 | + | 0.0703064i | ||||
\(745\) | 2.74904e7 | − | 1.25259e8i | 0.0664832 | − | 0.302929i | ||||
\(746\) | −2.56484e8 | − | 6.37082e8i | −0.617793 | − | 1.53454i | ||||
\(747\) | 7.18640e8 | 1.72405 | ||||||||
\(748\) | −4.46083e8 | + | 4.28655e8i | −1.06589 | + | 1.02424i | ||||
\(749\) | 4.26589e8 | 1.01523 | ||||||||
\(750\) | 2.49519e7 | − | 9.18020e7i | 0.0591454 | − | 0.217605i | ||||
\(751\) | 6.17586e8i | 1.45807i | 0.684477 | + | 0.729034i | \(0.260030\pi\) | ||||
−0.684477 | + | 0.729034i | \(0.739970\pi\) | |||||||
\(752\) | −4.93225e6 | + | 1.23728e8i | −0.0115982 | + | 0.290947i | ||||
\(753\) | 2.70293e7i | 0.0633067i | ||||||||
\(754\) | −8.37209e7 | − | 2.07955e8i | −0.195308 | − | 0.485127i | ||||
\(755\) | −5.71697e8 | − | 1.25469e8i | −1.32839 | − | 0.291539i | ||||
\(756\) | 1.68615e8 | − | 1.62027e8i | 0.390239 | − | 0.374992i | ||||
\(757\) | − | 3.20889e8i | − | 0.739719i | −0.929088 | − | 0.369859i | \(-0.879406\pi\) | ||
0.929088 | − | 0.369859i | \(-0.120594\pi\) | |||||||
\(758\) | −1.24107e8 | − | 3.08271e8i | −0.284964 | − | 0.707825i | ||||
\(759\) | 3.97121e7i | 0.0908232i | ||||||||
\(760\) | 3.39791e8 | − | 4.57688e8i | 0.774053 | − | 1.04263i | ||||
\(761\) | −7.08784e7 | −0.160827 | −0.0804136 | − | 0.996762i | \(-0.525624\pi\) | ||||
−0.0804136 | + | 0.996762i | \(0.525624\pi\) | |||||||
\(762\) | 5.18455e7 | − | 2.08725e7i | 0.117178 | − | 0.0471748i | ||||
\(763\) | 8.57290e7 | 0.192999 | ||||||||
\(764\) | 4.89405e8 | + | 5.09303e8i | 1.09746 | + | 1.14208i | ||||
\(765\) | −4.68272e8 | − | 1.02771e8i | −1.04596 | − | 0.229554i | ||||
\(766\) | 3.66629e8 | − | 1.47602e8i | 0.815718 | − | 0.328401i | ||||
\(767\) | 2.64509e8 | 0.586212 | ||||||||
\(768\) | 1.01824e8 | + | 8.13106e6i | 0.224784 | + | 0.0179500i | ||||
\(769\) | 2.07387e8 | 0.456040 | 0.228020 | − | 0.973656i | \(-0.426775\pi\) | ||||
0.228020 | + | 0.973656i | \(0.426775\pi\) | |||||||
\(770\) | 7.26329e8 | − | 1.22210e8i | 1.59097 | − | 0.267691i | ||||
\(771\) | − | 1.83933e8i | − | 0.401324i | ||||||
\(772\) | 4.25926e8 | + | 4.43243e8i | 0.925726 | + | 0.963364i | ||||
\(773\) | − | 4.62098e8i | − | 1.00045i | −0.865895 | − | 0.500226i | \(-0.833250\pi\) | ||
0.865895 | − | 0.500226i | \(-0.166750\pi\) | |||||||
\(774\) | 4.16330e8 | − | 1.67611e8i | 0.897872 | − | 0.361476i | ||||
\(775\) | −1.48190e8 | + | 3.21351e8i | −0.318357 | + | 0.690358i | ||||
\(776\) | −4.46962e8 | − | 2.00986e8i | −0.956502 | − | 0.430112i | ||||
\(777\) | 3.85651e7i | 0.0822112i | ||||||||
\(778\) | −1.84786e8 | + | 7.43934e7i | −0.392402 | + | 0.157978i | ||||
\(779\) | 5.87733e7i | 0.124328i | ||||||||
\(780\) | 3.73313e7 | − | 2.28590e7i | 0.0786665 | − | 0.0481696i | ||||
\(781\) | −4.29680e8 | −0.901970 | ||||||||
\(782\) | −6.19387e7 | − | 1.53850e8i | −0.129521 | − | 0.321719i | ||||
\(783\) | 2.69751e8 | 0.561924 | ||||||||
\(784\) | 9.90760e6 | − | 2.48537e8i | 0.0205599 | − | 0.515754i | ||||
\(785\) | 4.22539e8 | + | 9.27338e7i | 0.873489 | + | 0.191703i | ||||
\(786\) | −5.18969e7 | − | 1.28907e8i | −0.106874 | − | 0.265466i | ||||
\(787\) | −6.57367e8 | −1.34860 | −0.674301 | − | 0.738457i | \(-0.735555\pi\) | ||||
−0.674301 | + | 0.738457i | \(0.735555\pi\) | |||||||
\(788\) | −1.56406e8 | − | 1.62765e8i | −0.319650 | − | 0.332646i | ||||
\(789\) | 1.77433e8 | 0.361247 | ||||||||
\(790\) | −6.71035e8 | + | 1.12906e8i | −1.36102 | + | 0.229001i | ||||
\(791\) | − | 6.35498e8i | − | 1.28406i | ||||||
\(792\) | −5.63471e8 | − | 2.53377e8i | −1.13422 | − | 0.510025i | ||||
\(793\) | 1.90518e8i | 0.382047i | ||||||||
\(794\) | 3.09460e8 | + | 7.68669e8i | 0.618219 | + | 1.53560i | ||||
\(795\) | 1.28281e7 | + | 2.81536e6i | 0.0255306 | + | 0.00560315i | ||||
\(796\) | −7.49059e7 | − | 7.79515e7i | −0.148517 | − | 0.154556i | ||||
\(797\) | − | 3.81335e8i | − | 0.753238i | −0.926368 | − | 0.376619i | \(-0.877087\pi\) | ||
0.926368 | − | 0.376619i | \(-0.122913\pi\) | |||||||
\(798\) | −6.84277e7 | − | 1.69968e8i | −0.134655 | − | 0.334471i | ||||
\(799\) | − | 1.67569e8i | − | 0.328513i | ||||||
\(800\) | −4.56048e7 | + | 5.09965e8i | −0.0890719 | + | 0.996025i | ||||
\(801\) | 6.48358e8 | 1.26159 | ||||||||
\(802\) | 6.04366e8 | − | 2.43313e8i | 1.17159 | − | 0.471673i | ||||
\(803\) | 8.31613e8 | 1.60611 | ||||||||
\(804\) | −1.27245e8 | + | 1.22274e8i | −0.244835 | + | 0.235270i | ||||
\(805\) | −4.23271e7 | + | 1.92862e8i | −0.0811392 | + | 0.369708i | ||||
\(806\) | −1.51049e8 | + | 6.08109e7i | −0.288477 | + | 0.116139i | ||||
\(807\) | −1.37497e8 | −0.261620 | ||||||||
\(808\) | 1.17832e8 | − | 2.62041e8i | 0.223373 | − | 0.496747i | ||||
\(809\) | −2.89351e8 | −0.546487 | −0.273243 | − | 0.961945i | \(-0.588096\pi\) | ||||
−0.273243 | + | 0.961945i | \(0.588096\pi\) | |||||||
\(810\) | −7.49554e7 | − | 4.45482e8i | −0.141042 | − | 0.838253i | ||||
\(811\) | − | 2.32956e8i | − | 0.436729i | −0.975867 | − | 0.218364i | \(-0.929928\pi\) | ||
0.975867 | − | 0.218364i | \(-0.0700721\pi\) | |||||||
\(812\) | 6.07707e8 | − | 5.83964e8i | 1.13508 | − | 1.09073i | ||||
\(813\) | 4.56784e7i | 0.0850040i | ||||||||
\(814\) | 1.94097e8 | − | 7.81416e7i | 0.359869 | − | 0.144880i | ||||
\(815\) | 1.34661e8 | − | 6.13577e8i | 0.248753 | − | 1.13343i | ||||
\(816\) | −1.38123e8 | − | 5.50608e6i | −0.254211 | − | 0.0101338i | ||||
\(817\) | − | 7.22141e8i | − | 1.32421i | ||||||
\(818\) | −7.09952e8 | + | 2.85821e8i | −1.29709 | + | 0.522196i | ||||
\(819\) | 2.62631e8i | 0.478073i | ||||||||
\(820\) | −2.75672e7 | − | 4.50203e7i | −0.0499977 | − | 0.0816521i | ||||
\(821\) | −4.41895e8 | −0.798528 | −0.399264 | − | 0.916836i | \(-0.630734\pi\) | ||||
−0.399264 | + | 0.916836i | \(0.630734\pi\) | |||||||
\(822\) | 2.53454e7 | + | 6.29556e7i | 0.0456335 | + | 0.113349i | ||||
\(823\) | 8.93586e8 | 1.60301 | 0.801506 | − | 0.597987i | \(-0.204032\pi\) | ||||
0.801506 | + | 0.597987i | \(0.204032\pi\) | |||||||
\(824\) | −1.36330e8 | + | 3.03177e8i | −0.243675 | + | 0.541894i | ||||
\(825\) | −6.94751e7 | + | 1.50657e8i | −0.123728 | + | 0.268304i | ||||
\(826\) | 3.71388e8 | + | 9.22493e8i | 0.659003 | + | 1.63690i | ||||
\(827\) | −5.74698e8 | −1.01607 | −0.508034 | − | 0.861337i | \(-0.669628\pi\) | ||||
−0.508034 | + | 0.861337i | \(0.669628\pi\) | |||||||
\(828\) | 1.19425e8 | − | 1.14759e8i | 0.210379 | − | 0.202160i | ||||
\(829\) | −5.62396e7 | −0.0987139 | −0.0493570 | − | 0.998781i | \(-0.515717\pi\) | ||||
−0.0493570 | + | 0.998781i | \(0.515717\pi\) | |||||||
\(830\) | 1.72330e8 | + | 1.02421e9i | 0.301388 | + | 1.79124i | ||||
\(831\) | 1.44177e8i | 0.251242i | ||||||||
\(832\) | −1.76240e8 | + | 1.56340e8i | −0.306009 | + | 0.271456i | ||||
\(833\) | 3.36602e8i | 0.582346i | ||||||||
\(834\) | −8.90846e6 | − | 2.21278e7i | −0.0153569 | − | 0.0381452i | ||||
\(835\) | 4.86972e7 | − | 2.21887e8i | 0.0836459 | − | 0.381130i | ||||
\(836\) | −7.16793e8 | + | 6.88789e8i | −1.22680 | + | 1.17887i | ||||
\(837\) | − | 1.95934e8i | − | 0.334144i | ||||||
\(838\) | 7.25489e6 | + | 1.80205e7i | 0.0123282 | + | 0.0306220i | ||||
\(839\) | − | 6.14216e8i | − | 1.04001i | −0.854165 | − | 0.520003i | \(-0.825931\pi\) | ||
0.854165 | − | 0.520003i | \(-0.174069\pi\) | |||||||
\(840\) | 1.32138e8 | + | 9.81000e7i | 0.222941 | + | 0.165513i | ||||
\(841\) | 3.77390e8 | 0.634457 | ||||||||
\(842\) | −3.80979e8 | + | 1.53379e8i | −0.638211 | + | 0.256938i | ||||
\(843\) | −1.35764e8 | −0.226621 | ||||||||
\(844\) | 2.42475e8 | + | 2.52333e8i | 0.403310 | + | 0.419708i | ||||
\(845\) | 1.07696e8 | − | 4.90714e8i | 0.178496 | − | 0.813313i | ||||
\(846\) | 1.55234e8 | − | 6.24959e7i | 0.256375 | − | 0.103214i | ||||
\(847\) | −5.36260e8 | −0.882522 | ||||||||
\(848\) | −7.06274e7 | − | 2.81547e6i | −0.115821 | − | 0.00461704i | ||||
\(849\) | 1.22677e7 | 0.0200466 | ||||||||
\(850\) | 3.41774e7 | − | 6.92025e8i | 0.0556522 | − | 1.12685i | ||||
\(851\) | 5.60922e7i | 0.0910151i | ||||||||
\(852\) | −6.65219e7 | − | 6.92265e7i | −0.107559 | − | 0.111932i | ||||
\(853\) | 7.29239e8i | 1.17496i | 0.809239 | + | 0.587480i | \(0.199880\pi\) | ||||
−0.809239 | + | 0.587480i | \(0.800120\pi\) | |||||||
\(854\) | −6.64444e8 | + | 2.67500e8i | −1.06680 | + | 0.429486i | ||||
\(855\) | −7.52448e8 | − | 1.65138e8i | −1.20387 | − | 0.264210i | ||||
\(856\) | 2.12089e8 | − | 4.71654e8i | 0.338141 | − | 0.751973i | ||||
\(857\) | 5.93996e6i | 0.00943716i | 0.999989 | + | 0.00471858i | \(0.00150198\pi\) | ||||
−0.999989 | + | 0.00471858i | \(0.998498\pi\) | |||||||
\(858\) | −7.08152e7 | + | 2.85096e7i | −0.112115 | + | 0.0451366i | ||||
\(859\) | − | 2.37950e8i | − | 0.375410i | −0.982225 | − | 0.187705i | \(-0.939895\pi\) | ||
0.982225 | − | 0.187705i | \(-0.0601049\pi\) | |||||||
\(860\) | 3.38714e8 | + | 5.53160e8i | 0.532523 | + | 0.869672i | ||||
\(861\) | −1.69683e7 | −0.0265845 | ||||||||
\(862\) | 2.68594e8 | + | 6.67163e8i | 0.419348 | + | 1.04162i | ||||
\(863\) | −9.36443e8 | −1.45696 | −0.728482 | − | 0.685065i | \(-0.759774\pi\) | ||||
−0.728482 | + | 0.685065i | \(0.759774\pi\) | |||||||
\(864\) | −9.53125e7 | − | 2.66983e8i | −0.147778 | − | 0.413945i | ||||
\(865\) | 2.59262e8 | + | 5.68998e7i | 0.400581 | + | 0.0879148i | ||||
\(866\) | 1.08395e8 | + | 2.69244e8i | 0.166900 | + | 0.414565i | ||||
\(867\) | 4.01028e7 | 0.0615344 | ||||||||
\(868\) | −4.24164e8 | − | 4.41410e8i | −0.648597 | − | 0.674967i | ||||
\(869\) | 1.18669e9 | 1.80832 | ||||||||
\(870\) | 3.14993e7 | + | 1.87209e8i | 0.0478347 | + | 0.284296i | ||||
\(871\) | − | 4.07008e8i | − | 0.615955i | ||||||
\(872\) | 4.26223e7 | − | 9.47854e7i | 0.0642818 | − | 0.142953i | ||||
\(873\) | 6.62297e8i | 0.995428i | ||||||||
\(874\) | −9.95269e7 | − | 2.47216e8i | −0.149075 | − | 0.370290i | ||||
\(875\) | −4.97984e8 | + | 6.57616e8i | −0.743346 | + | 0.981631i | ||||
\(876\) | 1.28748e8 | + | 1.33983e8i | 0.191526 | + | 0.199313i | ||||
\(877\) | 4.37126e8i | 0.648050i | 0.946049 | + | 0.324025i | \(0.105036\pi\) | ||||
−0.946049 | + | 0.324025i | \(0.894964\pi\) | |||||||
\(878\) | 6.05141e7 | + | 1.50312e8i | 0.0894074 | + | 0.222080i | ||||
\(879\) | 1.94762e8i | 0.286773i | ||||||||
\(880\) | 2.25993e8 | − | 8.63818e8i | 0.331624 | − | 1.26758i | ||||
\(881\) | −3.67911e8 | −0.538041 | −0.269020 | − | 0.963134i | \(-0.586700\pi\) | ||||
−0.269020 | + | 0.963134i | \(0.586700\pi\) | |||||||
\(882\) | −3.11824e8 | + | 1.25538e8i | −0.454469 | + | 0.182965i | ||||
\(883\) | 9.70524e8 | 1.40969 | 0.704846 | − | 0.709360i | \(-0.251016\pi\) | ||||
0.704846 | + | 0.709360i | \(0.251016\pi\) | |||||||
\(884\) | 2.29881e8 | − | 2.20900e8i | 0.332772 | − | 0.319771i | ||||
\(885\) | −2.18790e8 | − | 4.80175e7i | −0.315645 | − | 0.0692739i | ||||
\(886\) | 1.05768e9 | − | 4.25814e8i | 1.52074 | − | 0.612236i | ||||
\(887\) | 8.13859e8 | 1.16621 | 0.583107 | − | 0.812395i | \(-0.301837\pi\) | ||||
0.583107 | + | 0.812395i | \(0.301837\pi\) | |||||||
\(888\) | 4.26390e7 | + | 1.91736e7i | 0.0608932 | + | 0.0273819i | ||||
\(889\) | −4.84615e8 | −0.689750 | ||||||||
\(890\) | 1.55476e8 | + | 9.24039e8i | 0.220543 | + | 1.31075i | ||||
\(891\) | 7.87808e8i | 1.11375i | ||||||||
\(892\) | 3.12488e8 | − | 3.00280e8i | 0.440290 | − | 0.423089i | ||||
\(893\) | − | 2.69260e8i | − | 0.378109i | ||||||
\(894\) | −4.63549e7 | + | 1.86621e7i | −0.0648758 | + | 0.0261185i | ||||
\(895\) | 1.56880e8 | + | 3.44302e7i | 0.218826 | + | 0.0480254i | ||||
\(896\) | −7.92697e8 | − | 3.95137e8i | −1.10200 | − | 0.549317i | ||||
\(897\) | − | 2.04650e7i | − | 0.0283552i | ||||||
\(898\) | −6.16602e8 | + | 2.48239e8i | −0.851482 | + | 0.342800i | ||||
\(899\) | − | 7.06169e8i | − | 0.971919i | ||||||
\(900\) | 6.53831e8 | − | 2.26434e8i | 0.896888 | − | 0.310609i | ||||
\(901\) | 9.56531e7 | 0.130775 | ||||||||
\(902\) | 3.43816e7 | + | 8.54008e7i | 0.0468497 | + | 0.116370i | ||||
\(903\) | 2.08487e8 | 0.283150 | ||||||||
\(904\) | −7.02631e8 | − | 3.15954e8i | −0.951091 | − | 0.427679i | ||||
\(905\) | 5.08671e7 | − | 2.31774e8i | 0.0686264 | − | 0.312694i | ||||
\(906\) | 8.51760e7 | + | 2.11569e8i | 0.114534 | + | 0.284491i | ||||
\(907\) | −1.02901e8 | −0.137910 | −0.0689551 | − | 0.997620i | \(-0.521967\pi\) | ||||
−0.0689551 | + | 0.997620i | \(0.521967\pi\) | |||||||
\(908\) | −2.38654e8 | + | 2.29330e8i | −0.318795 | + | 0.306340i | ||||
\(909\) | −3.88285e8 | −0.516962 | ||||||||
\(910\) | −3.74302e8 | + | 6.29788e7i | −0.496704 | + | 0.0835739i | ||||
\(911\) | − | 1.62697e8i | − | 0.215191i | −0.994195 | − | 0.107596i | \(-0.965685\pi\) | ||
0.994195 | − | 0.107596i | \(-0.0343152\pi\) | |||||||
\(912\) | −2.21944e8 | − | 8.84751e6i | −0.292590 | − | 0.0116637i | ||||
\(913\) | − | 1.81125e9i | − | 2.37994i | ||||||
\(914\) | −5.16258e8 | − | 1.28234e9i | −0.676126 | − | 1.67944i | ||||
\(915\) | 3.45856e7 | − | 1.57588e8i | 0.0451473 | − | 0.205712i | ||||
\(916\) | −5.30038e8 | + | 5.09330e8i | −0.689637 | + | 0.662693i | ||||
\(917\) | 1.20493e9i | 1.56263i | ||||||||
\(918\) | 1.43271e8 | + | 3.55873e8i | 0.185196 | + | 0.460009i | ||||
\(919\) | 1.40533e9i | 1.81064i | 0.424730 | + | 0.905320i | \(0.360369\pi\) | ||||
−0.424730 | + | 0.905320i | \(0.639631\pi\) | |||||||
\(920\) | 1.92192e8 | + | 1.42685e8i | 0.246815 | + | 0.183237i | ||||
\(921\) | −8.84936e7 | −0.113275 | ||||||||
\(922\) | 1.44441e8 | − | 5.81509e7i | 0.184289 | − | 0.0741931i | ||||
\(923\) | 2.21428e8 | 0.281597 | ||||||||
\(924\) | −1.98858e8 | − | 2.06943e8i | −0.252074 | − | 0.262322i | ||||
\(925\) | −9.81316e7 | + | 2.12798e8i | −0.123989 | + | 0.268871i | ||||
\(926\) | 1.20030e9 | − | 4.83229e8i | 1.51166 | − | 0.608583i | ||||
\(927\) | 4.49239e8 | 0.563948 | ||||||||
\(928\) | −3.43517e8 | − | 9.62238e8i | −0.429838 | − | 1.20403i | ||||
\(929\) | −1.57221e9 | −1.96093 | −0.980467 | − | 0.196685i | \(-0.936982\pi\) | ||||
−0.980467 | + | 0.196685i | \(0.936982\pi\) | |||||||
\(930\) | 1.35980e8 | − | 2.28796e7i | 0.169054 | − | 0.0284446i | ||||
\(931\) | 5.40872e8i | 0.670264i | ||||||||
\(932\) | −2.71334e7 | − | 2.82366e7i | −0.0335163 | − | 0.0348790i | ||||
\(933\) | − | 3.50176e7i | − | 0.0431163i | ||||||
\(934\) | −3.96742e8 | + | 1.59725e8i | −0.486931 | + | 0.196034i | ||||
\(935\) | −2.59021e8 | + | 1.18022e9i | −0.316884 | + | 1.44387i | ||||
\(936\) | 2.90375e8 | + | 1.30574e8i | 0.354105 | + | 0.159231i | ||||
\(937\) | − | 5.23220e8i | − | 0.636013i | −0.948089 | − | 0.318006i | \(-0.896987\pi\) | ||
0.948089 | − | 0.318006i | \(-0.103013\pi\) | |||||||
\(938\) | 1.41947e9 | − | 5.71466e8i | 1.71996 | − | 0.692440i | ||||
\(939\) | − | 5.02239e7i | − | 0.0606616i | ||||||
\(940\) | 1.26294e8 | + | 2.06253e8i | 0.152055 | + | 0.248323i | ||||
\(941\) | 3.00726e8 | 0.360912 | 0.180456 | − | 0.983583i | \(-0.442243\pi\) | ||||
0.180456 | + | 0.983583i | \(0.442243\pi\) | |||||||
\(942\) | −6.29531e7 | − | 1.56370e8i | −0.0753121 | − | 0.187068i | ||||
\(943\) | −2.46801e7 | −0.0294314 | ||||||||
\(944\) | 1.20459e9 | + | 4.80194e7i | 1.43193 | + | 0.0570822i | ||||
\(945\) | 9.79074e7 | − | 4.46112e8i | 0.116017 | − | 0.528626i | ||||
\(946\) | −4.22443e8 | − | 1.04931e9i | −0.498993 | − | 1.23945i | ||||
\(947\) | −4.73433e8 | −0.557453 | −0.278727 | − | 0.960370i | \(-0.589912\pi\) | ||||
−0.278727 | + | 0.960370i | \(0.589912\pi\) | |||||||
\(948\) | 1.83719e8 | + | 1.91189e8i | 0.215640 | + | 0.224408i | ||||
\(949\) | −4.28558e8 | −0.501431 | ||||||||
\(950\) | 5.49184e7 | − | 1.11199e9i | 0.0640541 | − | 1.29697i | ||||
\(951\) | 1.45004e8i | 0.168593i | ||||||||
\(952\) | 1.09317e9 | + | 4.91569e8i | 1.26700 | + | 0.569736i | ||||
\(953\) | 6.45528e8i | 0.745824i | 0.927867 | + | 0.372912i | \(0.121641\pi\) | ||||
−0.927867 | + | 0.372912i | \(0.878359\pi\) | |||||||
\(954\) | 3.56744e7 | + | 8.86120e7i | 0.0410877 | + | 0.102058i | ||||
\(955\) | 1.34749e9 | + | 2.95731e8i | 1.54709 | + | 0.339536i | ||||
\(956\) | −8.36174e8 | − | 8.70171e8i | −0.957025 | − | 0.995935i | ||||
\(957\) | − | 3.31069e8i | − | 0.377731i | ||||||
\(958\) | −1.55648e8 | − | 3.86616e8i | −0.177030 | − | 0.439727i | ||||
\(959\) | − | 5.88465e8i | − | 0.667213i | ||||||
\(960\) | 1.74159e8 | − | 9.73238e7i | 0.196848 | − | 0.110003i | ||||
\(961\) | 3.74576e8 | 0.422055 | ||||||||
\(962\) | −1.00024e8 | + | 4.02690e7i | −0.112352 | + | 0.0452320i | ||||
\(963\) | −6.98884e8 | −0.782575 | ||||||||
\(964\) | 5.51824e8 | − | 5.30264e8i | 0.615984 | − | 0.591918i | ||||
\(965\) | 1.17271e9 | + | 2.57372e8i | 1.30499 | + | 0.286405i | ||||
\(966\) | 7.13729e7 | − | 2.87341e7i | 0.0791775 | − | 0.0318762i | ||||
\(967\) | 6.01748e8 | 0.665481 | 0.332740 | − | 0.943018i | \(-0.392027\pi\) | ||||
0.332740 | + | 0.943018i | \(0.392027\pi\) | |||||||
\(968\) | −2.66615e8 | + | 5.92911e8i | −0.293940 | + | 0.653677i | ||||
\(969\) | 3.00586e8 | 0.330368 | ||||||||
\(970\) | −9.43904e8 | + | 1.58818e8i | −1.03422 | + | 0.174015i | ||||
\(971\) | − | 3.59534e8i | − | 0.392719i | −0.980532 | − | 0.196360i | \(-0.937088\pi\) | ||
0.980532 | − | 0.196360i | \(-0.0629120\pi\) | |||||||
\(972\) | −4.17968e8 | + | 4.01638e8i | −0.455139 | + | 0.437357i | ||||
\(973\) | 2.06835e8i | 0.224536i | ||||||||
\(974\) | −3.33523e8 | + | 1.34274e8i | −0.360952 | + | 0.145316i | ||||
\(975\) | 3.58028e7 | − | 7.76385e7i | 0.0386281 | − | 0.0837651i | ||||
\(976\) | −3.45869e7 | + | 8.67630e8i | −0.0372017 | + | 0.933222i | ||||
\(977\) | − | 3.41034e8i | − | 0.365691i | −0.983142 | − | 0.182845i | \(-0.941469\pi\) | ||
0.983142 | − | 0.182845i | \(-0.0585308\pi\) | |||||||
\(978\) | −2.27068e8 | + | 9.14155e7i | −0.242739 | + | 0.0977245i | ||||
\(979\) | − | 1.63411e9i | − | 1.74154i | ||||||
\(980\) | −2.53692e8 | − | 4.14308e8i | −0.269543 | − | 0.440195i | ||||
\(981\) | −1.40450e8 | −0.148770 | ||||||||
\(982\) | 7.72892e7 | + | 1.91979e8i | 0.0816177 | + | 0.202731i | ||||
\(983\) | −7.22351e8 | −0.760480 | −0.380240 | − | 0.924888i | \(-0.624159\pi\) | ||||
−0.380240 | + | 0.924888i | \(0.624159\pi\) | |||||||
\(984\) | −8.43620e6 | + | 1.87608e7i | −0.00885445 | + | 0.0196909i | ||||
\(985\) | −4.30635e8 | − | 9.45106e7i | −0.450610 | − | 0.0988945i | ||||
\(986\) | 5.16366e8 | + | 1.28261e9i | 0.538675 | + | 1.33802i | ||||
\(987\) | 7.77372e7 | 0.0808495 | ||||||||
\(988\) | 3.69388e8 | − | 3.54956e8i | 0.383011 | − | 0.368047i | ||||
\(989\) | 3.03241e8 | 0.313472 | ||||||||
\(990\) | −1.18995e9 | + | 2.00217e8i | −1.22637 | + | 0.206346i | ||||
\(991\) | 1.09281e9i | 1.12286i | 0.827526 | + | 0.561428i | \(0.189748\pi\) | ||||
−0.827526 | + | 0.561428i | \(0.810252\pi\) | |||||||
\(992\) | −6.98924e8 | + | 2.49515e8i | −0.715970 | + | 0.255600i | ||||
\(993\) | 2.84641e6i | 0.00290703i | ||||||||
\(994\) | 3.10900e8 | + | 7.72246e8i | 0.316564 | + | 0.786315i | ||||
\(995\) | −2.06240e8 | − | 4.52631e7i | −0.209365 | − | 0.0459489i | ||||
\(996\) | 2.91813e8 | − | 2.80412e8i | 0.295343 | − | 0.283804i | ||||
\(997\) | 9.59556e8i | 0.968245i | 0.875000 | + | 0.484122i | \(0.160861\pi\) | ||||
−0.875000 | + | 0.484122i | \(0.839139\pi\) | |||||||
\(998\) | 6.40980e7 | + | 1.59213e8i | 0.0644841 | + | 0.160173i | ||||
\(999\) | − | 1.29748e8i | − | 0.130138i |
(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 | 20.7.d.d.19.11 | yes | 12 | |
3.2 | odd | 2 | 180.7.f.e.19.2 | 12 | |||
4.3 | odd | 2 | inner | 20.7.d.d.19.1 | ✓ | 12 | |
5.2 | odd | 4 | 100.7.b.f.51.8 | 12 | |||
5.3 | odd | 4 | 100.7.b.f.51.5 | 12 | |||
5.4 | even | 2 | inner | 20.7.d.d.19.2 | yes | 12 | |
8.3 | odd | 2 | 320.7.h.f.319.6 | 12 | |||
8.5 | even | 2 | 320.7.h.f.319.8 | 12 | |||
12.11 | even | 2 | 180.7.f.e.19.12 | 12 | |||
15.14 | odd | 2 | 180.7.f.e.19.11 | 12 | |||
20.3 | even | 4 | 100.7.b.f.51.6 | 12 | |||
20.7 | even | 4 | 100.7.b.f.51.7 | 12 | |||
20.19 | odd | 2 | inner | 20.7.d.d.19.12 | yes | 12 | |
40.19 | odd | 2 | 320.7.h.f.319.7 | 12 | |||
40.29 | even | 2 | 320.7.h.f.319.5 | 12 | |||
60.59 | even | 2 | 180.7.f.e.19.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.7.d.d.19.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
20.7.d.d.19.2 | yes | 12 | 5.4 | even | 2 | inner | |
20.7.d.d.19.11 | yes | 12 | 1.1 | even | 1 | trivial | |
20.7.d.d.19.12 | yes | 12 | 20.19 | odd | 2 | inner | |
100.7.b.f.51.5 | 12 | 5.3 | odd | 4 | |||
100.7.b.f.51.6 | 12 | 20.3 | even | 4 | |||
100.7.b.f.51.7 | 12 | 20.7 | even | 4 | |||
100.7.b.f.51.8 | 12 | 5.2 | odd | 4 | |||
180.7.f.e.19.1 | 12 | 60.59 | even | 2 | |||
180.7.f.e.19.2 | 12 | 3.2 | odd | 2 | |||
180.7.f.e.19.11 | 12 | 15.14 | odd | 2 | |||
180.7.f.e.19.12 | 12 | 12.11 | even | 2 | |||
320.7.h.f.319.5 | 12 | 40.29 | even | 2 | |||
320.7.h.f.319.6 | 12 | 8.3 | odd | 2 | |||
320.7.h.f.319.7 | 12 | 40.19 | odd | 2 | |||
320.7.h.f.319.8 | 12 | 8.5 | even | 2 |