Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,6,Mod(36,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.36");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.b (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: | \(5.93420133308\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 390 x^{14} + 60701 x^{12} + 4799932 x^{10} + 203487156 x^{8} + 4519465040 x^{6} + \cdots + 178006118400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 36.8 | ||
Root | \(-1.04262i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.36 |
Dual form | 37.6.b.a.36.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.04262i | − | 0.184311i | −0.995745 | − | 0.0921556i | \(-0.970624\pi\) | ||
0.995745 | − | 0.0921556i | \(-0.0293757\pi\) | |||||||
\(3\) | 19.6295 | 1.25923 | 0.629617 | − | 0.776905i | \(-0.283212\pi\) | ||||
0.629617 | + | 0.776905i | \(0.283212\pi\) | |||||||
\(4\) | 30.9129 | 0.966029 | ||||||||
\(5\) | 86.4713i | 1.54685i | 0.633891 | + | 0.773423i | \(0.281457\pi\) | ||||
−0.633891 | + | 0.773423i | \(0.718543\pi\) | |||||||
\(6\) | − | 20.4662i | − | 0.232091i | ||||||
\(7\) | −87.1072 | −0.671907 | −0.335954 | − | 0.941879i | \(-0.609059\pi\) | ||||
−0.335954 | + | 0.941879i | \(0.609059\pi\) | |||||||
\(8\) | − | 65.5944i | − | 0.362361i | ||||||
\(9\) | 142.318 | 0.585673 | ||||||||
\(10\) | 90.1568 | 0.285101 | ||||||||
\(11\) | 153.498 | 0.382491 | 0.191246 | − | 0.981542i | \(-0.438747\pi\) | ||||
0.191246 | + | 0.981542i | \(0.438747\pi\) | |||||||
\(12\) | 606.806 | 1.21646 | ||||||||
\(13\) | − | 27.6086i | − | 0.0453092i | −0.999743 | − | 0.0226546i | \(-0.992788\pi\) | ||
0.999743 | − | 0.0226546i | \(-0.00721181\pi\) | |||||||
\(14\) | 90.8199i | 0.123840i | ||||||||
\(15\) | 1697.39i | 1.94784i | ||||||||
\(16\) | 920.824 | 0.899242 | ||||||||
\(17\) | − | 926.725i | − | 0.777730i | −0.921295 | − | 0.388865i | \(-0.872867\pi\) | ||
0.921295 | − | 0.388865i | \(-0.127133\pi\) | |||||||
\(18\) | − | 148.384i | − | 0.107946i | ||||||
\(19\) | − | 2749.94i | − | 1.74759i | −0.486298 | − | 0.873793i | \(-0.661653\pi\) | ||
0.486298 | − | 0.873793i | \(-0.338347\pi\) | |||||||
\(20\) | 2673.08i | 1.49430i | ||||||||
\(21\) | −1709.87 | −0.846089 | ||||||||
\(22\) | − | 160.041i | − | 0.0704974i | ||||||
\(23\) | − | 1336.01i | − | 0.526611i | −0.964713 | − | 0.263305i | \(-0.915187\pi\) | ||
0.964713 | − | 0.263305i | \(-0.0848127\pi\) | |||||||
\(24\) | − | 1287.59i | − | 0.456298i | ||||||
\(25\) | −4352.28 | −1.39273 | ||||||||
\(26\) | −28.7854 | −0.00835100 | ||||||||
\(27\) | −1976.33 | −0.521736 | ||||||||
\(28\) | −2692.74 | −0.649082 | ||||||||
\(29\) | 7147.31i | 1.57815i | 0.614299 | + | 0.789073i | \(0.289439\pi\) | ||||
−0.614299 | + | 0.789073i | \(0.710561\pi\) | |||||||
\(30\) | 1769.74 | 0.359009 | ||||||||
\(31\) | − | 4026.24i | − | 0.752481i | −0.926522 | − | 0.376240i | \(-0.877217\pi\) | ||
0.926522 | − | 0.376240i | \(-0.122783\pi\) | |||||||
\(32\) | − | 3059.09i | − | 0.528102i | ||||||
\(33\) | 3013.10 | 0.481646 | ||||||||
\(34\) | −966.224 | −0.143344 | ||||||||
\(35\) | − | 7532.28i | − | 1.03934i | ||||||
\(36\) | 4399.48 | 0.565777 | ||||||||
\(37\) | −7808.85 | + | 2892.37i | −0.937741 | + | 0.347336i | ||||
\(38\) | −2867.14 | −0.322100 | ||||||||
\(39\) | − | 541.945i | − | 0.0570550i | ||||||
\(40\) | 5672.03 | 0.560517 | ||||||||
\(41\) | 11398.2 | 1.05896 | 0.529478 | − | 0.848324i | \(-0.322388\pi\) | ||||
0.529478 | + | 0.848324i | \(0.322388\pi\) | |||||||
\(42\) | 1782.75i | 0.155944i | ||||||||
\(43\) | 8183.21i | 0.674920i | 0.941340 | + | 0.337460i | \(0.109568\pi\) | ||||
−0.941340 | + | 0.337460i | \(0.890432\pi\) | |||||||
\(44\) | 4745.08 | 0.369498 | ||||||||
\(45\) | 12306.5i | 0.905945i | ||||||||
\(46\) | −1392.95 | −0.0970603 | ||||||||
\(47\) | −13313.5 | −0.879122 | −0.439561 | − | 0.898213i | \(-0.644866\pi\) | ||||
−0.439561 | + | 0.898213i | \(0.644866\pi\) | |||||||
\(48\) | 18075.3 | 1.13236 | ||||||||
\(49\) | −9219.33 | −0.548541 | ||||||||
\(50\) | 4537.78i | 0.256696i | ||||||||
\(51\) | − | 18191.2i | − | 0.979344i | ||||||
\(52\) | − | 853.464i | − | 0.0437701i | ||||||
\(53\) | 27617.4 | 1.35050 | 0.675248 | − | 0.737591i | \(-0.264037\pi\) | ||||
0.675248 | + | 0.737591i | \(0.264037\pi\) | |||||||
\(54\) | 2060.57i | 0.0961617i | ||||||||
\(55\) | 13273.2i | 0.591655i | ||||||||
\(56\) | 5713.75i | 0.243473i | ||||||||
\(57\) | − | 53980.0i | − | 2.20062i | ||||||
\(58\) | 7451.94 | 0.290870 | ||||||||
\(59\) | − | 16008.1i | − | 0.598700i | −0.954143 | − | 0.299350i | \(-0.903230\pi\) | ||
0.954143 | − | 0.299350i | \(-0.0967699\pi\) | |||||||
\(60\) | 52471.3i | 1.88167i | ||||||||
\(61\) | 44974.5i | 1.54754i | 0.633466 | + | 0.773770i | \(0.281631\pi\) | ||||
−0.633466 | + | 0.773770i | \(0.718369\pi\) | |||||||
\(62\) | −4197.84 | −0.138691 | ||||||||
\(63\) | −12397.0 | −0.393518 | ||||||||
\(64\) | 26276.9 | 0.801907 | ||||||||
\(65\) | 2387.35 | 0.0700864 | ||||||||
\(66\) | − | 3141.52i | − | 0.0887728i | ||||||
\(67\) | −45824.8 | −1.24713 | −0.623567 | − | 0.781770i | \(-0.714317\pi\) | ||||
−0.623567 | + | 0.781770i | \(0.714317\pi\) | |||||||
\(68\) | − | 28647.8i | − | 0.751310i | ||||||
\(69\) | − | 26225.2i | − | 0.663127i | ||||||
\(70\) | −7853.31 | −0.191561 | ||||||||
\(71\) | −18749.2 | −0.441404 | −0.220702 | − | 0.975341i | \(-0.570835\pi\) | ||||
−0.220702 | + | 0.975341i | \(0.570835\pi\) | |||||||
\(72\) | − | 9335.29i | − | 0.212225i | ||||||
\(73\) | −6614.81 | −0.145281 | −0.0726407 | − | 0.997358i | \(-0.523143\pi\) | ||||
−0.0726407 | + | 0.997358i | \(0.523143\pi\) | |||||||
\(74\) | 3015.65 | + | 8141.68i | 0.0640179 | + | 0.172836i | ||||
\(75\) | −85433.3 | −1.75377 | ||||||||
\(76\) | − | 85008.6i | − | 1.68822i | ||||||
\(77\) | −13370.8 | −0.256999 | ||||||||
\(78\) | −565.043 | −0.0105159 | ||||||||
\(79\) | − | 69916.6i | − | 1.26041i | −0.776428 | − | 0.630206i | \(-0.782970\pi\) | ||
0.776428 | − | 0.630206i | \(-0.217030\pi\) | |||||||
\(80\) | 79624.8i | 1.39099i | ||||||||
\(81\) | −73377.8 | −1.24266 | ||||||||
\(82\) | − | 11884.0i | − | 0.195177i | ||||||
\(83\) | 81375.6 | 1.29658 | 0.648289 | − | 0.761394i | \(-0.275485\pi\) | ||||
0.648289 | + | 0.761394i | \(0.275485\pi\) | |||||||
\(84\) | −52857.2 | −0.817347 | ||||||||
\(85\) | 80135.1 | 1.20303 | ||||||||
\(86\) | 8531.99 | 0.124395 | ||||||||
\(87\) | 140298.i | 1.98726i | ||||||||
\(88\) | − | 10068.6i | − | 0.138600i | ||||||
\(89\) | 120861.i | 1.61738i | 0.588235 | + | 0.808690i | \(0.299823\pi\) | ||||
−0.588235 | + | 0.808690i | \(0.700177\pi\) | |||||||
\(90\) | 12831.0 | 0.166976 | ||||||||
\(91\) | 2404.91i | 0.0304436i | ||||||||
\(92\) | − | 41300.0i | − | 0.508722i | ||||||
\(93\) | − | 79033.2i | − | 0.947550i | ||||||
\(94\) | 13881.0i | 0.162032i | ||||||||
\(95\) | 237791. | 2.70325 | ||||||||
\(96\) | − | 60048.5i | − | 0.665004i | ||||||
\(97\) | − | 5970.34i | − | 0.0644273i | −0.999481 | − | 0.0322137i | \(-0.989744\pi\) | ||
0.999481 | − | 0.0322137i | \(-0.0102557\pi\) | |||||||
\(98\) | 9612.27i | 0.101102i | ||||||||
\(99\) | 21845.6 | 0.224015 | ||||||||
\(100\) | −134542. | −1.34542 | ||||||||
\(101\) | 102083. | 0.995754 | 0.497877 | − | 0.867248i | \(-0.334113\pi\) | ||||
0.497877 | + | 0.867248i | \(0.334113\pi\) | |||||||
\(102\) | −18966.5 | −0.180504 | ||||||||
\(103\) | 193144.i | 1.79386i | 0.442172 | + | 0.896930i | \(0.354208\pi\) | ||||
−0.442172 | + | 0.896930i | \(0.645792\pi\) | |||||||
\(104\) | −1810.97 | −0.0164183 | ||||||||
\(105\) | − | 147855.i | − | 1.30877i | ||||||
\(106\) | − | 28794.5i | − | 0.248911i | ||||||
\(107\) | 120881. | 1.02070 | 0.510351 | − | 0.859966i | \(-0.329515\pi\) | ||||
0.510351 | + | 0.859966i | \(0.329515\pi\) | |||||||
\(108\) | −61094.2 | −0.504012 | ||||||||
\(109\) | − | 153803.i | − | 1.23993i | −0.784629 | − | 0.619966i | \(-0.787147\pi\) | ||
0.784629 | − | 0.619966i | \(-0.212853\pi\) | |||||||
\(110\) | 13838.9 | 0.109049 | ||||||||
\(111\) | −153284. | + | 56775.9i | −1.18084 | + | 0.437378i | ||||
\(112\) | −80210.4 | −0.604207 | ||||||||
\(113\) | 19713.0i | 0.145230i | 0.997360 | + | 0.0726150i | \(0.0231344\pi\) | ||||
−0.997360 | + | 0.0726150i | \(0.976866\pi\) | |||||||
\(114\) | −56280.7 | −0.405599 | ||||||||
\(115\) | 115526. | 0.814586 | ||||||||
\(116\) | 220944.i | 1.52454i | ||||||||
\(117\) | − | 3929.22i | − | 0.0265364i | ||||||
\(118\) | −16690.4 | −0.110347 | ||||||||
\(119\) | 80724.5i | 0.522562i | ||||||||
\(120\) | 111339. | 0.705822 | ||||||||
\(121\) | −137489. | −0.853700 | ||||||||
\(122\) | 46891.4 | 0.285229 | ||||||||
\(123\) | 223742. | 1.33347 | ||||||||
\(124\) | − | 124463.i | − | 0.726918i | ||||||
\(125\) | − | 106125.i | − | 0.607493i | ||||||
\(126\) | 12925.3i | 0.0725297i | ||||||||
\(127\) | −41588.5 | −0.228804 | −0.114402 | − | 0.993435i | \(-0.536495\pi\) | ||||
−0.114402 | + | 0.993435i | \(0.536495\pi\) | |||||||
\(128\) | − | 125288.i | − | 0.675902i | ||||||
\(129\) | 160633.i | 0.849883i | ||||||||
\(130\) | − | 2489.11i | − | 0.0129177i | ||||||
\(131\) | − | 167404.i | − | 0.852289i | −0.904655 | − | 0.426145i | \(-0.859871\pi\) | ||
0.904655 | − | 0.426145i | \(-0.140129\pi\) | |||||||
\(132\) | 93143.7 | 0.465284 | ||||||||
\(133\) | 239539.i | 1.17422i | ||||||||
\(134\) | 47777.9i | 0.229861i | ||||||||
\(135\) | − | 170896.i | − | 0.807044i | ||||||
\(136\) | −60788.0 | −0.281819 | ||||||||
\(137\) | −326960. | −1.48831 | −0.744155 | − | 0.668007i | \(-0.767148\pi\) | ||||
−0.744155 | + | 0.668007i | \(0.767148\pi\) | |||||||
\(138\) | −27343.0 | −0.122222 | ||||||||
\(139\) | 62658.9 | 0.275071 | 0.137536 | − | 0.990497i | \(-0.456082\pi\) | ||||
0.137536 | + | 0.990497i | \(0.456082\pi\) | |||||||
\(140\) | − | 232845.i | − | 1.00403i | ||||||
\(141\) | −261339. | −1.10702 | ||||||||
\(142\) | 19548.3i | 0.0813557i | ||||||||
\(143\) | − | 4237.88i | − | 0.0173304i | ||||||
\(144\) | 131050. | 0.526661 | ||||||||
\(145\) | −618037. | −2.44115 | ||||||||
\(146\) | 6896.74i | 0.0267770i | ||||||||
\(147\) | −180971. | −0.690742 | ||||||||
\(148\) | −241395. | + | 89411.8i | −0.905885 | + | 0.335537i | ||||
\(149\) | −65982.0 | −0.243478 | −0.121739 | − | 0.992562i | \(-0.538847\pi\) | ||||
−0.121739 | + | 0.992562i | \(0.538847\pi\) | |||||||
\(150\) | 89074.6i | 0.323240i | ||||||||
\(151\) | 95460.7 | 0.340708 | 0.170354 | − | 0.985383i | \(-0.445509\pi\) | ||||
0.170354 | + | 0.985383i | \(0.445509\pi\) | |||||||
\(152\) | −180380. | −0.633258 | ||||||||
\(153\) | − | 131890.i | − | 0.455495i | ||||||
\(154\) | 13940.7i | 0.0473677i | ||||||||
\(155\) | 348154. | 1.16397 | ||||||||
\(156\) | − | 16753.1i | − | 0.0551168i | ||||||
\(157\) | 290753. | 0.941403 | 0.470702 | − | 0.882292i | \(-0.344001\pi\) | ||||
0.470702 | + | 0.882292i | \(0.344001\pi\) | |||||||
\(158\) | −72896.6 | −0.232308 | ||||||||
\(159\) | 542117. | 1.70059 | ||||||||
\(160\) | 264524. | 0.816892 | ||||||||
\(161\) | 116376.i | 0.353834i | ||||||||
\(162\) | 76505.3i | 0.229036i | ||||||||
\(163\) | − | 522500.i | − | 1.54034i | −0.637837 | − | 0.770171i | \(-0.720171\pi\) | ||
0.637837 | − | 0.770171i | \(-0.279829\pi\) | |||||||
\(164\) | 352353. | 1.02298 | ||||||||
\(165\) | 260546.i | 0.745032i | ||||||||
\(166\) | − | 84843.9i | − | 0.238974i | ||||||
\(167\) | 320029.i | 0.887968i | 0.896035 | + | 0.443984i | \(0.146435\pi\) | ||||
−0.896035 | + | 0.443984i | \(0.853565\pi\) | |||||||
\(168\) | 112158.i | 0.306590i | ||||||||
\(169\) | 370531. | 0.997947 | ||||||||
\(170\) | − | 83550.6i | − | 0.221731i | ||||||
\(171\) | − | 391367.i | − | 1.02351i | ||||||
\(172\) | 252967.i | 0.651993i | ||||||||
\(173\) | −386890. | −0.982816 | −0.491408 | − | 0.870929i | \(-0.663518\pi\) | ||||
−0.491408 | + | 0.870929i | \(0.663518\pi\) | |||||||
\(174\) | 146278. | 0.366274 | ||||||||
\(175\) | 379115. | 0.935785 | ||||||||
\(176\) | 141345. | 0.343952 | ||||||||
\(177\) | − | 314231.i | − | 0.753905i | ||||||
\(178\) | 126013. | 0.298101 | ||||||||
\(179\) | 772439.i | 1.80190i | 0.433918 | + | 0.900952i | \(0.357131\pi\) | ||||
−0.433918 | + | 0.900952i | \(0.642869\pi\) | |||||||
\(180\) | 380429.i | 0.875169i | ||||||||
\(181\) | −219471. | −0.497944 | −0.248972 | − | 0.968511i | \(-0.580093\pi\) | ||||
−0.248972 | + | 0.968511i | \(0.580093\pi\) | |||||||
\(182\) | 2507.41 | 0.00561110 | ||||||||
\(183\) | 882829.i | 1.94872i | ||||||||
\(184\) | −87634.7 | −0.190823 | ||||||||
\(185\) | −250107. | − | 675241.i | −0.537275 | − | 1.45054i | ||||
\(186\) | −82401.7 | −0.174644 | ||||||||
\(187\) | − | 142251.i | − | 0.297475i | ||||||
\(188\) | −411561. | −0.849257 | ||||||||
\(189\) | 172153. | 0.350558 | ||||||||
\(190\) | − | 247926.i | − | 0.498238i | ||||||
\(191\) | − | 119268.i | − | 0.236559i | −0.992980 | − | 0.118279i | \(-0.962262\pi\) | ||
0.992980 | − | 0.118279i | \(-0.0377378\pi\) | |||||||
\(192\) | 515803. | 1.00979 | ||||||||
\(193\) | − | 606131.i | − | 1.17131i | −0.810559 | − | 0.585657i | \(-0.800836\pi\) | ||
0.810559 | − | 0.585657i | \(-0.199164\pi\) | |||||||
\(194\) | −6224.81 | −0.0118747 | ||||||||
\(195\) | 46862.7 | 0.0882552 | ||||||||
\(196\) | −284997. | −0.529907 | ||||||||
\(197\) | −48998.3 | −0.0899529 | −0.0449765 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449765 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(198\) | − | 22776.7i | − | 0.0412884i | ||||||
\(199\) | 401960.i | 0.719532i | 0.933043 | + | 0.359766i | \(0.117143\pi\) | ||||
−0.933043 | + | 0.359766i | \(0.882857\pi\) | |||||||
\(200\) | 285485.i | 0.504671i | ||||||||
\(201\) | −899519. | −1.57044 | ||||||||
\(202\) | − | 106434.i | − | 0.183529i | ||||||
\(203\) | − | 622582.i | − | 1.06037i | ||||||
\(204\) | − | 562343.i | − | 0.946075i | ||||||
\(205\) | 985619.i | 1.63804i | ||||||||
\(206\) | 201376. | 0.330629 | ||||||||
\(207\) | − | 190139.i | − | 0.308422i | ||||||
\(208\) | − | 25422.7i | − | 0.0407440i | ||||||
\(209\) | − | 422110.i | − | 0.668436i | ||||||
\(210\) | −154157. | −0.241221 | ||||||||
\(211\) | 981075. | 1.51704 | 0.758518 | − | 0.651652i | \(-0.225924\pi\) | ||||
0.758518 | + | 0.651652i | \(0.225924\pi\) | |||||||
\(212\) | 853735. | 1.30462 | ||||||||
\(213\) | −368037. | −0.555831 | ||||||||
\(214\) | − | 126033.i | − | 0.188127i | ||||||
\(215\) | −707613. | −1.04400 | ||||||||
\(216\) | 129636.i | 0.189057i | ||||||||
\(217\) | 350715.i | 0.505597i | ||||||||
\(218\) | −160358. | −0.228533 | ||||||||
\(219\) | −129846. | −0.182943 | ||||||||
\(220\) | 410313.i | 0.571556i | ||||||||
\(221\) | −25585.6 | −0.0352383 | ||||||||
\(222\) | 59195.8 | + | 159817.i | 0.0806136 | + | 0.217641i | ||||
\(223\) | −988479. | −1.33108 | −0.665542 | − | 0.746361i | \(-0.731799\pi\) | ||||
−0.665542 | + | 0.746361i | \(0.731799\pi\) | |||||||
\(224\) | 266469.i | 0.354835i | ||||||||
\(225\) | −619410. | −0.815684 | ||||||||
\(226\) | 20553.2 | 0.0267675 | ||||||||
\(227\) | 1.06424e6i | 1.37080i | 0.728168 | + | 0.685398i | \(0.240372\pi\) | ||||
−0.728168 | + | 0.685398i | \(0.759628\pi\) | |||||||
\(228\) | − | 1.66868e6i | − | 2.12587i | ||||||
\(229\) | 437725. | 0.551586 | 0.275793 | − | 0.961217i | \(-0.411060\pi\) | ||||
0.275793 | + | 0.961217i | \(0.411060\pi\) | |||||||
\(230\) | − | 120450.i | − | 0.150137i | ||||||
\(231\) | −262463. | −0.323622 | ||||||||
\(232\) | 468823. | 0.571859 | ||||||||
\(233\) | −1.01255e6 | −1.22188 | −0.610940 | − | 0.791677i | \(-0.709208\pi\) | ||||
−0.610940 | + | 0.791677i | \(0.709208\pi\) | |||||||
\(234\) | −4096.69 | −0.00489095 | ||||||||
\(235\) | − | 1.15124e6i | − | 1.35987i | ||||||
\(236\) | − | 494857.i | − | 0.578362i | ||||||
\(237\) | − | 1.37243e6i | − | 1.58716i | ||||||
\(238\) | 84165.1 | 0.0963140 | ||||||||
\(239\) | − | 286370.i | − | 0.324290i | −0.986767 | − | 0.162145i | \(-0.948159\pi\) | ||
0.986767 | − | 0.162145i | \(-0.0518412\pi\) | |||||||
\(240\) | 1.56300e6i | 1.75158i | ||||||||
\(241\) | 372657.i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662564\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(242\) | 143349.i | 0.157347i | ||||||||
\(243\) | −960124. | −1.04307 | ||||||||
\(244\) | 1.39029e6i | 1.49497i | ||||||||
\(245\) | − | 797207.i | − | 0.848508i | ||||||
\(246\) | − | 233278.i | − | 0.245774i | ||||||
\(247\) | −75922.0 | −0.0791818 | ||||||||
\(248\) | −264099. | −0.272670 | ||||||||
\(249\) | 1.59736e6 | 1.63270 | ||||||||
\(250\) | −110648. | −0.111968 | ||||||||
\(251\) | 807096.i | 0.808613i | 0.914624 | + | 0.404306i | \(0.132487\pi\) | ||||
−0.914624 | + | 0.404306i | \(0.867513\pi\) | |||||||
\(252\) | −383227. | −0.380150 | ||||||||
\(253\) | − | 205075.i | − | 0.201424i | ||||||
\(254\) | 43361.1i | 0.0421712i | ||||||||
\(255\) | 1.57301e6 | 1.51489 | ||||||||
\(256\) | 710233. | 0.677331 | ||||||||
\(257\) | − | 1.29694e6i | − | 1.22486i | −0.790524 | − | 0.612432i | \(-0.790191\pi\) | ||
0.790524 | − | 0.612432i | \(-0.209809\pi\) | |||||||
\(258\) | 167479. | 0.156643 | ||||||||
\(259\) | 680207. | − | 251947.i | 0.630075 | − | 0.233378i | ||||
\(260\) | 73800.2 | 0.0677055 | ||||||||
\(261\) | 1.01719e6i | 0.924277i | ||||||||
\(262\) | −174539. | −0.157086 | ||||||||
\(263\) | −358188. | −0.319317 | −0.159658 | − | 0.987172i | \(-0.551039\pi\) | ||||
−0.159658 | + | 0.987172i | \(0.551039\pi\) | |||||||
\(264\) | − | 197642.i | − | 0.174530i | ||||||
\(265\) | 2.38811e6i | 2.08901i | ||||||||
\(266\) | 249749. | 0.216421 | ||||||||
\(267\) | 2.37245e6i | 2.03666i | ||||||||
\(268\) | −1.41658e6 | −1.20477 | ||||||||
\(269\) | 2.26507e6 | 1.90853 | 0.954267 | − | 0.298955i | \(-0.0966379\pi\) | ||||
0.954267 | + | 0.298955i | \(0.0966379\pi\) | |||||||
\(270\) | −178180. | −0.148747 | ||||||||
\(271\) | 1.06501e6 | 0.880910 | 0.440455 | − | 0.897775i | \(-0.354817\pi\) | ||||
0.440455 | + | 0.897775i | \(0.354817\pi\) | |||||||
\(272\) | − | 853351.i | − | 0.699367i | ||||||
\(273\) | 47207.3i | 0.0383356i | ||||||||
\(274\) | 340896.i | 0.274312i | ||||||||
\(275\) | −668067. | −0.532707 | ||||||||
\(276\) | − | 810699.i | − | 0.640600i | ||||||
\(277\) | − | 1.07621e6i | − | 0.842751i | −0.906886 | − | 0.421375i | \(-0.861547\pi\) | ||
0.906886 | − | 0.421375i | \(-0.138453\pi\) | |||||||
\(278\) | − | 65329.5i | − | 0.0506988i | ||||||
\(279\) | − | 573008.i | − | 0.440707i | ||||||
\(280\) | −494075. | −0.376615 | ||||||||
\(281\) | − | 540316.i | − | 0.408208i | −0.978949 | − | 0.204104i | \(-0.934572\pi\) | ||
0.978949 | − | 0.204104i | \(-0.0654281\pi\) | |||||||
\(282\) | 272477.i | 0.204036i | ||||||||
\(283\) | − | 669160.i | − | 0.496665i | −0.968675 | − | 0.248333i | \(-0.920117\pi\) | ||
0.968675 | − | 0.248333i | \(-0.0798826\pi\) | |||||||
\(284\) | −579592. | −0.426409 | ||||||||
\(285\) | 4.66772e6 | 3.40402 | ||||||||
\(286\) | −4418.50 | −0.00319418 | ||||||||
\(287\) | −992868. | −0.711520 | ||||||||
\(288\) | − | 435365.i | − | 0.309295i | ||||||
\(289\) | 561038. | 0.395137 | ||||||||
\(290\) | 644378.i | 0.449931i | ||||||||
\(291\) | − | 117195.i | − | 0.0811291i | ||||||
\(292\) | −204483. | −0.140346 | ||||||||
\(293\) | −2.14251e6 | −1.45799 | −0.728994 | − | 0.684521i | \(-0.760012\pi\) | ||||
−0.728994 | + | 0.684521i | \(0.760012\pi\) | |||||||
\(294\) | 188684.i | 0.127311i | ||||||||
\(295\) | 1.38424e6 | 0.926097 | ||||||||
\(296\) | 189723. | + | 512217.i | 0.125861 | + | 0.339801i | ||||
\(297\) | −303363. | −0.199559 | ||||||||
\(298\) | 68794.2i | 0.0448757i | ||||||||
\(299\) | −36885.4 | −0.0238603 | ||||||||
\(300\) | −2.64099e6 | −1.69420 | ||||||||
\(301\) | − | 712817.i | − | 0.453484i | ||||||
\(302\) | − | 99529.4i | − | 0.0627963i | ||||||
\(303\) | 2.00385e6 | 1.25389 | ||||||||
\(304\) | − | 2.53221e6i | − | 1.57150i | ||||||
\(305\) | −3.88900e6 | −2.39381 | ||||||||
\(306\) | −137511. | −0.0839528 | ||||||||
\(307\) | −1.35256e6 | −0.819047 | −0.409524 | − | 0.912299i | \(-0.634305\pi\) | ||||
−0.409524 | + | 0.912299i | \(0.634305\pi\) | |||||||
\(308\) | −413331. | −0.248268 | ||||||||
\(309\) | 3.79133e6i | 2.25889i | ||||||||
\(310\) | − | 362993.i | − | 0.214533i | ||||||
\(311\) | 371845.i | 0.218002i | 0.994042 | + | 0.109001i | \(0.0347652\pi\) | ||||
−0.994042 | + | 0.109001i | \(0.965235\pi\) | |||||||
\(312\) | −35548.5 | −0.0206745 | ||||||||
\(313\) | 1.27822e6i | 0.737470i | 0.929535 | + | 0.368735i | \(0.120209\pi\) | ||||
−0.929535 | + | 0.368735i | \(0.879791\pi\) | |||||||
\(314\) | − | 303146.i | − | 0.173511i | ||||||
\(315\) | − | 1.07198e6i | − | 0.608711i | ||||||
\(316\) | − | 2.16133e6i | − | 1.21760i | ||||||
\(317\) | −888017. | −0.496333 | −0.248166 | − | 0.968717i | \(-0.579828\pi\) | ||||
−0.248166 | + | 0.968717i | \(0.579828\pi\) | |||||||
\(318\) | − | 565222.i | − | 0.313438i | ||||||
\(319\) | 1.09710e6i | 0.603627i | ||||||||
\(320\) | 2.27220e6i | 1.24043i | ||||||||
\(321\) | 2.37284e6 | 1.28530 | ||||||||
\(322\) | 121336. | 0.0652155 | ||||||||
\(323\) | −2.54843e6 | −1.35915 | ||||||||
\(324\) | −2.26832e6 | −1.20045 | ||||||||
\(325\) | 120161.i | 0.0631035i | ||||||||
\(326\) | −544770. | −0.283902 | ||||||||
\(327\) | − | 3.01907e6i | − | 1.56136i | ||||||
\(328\) | − | 747660.i | − | 0.383724i | ||||||
\(329\) | 1.15971e6 | 0.590688 | ||||||||
\(330\) | 271651. | 0.137318 | ||||||||
\(331\) | 1.13045e6i | 0.567129i | 0.958953 | + | 0.283565i | \(0.0915171\pi\) | ||||
−0.958953 | + | 0.283565i | \(0.908483\pi\) | |||||||
\(332\) | 2.51556e6 | 1.25253 | ||||||||
\(333\) | −1.11134e6 | + | 411638.i | −0.549209 | + | 0.203425i | ||||
\(334\) | 333669. | 0.163663 | ||||||||
\(335\) | − | 3.96253e6i | − | 1.92912i | ||||||
\(336\) | −1.57449e6 | −0.760839 | ||||||||
\(337\) | −2.75184e6 | −1.31992 | −0.659961 | − | 0.751300i | \(-0.729427\pi\) | ||||
−0.659961 | + | 0.751300i | \(0.729427\pi\) | |||||||
\(338\) | − | 386323.i | − | 0.183933i | ||||||
\(339\) | 386956.i | 0.182879i | ||||||||
\(340\) | 2.47721e6 | 1.16216 | ||||||||
\(341\) | − | 618020.i | − | 0.287817i | ||||||
\(342\) | −408047. | −0.188645 | ||||||||
\(343\) | 2.26708e6 | 1.04048 | ||||||||
\(344\) | 536773. | 0.244565 | ||||||||
\(345\) | 2.26773e6 | 1.02575 | ||||||||
\(346\) | 403380.i | 0.181144i | ||||||||
\(347\) | 883744.i | 0.394006i | 0.980403 | + | 0.197003i | \(0.0631208\pi\) | ||||
−0.980403 | + | 0.197003i | \(0.936879\pi\) | |||||||
\(348\) | 4.33703e6i | 1.91975i | ||||||||
\(349\) | −55889.7 | −0.0245623 | −0.0122811 | − | 0.999925i | \(-0.503909\pi\) | ||||
−0.0122811 | + | 0.999925i | \(0.503909\pi\) | |||||||
\(350\) | − | 395274.i | − | 0.172476i | ||||||
\(351\) | 54563.8i | 0.0236394i | ||||||||
\(352\) | − | 469565.i | − | 0.201994i | ||||||
\(353\) | − | 388952.i | − | 0.166134i | −0.996544 | − | 0.0830672i | \(-0.973528\pi\) | ||
0.996544 | − | 0.0830672i | \(-0.0264716\pi\) | |||||||
\(354\) | −327624. | −0.138953 | ||||||||
\(355\) | − | 1.62127e6i | − | 0.682784i | ||||||
\(356\) | 3.73618e6i | 1.56244i | ||||||||
\(357\) | 1.58458e6i | 0.658028i | ||||||||
\(358\) | 805362. | 0.332111 | ||||||||
\(359\) | 3.13551e6 | 1.28402 | 0.642010 | − | 0.766697i | \(-0.278101\pi\) | ||||
0.642010 | + | 0.766697i | \(0.278101\pi\) | |||||||
\(360\) | 807235. | 0.328279 | ||||||||
\(361\) | −5.08605e6 | −2.05406 | ||||||||
\(362\) | 228825.i | 0.0917767i | ||||||||
\(363\) | −2.69885e6 | −1.07501 | ||||||||
\(364\) | 74342.9i | 0.0294094i | ||||||||
\(365\) | − | 571991.i | − | 0.224728i | ||||||
\(366\) | 920456. | 0.359170 | ||||||||
\(367\) | −160181. | −0.0620793 | −0.0310396 | − | 0.999518i | \(-0.509882\pi\) | ||||
−0.0310396 | + | 0.999518i | \(0.509882\pi\) | |||||||
\(368\) | − | 1.23023e6i | − | 0.473551i | ||||||
\(369\) | 1.62218e6 | 0.620201 | ||||||||
\(370\) | −704021. | + | 260767.i | −0.267351 | + | 0.0990259i | ||||
\(371\) | −2.40568e6 | −0.907407 | ||||||||
\(372\) | − | 2.44315e6i | − | 0.915361i | ||||||
\(373\) | 3.26910e6 | 1.21662 | 0.608311 | − | 0.793699i | \(-0.291847\pi\) | ||||
0.608311 | + | 0.793699i | \(0.291847\pi\) | |||||||
\(374\) | −148314. | −0.0548279 | ||||||||
\(375\) | − | 2.08318e6i | − | 0.764976i | ||||||
\(376\) | 873294.i | 0.318560i | ||||||||
\(377\) | 197327. | 0.0715046 | ||||||||
\(378\) | − | 179490.i | − | 0.0646117i | ||||||
\(379\) | −756174. | −0.270411 | −0.135205 | − | 0.990818i | \(-0.543169\pi\) | ||||
−0.135205 | + | 0.990818i | \(0.543169\pi\) | |||||||
\(380\) | 7.35080e6 | 2.61141 | ||||||||
\(381\) | −816364. | −0.288119 | ||||||||
\(382\) | −124351. | −0.0436004 | ||||||||
\(383\) | 3.40102e6i | 1.18471i | 0.805677 | + | 0.592355i | \(0.201802\pi\) | ||||
−0.805677 | + | 0.592355i | \(0.798198\pi\) | |||||||
\(384\) | − | 2.45934e6i | − | 0.851120i | ||||||
\(385\) | − | 1.15619e6i | − | 0.397537i | ||||||
\(386\) | −631966. | −0.215886 | ||||||||
\(387\) | 1.16462e6i | 0.395282i | ||||||||
\(388\) | − | 184561.i | − | 0.0622387i | ||||||
\(389\) | 3.01289e6i | 1.00951i | 0.863263 | + | 0.504754i | \(0.168417\pi\) | ||||
−0.863263 | + | 0.504754i | \(0.831583\pi\) | |||||||
\(390\) | − | 48860.0i | − | 0.0162664i | ||||||
\(391\) | −1.23811e6 | −0.409561 | ||||||||
\(392\) | 604736.i | 0.198770i | ||||||||
\(393\) | − | 3.28606e6i | − | 1.07323i | ||||||
\(394\) | 51086.7i | 0.0165793i | ||||||||
\(395\) | 6.04578e6 | 1.94966 | ||||||||
\(396\) | 675312. | 0.216405 | ||||||||
\(397\) | 2.29374e6 | 0.730413 | 0.365207 | − | 0.930926i | \(-0.380998\pi\) | ||||
0.365207 | + | 0.930926i | \(0.380998\pi\) | |||||||
\(398\) | 419092. | 0.132618 | ||||||||
\(399\) | 4.70205e6i | 1.47861i | ||||||||
\(400\) | −4.00769e6 | −1.25240 | ||||||||
\(401\) | − | 3.73275e6i | − | 1.15922i | −0.814892 | − | 0.579612i | \(-0.803204\pi\) | ||
0.814892 | − | 0.579612i | \(-0.196796\pi\) | |||||||
\(402\) | 937858.i | 0.289449i | ||||||||
\(403\) | −111159. | −0.0340943 | ||||||||
\(404\) | 3.15570e6 | 0.961927 | ||||||||
\(405\) | − | 6.34508e6i | − | 1.92220i | ||||||
\(406\) | −649118. | −0.195438 | ||||||||
\(407\) | −1.19864e6 | + | 443974.i | −0.358678 | + | 0.132853i | ||||
\(408\) | −1.19324e6 | −0.354876 | ||||||||
\(409\) | 4.34834e6i | 1.28533i | 0.766146 | + | 0.642667i | \(0.222172\pi\) | ||||
−0.766146 | + | 0.642667i | \(0.777828\pi\) | |||||||
\(410\) | 1.02763e6 | 0.301909 | ||||||||
\(411\) | −6.41807e6 | −1.87413 | ||||||||
\(412\) | 5.97066e6i | 1.73292i | ||||||||
\(413\) | 1.39442e6i | 0.402271i | ||||||||
\(414\) | −198243. | −0.0568455 | ||||||||
\(415\) | 7.03665e6i | 2.00561i | ||||||||
\(416\) | −84457.4 | −0.0239279 | ||||||||
\(417\) | 1.22996e6 | 0.346380 | ||||||||
\(418\) | −440101. | −0.123200 | ||||||||
\(419\) | 3.92059e6 | 1.09098 | 0.545490 | − | 0.838117i | \(-0.316344\pi\) | ||||
0.545490 | + | 0.838117i | \(0.316344\pi\) | |||||||
\(420\) | − | 4.57063e6i | − | 1.26431i | ||||||
\(421\) | − | 252803.i | − | 0.0695146i | −0.999396 | − | 0.0347573i | \(-0.988934\pi\) | ||
0.999396 | − | 0.0347573i | \(-0.0110658\pi\) | |||||||
\(422\) | − | 1.02289e6i | − | 0.279607i | ||||||
\(423\) | −1.89476e6 | −0.514877 | ||||||||
\(424\) | − | 1.81155e6i | − | 0.489367i | ||||||
\(425\) | 4.03337e6i | 1.08317i | ||||||||
\(426\) | 383724.i | 0.102446i | ||||||||
\(427\) | − | 3.91761e6i | − | 1.03980i | ||||||
\(428\) | 3.73679e6 | 0.986029 | ||||||||
\(429\) | − | 83187.5i | − | 0.0218230i | ||||||
\(430\) | 737772.i | 0.192420i | ||||||||
\(431\) | − | 5.98928e6i | − | 1.55304i | −0.630095 | − | 0.776518i | \(-0.716984\pi\) | ||
0.630095 | − | 0.776518i | \(-0.283016\pi\) | |||||||
\(432\) | −1.81985e6 | −0.469167 | ||||||||
\(433\) | 2.64435e6 | 0.677795 | 0.338898 | − | 0.940823i | \(-0.389946\pi\) | ||||
0.338898 | + | 0.940823i | \(0.389946\pi\) | |||||||
\(434\) | 365663. | 0.0931872 | ||||||||
\(435\) | −1.21318e7 | −3.07398 | ||||||||
\(436\) | − | 4.75449e6i | − | 1.19781i | ||||||
\(437\) | −3.67394e6 | −0.920298 | ||||||||
\(438\) | 135380.i | 0.0337185i | ||||||||
\(439\) | − | 6.50479e6i | − | 1.61091i | −0.592655 | − | 0.805457i | \(-0.701920\pi\) | ||
0.592655 | − | 0.805457i | \(-0.298080\pi\) | |||||||
\(440\) | 870646. | 0.214393 | ||||||||
\(441\) | −1.31208e6 | −0.321265 | ||||||||
\(442\) | 26676.1i | 0.00649482i | ||||||||
\(443\) | 1.83180e6 | 0.443475 | 0.221738 | − | 0.975106i | \(-0.428827\pi\) | ||||
0.221738 | + | 0.975106i | \(0.428827\pi\) | |||||||
\(444\) | −4.73846e6 | + | 1.75511e6i | −1.14072 | + | 0.422520i | ||||
\(445\) | −1.04510e7 | −2.50184 | ||||||||
\(446\) | 1.03061e6i | 0.245334i | ||||||||
\(447\) | −1.29520e6 | −0.306596 | ||||||||
\(448\) | −2.28891e6 | −0.538807 | ||||||||
\(449\) | − | 3.59888e6i | − | 0.842465i | −0.906953 | − | 0.421233i | \(-0.861598\pi\) | ||
0.906953 | − | 0.421233i | \(-0.138402\pi\) | |||||||
\(450\) | 645810.i | 0.150340i | ||||||||
\(451\) | 1.74961e6 | 0.405041 | ||||||||
\(452\) | 609386.i | 0.140296i | ||||||||
\(453\) | 1.87385e6 | 0.429031 | ||||||||
\(454\) | 1.10959e6 | 0.252653 | ||||||||
\(455\) | −207956. | −0.0470915 | ||||||||
\(456\) | −3.54078e6 | −0.797420 | ||||||||
\(457\) | − | 2.96825e6i | − | 0.664829i | −0.943133 | − | 0.332415i | \(-0.892137\pi\) | ||
0.943133 | − | 0.332415i | \(-0.107863\pi\) | |||||||
\(458\) | − | 456382.i | − | 0.101663i | ||||||
\(459\) | 1.83152e6i | 0.405769i | ||||||||
\(460\) | 3.57126e6 | 0.786914 | ||||||||
\(461\) | 271586.i | 0.0595190i | 0.999557 | + | 0.0297595i | \(0.00947415\pi\) | ||||
−0.999557 | + | 0.0297595i | \(0.990526\pi\) | |||||||
\(462\) | 273649.i | 0.0596471i | ||||||||
\(463\) | − | 5.47928e6i | − | 1.18788i | −0.804511 | − | 0.593938i | \(-0.797573\pi\) | ||
0.804511 | − | 0.593938i | \(-0.202427\pi\) | |||||||
\(464\) | 6.58141e6i | 1.41914i | ||||||||
\(465\) | 6.83410e6 | 1.46571 | ||||||||
\(466\) | 1.05571e6i | 0.225206i | ||||||||
\(467\) | − | 361304.i | − | 0.0766621i | −0.999265 | − | 0.0383311i | \(-0.987796\pi\) | ||
0.999265 | − | 0.0383311i | \(-0.0122041\pi\) | |||||||
\(468\) | − | 121464.i | − | 0.0256349i | ||||||
\(469\) | 3.99167e6 | 0.837959 | ||||||||
\(470\) | −1.20031e6 | −0.250638 | ||||||||
\(471\) | 5.70735e6 | 1.18545 | ||||||||
\(472\) | −1.05004e6 | −0.216946 | ||||||||
\(473\) | 1.25611e6i | 0.258151i | ||||||||
\(474\) | −1.43093e6 | −0.292531 | ||||||||
\(475\) | 1.19685e7i | 2.43392i | ||||||||
\(476\) | 2.49543e6i | 0.504810i | ||||||||
\(477\) | 3.93046e6 | 0.790948 | ||||||||
\(478\) | −298576. | −0.0597703 | ||||||||
\(479\) | 6.39822e6i | 1.27415i | 0.770802 | + | 0.637074i | \(0.219856\pi\) | ||||
−0.770802 | + | 0.637074i | \(0.780144\pi\) | |||||||
\(480\) | 5.19247e6 | 1.02866 | ||||||||
\(481\) | 79854.5 | + | 215592.i | 0.0157375 | + | 0.0424883i | ||||
\(482\) | 388541. | 0.0761761 | ||||||||
\(483\) | 2.28441e6i | 0.445560i | ||||||||
\(484\) | −4.25020e6 | −0.824700 | ||||||||
\(485\) | 516263. | 0.0996591 | ||||||||
\(486\) | 1.00105e6i | 0.192249i | ||||||||
\(487\) | − | 5.35237e6i | − | 1.02264i | −0.859390 | − | 0.511321i | \(-0.829156\pi\) | ||
0.859390 | − | 0.511321i | \(-0.170844\pi\) | |||||||
\(488\) | 2.95008e6 | 0.560769 | ||||||||
\(489\) | − | 1.02564e7i | − | 1.93965i | ||||||
\(490\) | −831185. | −0.156390 | ||||||||
\(491\) | −6.11966e6 | −1.14557 | −0.572787 | − | 0.819704i | \(-0.694138\pi\) | ||||
−0.572787 | + | 0.819704i | \(0.694138\pi\) | |||||||
\(492\) | 6.91652e6 | 1.28817 | ||||||||
\(493\) | 6.62359e6 | 1.22737 | ||||||||
\(494\) | 79157.9i | 0.0145941i | ||||||||
\(495\) | 1.88902e6i | 0.346516i | ||||||||
\(496\) | − | 3.70746e6i | − | 0.676662i | ||||||
\(497\) | 1.63319e6 | 0.296582 | ||||||||
\(498\) | − | 1.66545e6i | − | 0.300924i | ||||||
\(499\) | − | 9.16295e6i | − | 1.64734i | −0.567067 | − | 0.823672i | \(-0.691922\pi\) | ||
0.567067 | − | 0.823672i | \(-0.308078\pi\) | |||||||
\(500\) | − | 3.28063e6i | − | 0.586856i | ||||||
\(501\) | 6.28201e6i | 1.11816i | ||||||||
\(502\) | 841495. | 0.149036 | ||||||||
\(503\) | − | 434586.i | − | 0.0765871i | −0.999267 | − | 0.0382935i | \(-0.987808\pi\) | ||
0.999267 | − | 0.0382935i | \(-0.0121922\pi\) | |||||||
\(504\) | 813172.i | 0.142596i | ||||||||
\(505\) | 8.82729e6i | 1.54028i | ||||||||
\(506\) | −213816. | −0.0371247 | ||||||||
\(507\) | 7.27334e6 | 1.25665 | ||||||||
\(508\) | −1.28562e6 | −0.221032 | ||||||||
\(509\) | 770690. | 0.131852 | 0.0659258 | − | 0.997825i | \(-0.479000\pi\) | ||||
0.0659258 | + | 0.997825i | \(0.479000\pi\) | |||||||
\(510\) | − | 1.64006e6i | − | 0.279212i | ||||||
\(511\) | 576198. | 0.0976156 | ||||||||
\(512\) | − | 4.74971e6i | − | 0.800742i | ||||||
\(513\) | 5.43479e6i | 0.911778i | ||||||||
\(514\) | −1.35222e6 | −0.225756 | ||||||||
\(515\) | −1.67014e7 | −2.77482 | ||||||||
\(516\) | 4.96562e6i | 0.821012i | ||||||||
\(517\) | −2.04360e6 | −0.336256 | ||||||||
\(518\) | −262685. | − | 709199.i | −0.0430141 | − | 0.116130i | ||||
\(519\) | −7.59447e6 | −1.23760 | ||||||||
\(520\) | − | 156597.i | − | 0.0253966i | ||||||
\(521\) | 401386. | 0.0647841 | 0.0323920 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323920 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(522\) | 1.06055e6 | 0.170355 | ||||||||
\(523\) | − | 2.01101e6i | − | 0.321485i | −0.986996 | − | 0.160743i | \(-0.948611\pi\) | ||
0.986996 | − | 0.160743i | \(-0.0513889\pi\) | |||||||
\(524\) | − | 5.17494e6i | − | 0.823336i | ||||||
\(525\) | 7.44186e6 | 1.17837 | ||||||||
\(526\) | 373455.i | 0.0588537i | ||||||||
\(527\) | −3.73122e6 | −0.585226 | ||||||||
\(528\) | 2.77453e6 | 0.433117 | ||||||||
\(529\) | 4.65142e6 | 0.722681 | ||||||||
\(530\) | 2.48990e6 | 0.385027 | ||||||||
\(531\) | − | 2.27825e6i | − | 0.350642i | ||||||
\(532\) | 7.40487e6i | 1.13433i | ||||||||
\(533\) | − | 314690.i | − | 0.0479805i | ||||||
\(534\) | 2.47357e6 | 0.375380 | ||||||||
\(535\) | 1.04528e7i | 1.57887i | ||||||||
\(536\) | 3.00585e6i | 0.451913i | ||||||||
\(537\) | 1.51626e7i | 2.26902i | ||||||||
\(538\) | − | 2.36161e6i | − | 0.351764i | ||||||
\(539\) | −1.41515e6 | −0.209812 | ||||||||
\(540\) | − | 5.28290e6i | − | 0.779628i | ||||||
\(541\) | − | 1.06718e7i | − | 1.56764i | −0.620990 | − | 0.783818i | \(-0.713269\pi\) | ||
0.620990 | − | 0.783818i | \(-0.286731\pi\) | |||||||
\(542\) | − | 1.11041e6i | − | 0.162362i | ||||||
\(543\) | −4.30811e6 | −0.627029 | ||||||||
\(544\) | −2.83494e6 | −0.410720 | ||||||||
\(545\) | 1.32995e7 | 1.91798 | ||||||||
\(546\) | 49219.4 | 0.00706569 | ||||||||
\(547\) | − | 8.72544e6i | − | 1.24686i | −0.781878 | − | 0.623432i | \(-0.785738\pi\) | ||
0.781878 | − | 0.623432i | \(-0.214262\pi\) | |||||||
\(548\) | −1.01073e7 | −1.43775 | ||||||||
\(549\) | 6.40070e6i | 0.906352i | ||||||||
\(550\) | 696541.i | 0.0981839i | ||||||||
\(551\) | 1.96546e7 | 2.75795 | ||||||||
\(552\) | −1.72023e6 | −0.240291 | ||||||||
\(553\) | 6.09024e6i | 0.846880i | ||||||||
\(554\) | −1.12208e6 | −0.155328 | ||||||||
\(555\) | −4.90949e6 | − | 1.32547e7i | −0.676556 | − | 1.82657i | ||||
\(556\) | 1.93697e6 | 0.265727 | ||||||||
\(557\) | − | 258227.i | − | 0.0352667i | −0.999845 | − | 0.0176333i | \(-0.994387\pi\) | ||
0.999845 | − | 0.0176333i | \(-0.00561316\pi\) | |||||||
\(558\) | −597431. | −0.0812273 | ||||||||
\(559\) | 225927. | 0.0305801 | ||||||||
\(560\) | − | 6.93590e6i | − | 0.934615i | ||||||
\(561\) | − | 2.79231e6i | − | 0.374591i | ||||||
\(562\) | −563345. | −0.0752374 | ||||||||
\(563\) | − | 1.26414e6i | − | 0.168083i | −0.996462 | − | 0.0840413i | \(-0.973217\pi\) | ||
0.996462 | − | 0.0840413i | \(-0.0267828\pi\) | |||||||
\(564\) | −8.07874e6 | −1.06941 | ||||||||
\(565\) | −1.70461e6 | −0.224648 | ||||||||
\(566\) | −697681. | −0.0915410 | ||||||||
\(567\) | 6.39174e6 | 0.834952 | ||||||||
\(568\) | 1.22984e6i | 0.159948i | ||||||||
\(569\) | 2.30163e6i | 0.298027i | 0.988835 | + | 0.149014i | \(0.0476098\pi\) | ||||
−0.988835 | + | 0.149014i | \(0.952390\pi\) | |||||||
\(570\) | − | 4.86666e6i | − | 0.627399i | ||||||
\(571\) | 1.11302e6 | 0.142861 | 0.0714305 | − | 0.997446i | \(-0.477244\pi\) | ||||
0.0714305 | + | 0.997446i | \(0.477244\pi\) | |||||||
\(572\) | − | 131005.i | − | 0.0167417i | ||||||
\(573\) | − | 2.34117e6i | − | 0.297883i | ||||||
\(574\) | 1.03519e6i | 0.131141i | ||||||||
\(575\) | 5.81469e6i | 0.733427i | ||||||||
\(576\) | 3.73969e6 | 0.469655 | ||||||||
\(577\) | 5.49305e6i | 0.686869i | 0.939177 | + | 0.343434i | \(0.111590\pi\) | ||||
−0.939177 | + | 0.343434i | \(0.888410\pi\) | |||||||
\(578\) | − | 584950.i | − | 0.0728281i | ||||||
\(579\) | − | 1.18981e7i | − | 1.47496i | ||||||
\(580\) | −1.91053e7 | −2.35822 | ||||||||
\(581\) | −7.08840e6 | −0.871180 | ||||||||
\(582\) | −122190. | −0.0149530 | ||||||||
\(583\) | 4.23922e6 | 0.516553 | ||||||||
\(584\) | 433894.i | 0.0526443i | ||||||||
\(585\) | 339765. | 0.0410477 | ||||||||
\(586\) | 2.23383e6i | 0.268723i | ||||||||
\(587\) | 4.66139e6i | 0.558367i | 0.960238 | + | 0.279184i | \(0.0900638\pi\) | ||||
−0.960238 | + | 0.279184i | \(0.909936\pi\) | |||||||
\(588\) | −5.59435e6 | −0.667277 | ||||||||
\(589\) | −1.10719e7 | −1.31502 | ||||||||
\(590\) | − | 1.44324e6i | − | 0.170690i | ||||||
\(591\) | −961813. | −0.113272 | ||||||||
\(592\) | −7.19058e6 | + | 2.66337e6i | −0.843256 | + | 0.312339i | ||||
\(593\) | −8.26345e6 | −0.964994 | −0.482497 | − | 0.875898i | \(-0.660270\pi\) | ||||
−0.482497 | + | 0.875898i | \(0.660270\pi\) | |||||||
\(594\) | 316293.i | 0.0367810i | ||||||||
\(595\) | −6.98035e6 | −0.808323 | ||||||||
\(596\) | −2.03970e6 | −0.235207 | ||||||||
\(597\) | 7.89028e6i | 0.906060i | ||||||||
\(598\) | 38457.5i | 0.00439773i | ||||||||
\(599\) | −3.84507e6 | −0.437862 | −0.218931 | − | 0.975740i | \(-0.570257\pi\) | ||||
−0.218931 | + | 0.975740i | \(0.570257\pi\) | |||||||
\(600\) | 5.60394e6i | 0.635500i | ||||||||
\(601\) | 1.18174e7 | 1.33456 | 0.667278 | − | 0.744809i | \(-0.267459\pi\) | ||||
0.667278 | + | 0.744809i | \(0.267459\pi\) | |||||||
\(602\) | −743198. | −0.0835821 | ||||||||
\(603\) | −6.52171e6 | −0.730413 | ||||||||
\(604\) | 2.95097e6 | 0.329134 | ||||||||
\(605\) | − | 1.18889e7i | − | 1.32054i | ||||||
\(606\) | − | 2.08926e6i | − | 0.231106i | ||||||
\(607\) | − | 8.13937e6i | − | 0.896642i | −0.893873 | − | 0.448321i | \(-0.852022\pi\) | ||
0.893873 | − | 0.448321i | \(-0.147978\pi\) | |||||||
\(608\) | −8.41231e6 | −0.922903 | ||||||||
\(609\) | − | 1.22210e7i | − | 1.33525i | ||||||
\(610\) | 4.05476e6i | 0.441205i | ||||||||
\(611\) | 367569.i | 0.0398323i | ||||||||
\(612\) | − | 4.07711e6i | − | 0.440021i | ||||||
\(613\) | 6.23345e6 | 0.670003 | 0.335002 | − | 0.942218i | \(-0.391263\pi\) | ||||
0.335002 | + | 0.942218i | \(0.391263\pi\) | |||||||
\(614\) | 1.41020e6i | 0.150960i | ||||||||
\(615\) | 1.93472e7i | 2.06268i | ||||||||
\(616\) | 877050.i | 0.0931263i | ||||||||
\(617\) | 1.61232e6 | 0.170506 | 0.0852530 | − | 0.996359i | \(-0.472830\pi\) | ||||
0.0852530 | + | 0.996359i | \(0.472830\pi\) | |||||||
\(618\) | 3.95292e6 | 0.416339 | ||||||||
\(619\) | 1.33080e7 | 1.39600 | 0.697999 | − | 0.716099i | \(-0.254074\pi\) | ||||
0.697999 | + | 0.716099i | \(0.254074\pi\) | |||||||
\(620\) | 1.07625e7 | 1.12443 | ||||||||
\(621\) | 2.64040e6i | 0.274752i | ||||||||
\(622\) | 387694. | 0.0401803 | ||||||||
\(623\) | − | 1.05279e7i | − | 1.08673i | ||||||
\(624\) | − | 499036.i | − | 0.0513062i | ||||||
\(625\) | −4.42415e6 | −0.453033 | ||||||||
\(626\) | 1.33270e6 | 0.135924 | ||||||||
\(627\) | − | 8.28582e6i | − | 0.841719i | ||||||
\(628\) | 8.98805e6 | 0.909423 | ||||||||
\(629\) | 2.68043e6 | + | 7.23666e6i | 0.270134 | + | 0.729309i | ||||
\(630\) | −1.11767e6 | −0.112192 | ||||||||
\(631\) | 1.16451e7i | 1.16431i | 0.813078 | + | 0.582154i | \(0.197790\pi\) | ||||
−0.813078 | + | 0.582154i | \(0.802210\pi\) | |||||||
\(632\) | −4.58614e6 | −0.456725 | ||||||||
\(633\) | 1.92580e7 | 1.91031 | ||||||||
\(634\) | 925866.i | 0.0914797i | ||||||||
\(635\) | − | 3.59621e6i | − | 0.353925i | ||||||
\(636\) | 1.67584e7 | 1.64282 | ||||||||
\(637\) | 254533.i | 0.0248540i | ||||||||
\(638\) | 1.14386e6 | 0.111255 | ||||||||
\(639\) | −2.66835e6 | −0.258518 | ||||||||
\(640\) | 1.08338e7 | 1.04552 | ||||||||
\(641\) | 1.89809e6 | 0.182462 | 0.0912309 | − | 0.995830i | \(-0.470920\pi\) | ||||
0.0912309 | + | 0.995830i | \(0.470920\pi\) | |||||||
\(642\) | − | 2.47398e6i | − | 0.236896i | ||||||
\(643\) | 3.21597e6i | 0.306750i | 0.988168 | + | 0.153375i | \(0.0490143\pi\) | ||||
−0.988168 | + | 0.153375i | \(0.950986\pi\) | |||||||
\(644\) | 3.59753e6i | 0.341814i | ||||||||
\(645\) | −1.38901e7 | −1.31464 | ||||||||
\(646\) | 2.65705e6i | 0.250506i | ||||||||
\(647\) | 9.14794e6i | 0.859137i | 0.903034 | + | 0.429568i | \(0.141334\pi\) | ||||
−0.903034 | + | 0.429568i | \(0.858666\pi\) | |||||||
\(648\) | 4.81318e6i | 0.450292i | ||||||||
\(649\) | − | 2.45721e6i | − | 0.228998i | ||||||
\(650\) | 125282. | 0.0116307 | ||||||||
\(651\) | 6.88436e6i | 0.636665i | ||||||||
\(652\) | − | 1.61520e7i | − | 1.48802i | ||||||
\(653\) | − | 2.31944e6i | − | 0.212863i | −0.994320 | − | 0.106432i | \(-0.966058\pi\) | ||
0.994320 | − | 0.106432i | \(-0.0339425\pi\) | |||||||
\(654\) | −3.14775e6 | −0.287777 | ||||||||
\(655\) | 1.44756e7 | 1.31836 | ||||||||
\(656\) | 1.04958e7 | 0.952257 | ||||||||
\(657\) | −941409. | −0.0850873 | ||||||||
\(658\) | − | 1.20913e6i | − | 0.108870i | ||||||
\(659\) | 916434. | 0.0822030 | 0.0411015 | − | 0.999155i | \(-0.486913\pi\) | ||||
0.0411015 | + | 0.999155i | \(0.486913\pi\) | |||||||
\(660\) | 8.05425e6i | 0.719723i | ||||||||
\(661\) | − | 2.37664e6i | − | 0.211572i | −0.994389 | − | 0.105786i | \(-0.966264\pi\) | ||
0.994389 | − | 0.105786i | \(-0.0337359\pi\) | |||||||
\(662\) | 1.17863e6 | 0.104528 | ||||||||
\(663\) | −502234. | −0.0443733 | ||||||||
\(664\) | − | 5.33778e6i | − | 0.469830i | ||||||
\(665\) | −2.07133e7 | −1.81633 | ||||||||
\(666\) | 429183. | + | 1.15871e6i | 0.0374936 | + | 0.101225i | ||||
\(667\) | 9.54887e6 | 0.831069 | ||||||||
\(668\) | 9.89302e6i | 0.857804i | ||||||||
\(669\) | −1.94034e7 | −1.67615 | ||||||||
\(670\) | −4.13142e6 | −0.355559 | ||||||||
\(671\) | 6.90351e6i | 0.591921i | ||||||||
\(672\) | 5.23066e6i | 0.446821i | ||||||||
\(673\) | 5.10059e6 | 0.434093 | 0.217047 | − | 0.976161i | \(-0.430358\pi\) | ||||
0.217047 | + | 0.976161i | \(0.430358\pi\) | |||||||
\(674\) | 2.86912e6i | 0.243276i | ||||||||
\(675\) | 8.60155e6 | 0.726637 | ||||||||
\(676\) | 1.14542e7 | 0.964046 | ||||||||
\(677\) | −1.83738e7 | −1.54073 | −0.770365 | − | 0.637603i | \(-0.779926\pi\) | ||||
−0.770365 | + | 0.637603i | \(0.779926\pi\) | |||||||
\(678\) | 403449. | 0.0337066 | ||||||||
\(679\) | 520060.i | 0.0432892i | ||||||||
\(680\) | − | 5.25641e6i | − | 0.435930i | ||||||
\(681\) | 2.08904e7i | 1.72615i | ||||||||
\(682\) | −644361. | −0.0530479 | ||||||||
\(683\) | − | 1.34013e7i | − | 1.09925i | −0.835413 | − | 0.549623i | \(-0.814771\pi\) | ||
0.835413 | − | 0.549623i | \(-0.185229\pi\) | |||||||
\(684\) | − | 1.20983e7i | − | 0.988744i | ||||||
\(685\) | − | 2.82727e7i | − | 2.30219i | ||||||
\(686\) | − | 2.36371e6i | − | 0.191771i | ||||||
\(687\) | 8.59234e6 | 0.694576 | ||||||||
\(688\) | 7.53530e6i | 0.606917i | ||||||||
\(689\) | − | 762479.i | − | 0.0611899i | ||||||
\(690\) | − | 2.36438e6i | − | 0.189058i | ||||||
\(691\) | −5.66245e6 | −0.451138 | −0.225569 | − | 0.974227i | \(-0.572424\pi\) | ||||
−0.225569 | + | 0.974227i | \(0.572424\pi\) | |||||||
\(692\) | −1.19599e7 | −0.949430 | ||||||||
\(693\) | −1.90291e6 | −0.150517 | ||||||||
\(694\) | 921410. | 0.0726197 | ||||||||
\(695\) | 5.41819e6i | 0.425493i | ||||||||
\(696\) | 9.20278e6 | 0.720105 | ||||||||
\(697\) | − | 1.05630e7i | − | 0.823581i | ||||||
\(698\) | 58271.9i | 0.00452710i | ||||||||
\(699\) | −1.98760e7 | −1.53863 | ||||||||
\(700\) | 1.17196e7 | 0.903996 | ||||||||
\(701\) | − | 4.15435e6i | − | 0.319306i | −0.987173 | − | 0.159653i | \(-0.948962\pi\) | ||
0.987173 | − | 0.159653i | \(-0.0510376\pi\) | |||||||
\(702\) | 56889.4 | 0.00435701 | ||||||||
\(703\) | 7.95384e6 | + | 2.14738e7i | 0.607000 | + | 1.63878i | ||||
\(704\) | 4.03345e6 | 0.306722 | ||||||||
\(705\) | − | 2.25983e7i | − | 1.71239i | ||||||
\(706\) | −405530. | −0.0306204 | ||||||||
\(707\) | −8.89221e6 | −0.669054 | ||||||||
\(708\) | − | 9.71381e6i | − | 0.728294i | ||||||
\(709\) | 2.41883e7i | 1.80713i | 0.428449 | + | 0.903566i | \(0.359060\pi\) | ||||
−0.428449 | + | 0.903566i | \(0.640940\pi\) | |||||||
\(710\) | −1.69037e6 | −0.125845 | ||||||||
\(711\) | − | 9.95042e6i | − | 0.738189i | ||||||
\(712\) | 7.92782e6 | 0.586076 | ||||||||
\(713\) | −5.37909e6 | −0.396265 | ||||||||
\(714\) | 1.65212e6 | 0.121282 | ||||||||
\(715\) | 366455. | 0.0268074 | ||||||||
\(716\) | 2.38784e7i | 1.74069i | ||||||||
\(717\) | − | 5.62132e6i | − | 0.408357i | ||||||
\(718\) | − | 3.26915e6i | − | 0.236659i | ||||||
\(719\) | −1.98486e6 | −0.143188 | −0.0715941 | − | 0.997434i | \(-0.522809\pi\) | ||||
−0.0715941 | + | 0.997434i | \(0.522809\pi\) | |||||||
\(720\) | 1.13321e7i | 0.814664i | ||||||||
\(721\) | − | 1.68243e7i | − | 1.20531i | ||||||
\(722\) | 5.30283e6i | 0.378586i | ||||||||
\(723\) | 7.31509e6i | 0.520444i | ||||||||
\(724\) | −6.78449e6 | −0.481029 | ||||||||
\(725\) | − | 3.11071e7i | − | 2.19793i | ||||||
\(726\) | 2.81388e6i | 0.198136i | ||||||||
\(727\) | 2.20799e7i | 1.54939i | 0.632333 | + | 0.774697i | \(0.282098\pi\) | ||||
−0.632333 | + | 0.774697i | \(0.717902\pi\) | |||||||
\(728\) | 157749. | 0.0110316 | ||||||||
\(729\) | −1.01597e6 | −0.0708044 | ||||||||
\(730\) | −596370. | −0.0414199 | ||||||||
\(731\) | 7.58359e6 | 0.524906 | ||||||||
\(732\) | 2.72908e7i | 1.88252i | ||||||||
\(733\) | −1.72118e7 | −1.18322 | −0.591612 | − | 0.806223i | \(-0.701508\pi\) | ||||
−0.591612 | + | 0.806223i | \(0.701508\pi\) | |||||||
\(734\) | 167008.i | 0.0114419i | ||||||||
\(735\) | − | 1.56488e7i | − | 1.06847i | ||||||
\(736\) | −4.08697e6 | −0.278104 | ||||||||
\(737\) | −7.03402e6 | −0.477018 | ||||||||
\(738\) | − | 1.69132e6i | − | 0.114310i | ||||||
\(739\) | −2.51693e7 | −1.69535 | −0.847675 | − | 0.530515i | \(-0.821998\pi\) | ||||
−0.847675 | + | 0.530515i | \(0.821998\pi\) | |||||||
\(740\) | −7.73155e6 | − | 2.08737e7i | −0.519024 | − | 1.40126i | ||||
\(741\) | −1.49031e6 | −0.0997085 | ||||||||
\(742\) | 2.50821e6i | 0.167245i | ||||||||
\(743\) | 2.36324e7 | 1.57049 | 0.785245 | − | 0.619185i | \(-0.212537\pi\) | ||||
0.785245 | + | 0.619185i | \(0.212537\pi\) | |||||||
\(744\) | −5.18413e6 | −0.343355 | ||||||||
\(745\) | − | 5.70555e6i | − | 0.376623i | ||||||
\(746\) | − | 3.40843e6i | − | 0.224237i | ||||||
\(747\) | 1.15812e7 | 0.759370 | ||||||||
\(748\) | − | 4.39738e6i | − | 0.287369i | ||||||
\(749\) | −1.05296e7 | −0.685817 | ||||||||
\(750\) | −2.17197e6 | −0.140994 | ||||||||
\(751\) | 761070. | 0.0492408 | 0.0246204 | − | 0.999697i | \(-0.492162\pi\) | ||||
0.0246204 | + | 0.999697i | \(0.492162\pi\) | |||||||
\(752\) | −1.22594e7 | −0.790543 | ||||||||
\(753\) | 1.58429e7i | 1.01823i | ||||||||
\(754\) | − | 205738.i | − | 0.0131791i | ||||||
\(755\) | 8.25461e6i | 0.527022i | ||||||||
\(756\) | 5.32175e6 | 0.338649 | ||||||||
\(757\) | 2.12851e7i | 1.35001i | 0.737814 | + | 0.675004i | \(0.235858\pi\) | ||||
−0.737814 | + | 0.675004i | \(0.764142\pi\) | |||||||
\(758\) | 788403.i | 0.0498397i | ||||||||
\(759\) | − | 4.02552e6i | − | 0.253640i | ||||||
\(760\) | − | 1.55977e7i | − | 0.979551i | ||||||
\(761\) | −1.99836e7 | −1.25087 | −0.625435 | − | 0.780277i | \(-0.715078\pi\) | ||||
−0.625435 | + | 0.780277i | \(0.715078\pi\) | |||||||
\(762\) | 851158.i | 0.0531035i | ||||||||
\(763\) | 1.33973e7i | 0.833118i | ||||||||
\(764\) | − | 3.68691e6i | − | 0.228523i | ||||||
\(765\) | 1.14047e7 | 0.704580 | ||||||||
\(766\) | 3.54597e6 | 0.218355 | ||||||||
\(767\) | −441962. | −0.0271267 | ||||||||
\(768\) | 1.39415e7 | 0.852919 | ||||||||
\(769\) | − | 1.94814e7i | − | 1.18797i | −0.804477 | − | 0.593984i | \(-0.797554\pi\) | ||
0.804477 | − | 0.593984i | \(-0.202446\pi\) | |||||||
\(770\) | −1.20547e6 | −0.0732705 | ||||||||
\(771\) | − | 2.54584e7i | − | 1.54239i | ||||||
\(772\) | − | 1.87373e7i | − | 1.13152i | ||||||
\(773\) | 1.13110e7 | 0.680849 | 0.340425 | − | 0.940272i | \(-0.389429\pi\) | ||||
0.340425 | + | 0.940272i | \(0.389429\pi\) | |||||||
\(774\) | 1.21426e6 | 0.0728550 | ||||||||
\(775\) | 1.75233e7i | 1.04800i | ||||||||
\(776\) | −391621. | −0.0233460 | ||||||||
\(777\) | 1.33522e7 | − | 4.94559e6i | 0.793412 | − | 0.293877i | ||||
\(778\) | 3.14131e6 | 0.186064 | ||||||||
\(779\) | − | 3.13444e7i | − | 1.85062i | ||||||
\(780\) | 1.44866e6 | 0.0852571 | ||||||||
\(781\) | −2.87796e6 | −0.168833 | ||||||||
\(782\) | 1.29088e6i | 0.0754867i | ||||||||
\(783\) | − | 1.41254e7i | − | 0.823375i | ||||||
\(784\) | −8.48938e6 | −0.493271 | ||||||||
\(785\) | 2.51418e7i | 1.45621i | ||||||||
\(786\) | −3.42611e6 | −0.197809 | ||||||||
\(787\) | −7.02612e6 | −0.404370 | −0.202185 | − | 0.979347i | \(-0.564804\pi\) | ||||
−0.202185 | + | 0.979347i | \(0.564804\pi\) | |||||||
\(788\) | −1.51468e6 | −0.0868972 | ||||||||
\(789\) | −7.03106e6 | −0.402095 | ||||||||
\(790\) | − | 6.30346e6i | − | 0.359345i | ||||||
\(791\) | − | 1.71714e6i | − | 0.0975810i | ||||||
\(792\) | − | 1.43295e6i | − | 0.0811742i | ||||||
\(793\) | 1.24169e6 | 0.0701179 | ||||||||
\(794\) | − | 2.39151e6i | − | 0.134623i | ||||||
\(795\) | 4.68775e7i | 2.63055i | ||||||||
\(796\) | 1.24258e7i | 0.695089i | ||||||||
\(797\) | − | 2.61247e7i | − | 1.45682i | −0.685143 | − | 0.728409i | \(-0.740260\pi\) | ||
0.685143 | − | 0.728409i | \(-0.259740\pi\) | |||||||
\(798\) | 4.90245e6 | 0.272525 | ||||||||
\(799\) | 1.23380e7i | 0.683719i | ||||||||
\(800\) | 1.33140e7i | 0.735503i | ||||||||
\(801\) | 1.72008e7i | 0.947255i | ||||||||
\(802\) | −3.89184e6 | −0.213658 | ||||||||
\(803\) | −1.01536e6 | −0.0555689 | ||||||||
\(804\) | −2.78068e7 | −1.51709 | ||||||||
\(805\) | −1.00632e7 | −0.547326 | ||||||||
\(806\) | 115897.i | 0.00628397i | ||||||||
\(807\) | 4.44622e7 | 2.40329 | ||||||||
\(808\) | − | 6.69610e6i | − | 0.360823i | ||||||
\(809\) | 2.91750e7i | 1.56725i | 0.621233 | + | 0.783626i | \(0.286632\pi\) | ||||
−0.621233 | + | 0.783626i | \(0.713368\pi\) | |||||||
\(810\) | −6.61551e6 | −0.354284 | ||||||||
\(811\) | 3.56190e6 | 0.190164 | 0.0950822 | − | 0.995469i | \(-0.469689\pi\) | ||||
0.0950822 | + | 0.995469i | \(0.469689\pi\) | |||||||
\(812\) | − | 1.92458e7i | − | 1.02435i | ||||||
\(813\) | 2.09057e7 | 1.10927 | ||||||||
\(814\) | 462897. | + | 1.24973e6i | 0.0244863 | + | 0.0661083i | ||||
\(815\) | 4.51812e7 | 2.38267 | ||||||||
\(816\) | − | 1.67509e7i | − | 0.880668i | ||||||
\(817\) | 2.25033e7 | 1.17948 | ||||||||
\(818\) | 4.53368e6 | 0.236901 | ||||||||
\(819\) | 342263.i | 0.0178300i | ||||||||
\(820\) | 3.04684e7i | 1.58239i | ||||||||
\(821\) | −1.48511e7 | −0.768954 | −0.384477 | − | 0.923135i | \(-0.625618\pi\) | ||||
−0.384477 | + | 0.923135i | \(0.625618\pi\) | |||||||
\(822\) | 6.69162e6i | 0.345424i | ||||||||
\(823\) | 4.45575e6 | 0.229309 | 0.114654 | − | 0.993405i | \(-0.463424\pi\) | ||||
0.114654 | + | 0.993405i | \(0.463424\pi\) | |||||||
\(824\) | 1.26692e7 | 0.650026 | ||||||||
\(825\) | −1.31138e7 | −0.670803 | ||||||||
\(826\) | 1.45385e6 | 0.0741431 | ||||||||
\(827\) | 9.37369e6i | 0.476592i | 0.971193 | + | 0.238296i | \(0.0765889\pi\) | ||||
−0.971193 | + | 0.238296i | \(0.923411\pi\) | |||||||
\(828\) | − | 5.87775e6i | − | 0.297944i | ||||||
\(829\) | 4.05029e6i | 0.204692i | 0.994749 | + | 0.102346i | \(0.0326348\pi\) | ||||
−0.994749 | + | 0.102346i | \(0.967365\pi\) | |||||||
\(830\) | 7.33656e6 | 0.369656 | ||||||||
\(831\) | − | 2.11256e7i | − | 1.06122i | ||||||
\(832\) | − | 725469.i | − | 0.0363338i | ||||||
\(833\) | 8.54378e6i | 0.426617i | ||||||||
\(834\) | − | 1.28239e6i | − | 0.0638416i | ||||||
\(835\) | −2.76733e7 | −1.37355 | ||||||||
\(836\) | − | 1.30487e7i | − | 0.645729i | ||||||
\(837\) | 7.95718e6i | 0.392596i | ||||||||
\(838\) | − | 4.08769e6i | − | 0.201080i | ||||||
\(839\) | 2.21153e7 | 1.08465 | 0.542323 | − | 0.840170i | \(-0.317545\pi\) | ||||
0.542323 | + | 0.840170i | \(0.317545\pi\) | |||||||
\(840\) | −9.69846e6 | −0.474247 | ||||||||
\(841\) | −3.05728e7 | −1.49055 | ||||||||
\(842\) | −263577. | −0.0128123 | ||||||||
\(843\) | − | 1.06061e7i | − | 0.514030i | ||||||
\(844\) | 3.03279e7 | 1.46550 | ||||||||
\(845\) | 3.20403e7i | 1.54367i | ||||||||
\(846\) | 1.97552e6i | 0.0948977i | ||||||||
\(847\) | 1.19763e7 | 0.573607 | ||||||||
\(848\) | 2.54308e7 | 1.21442 | ||||||||
\(849\) | − | 1.31353e7i | − | 0.625419i | ||||||
\(850\) | 4.20528e6 | 0.199640 | ||||||||
\(851\) | 3.86424e6 | + | 1.04327e7i | 0.182911 | + | 0.493824i | ||||
\(852\) | −1.13771e7 | −0.536949 | ||||||||
\(853\) | 1.41295e7i | 0.664898i | 0.943121 | + | 0.332449i | \(0.107875\pi\) | ||||
−0.943121 | + | 0.332449i | \(0.892125\pi\) | |||||||
\(854\) | −4.08458e6 | −0.191647 | ||||||||
\(855\) | 3.38420e7 | 1.58322 | ||||||||
\(856\) | − | 7.92913e6i | − | 0.369863i | ||||||
\(857\) | − | 2.53580e7i | − | 1.17940i | −0.807621 | − | 0.589702i | \(-0.799245\pi\) | ||
0.807621 | − | 0.589702i | \(-0.200755\pi\) | |||||||
\(858\) | −86733.1 | −0.00402223 | ||||||||
\(859\) | − | 2.22970e7i | − | 1.03101i | −0.856886 | − | 0.515506i | \(-0.827604\pi\) | ||
0.856886 | − | 0.515506i | \(-0.172396\pi\) | |||||||
\(860\) | −2.18744e7 | −1.00853 | ||||||||
\(861\) | −1.94895e7 | −0.895970 | ||||||||
\(862\) | −6.24456e6 | −0.286242 | ||||||||
\(863\) | −125737. | −0.00574694 | −0.00287347 | − | 0.999996i | \(-0.500915\pi\) | ||||
−0.00287347 | + | 0.999996i | \(0.500915\pi\) | |||||||
\(864\) | 6.04578e6i | 0.275529i | ||||||||
\(865\) | − | 3.34549e7i | − | 1.52026i | ||||||
\(866\) | − | 2.75705e6i | − | 0.124925i | ||||||
\(867\) | 1.10129e7 | 0.497570 | ||||||||
\(868\) | 1.08416e7i | 0.488422i | ||||||||
\(869\) | − | 1.07321e7i | − | 0.482097i | ||||||
\(870\) | 1.26488e7i | 0.566569i | ||||||||
\(871\) | 1.26516e6i | 0.0565067i | ||||||||
\(872\) | −1.00886e7 | −0.449303 | ||||||||
\(873\) | − | 849690.i | − | 0.0377333i | ||||||
\(874\) | 3.83053e6i | 0.169621i | ||||||||
\(875\) | 9.24423e6i | 0.408179i | ||||||||
\(876\) | −4.01391e6 | −0.176729 | ||||||||
\(877\) | −6.73604e6 | −0.295737 | −0.147869 | − | 0.989007i | \(-0.547241\pi\) | ||||
−0.147869 | + | 0.989007i | \(0.547241\pi\) | |||||||
\(878\) | −6.78204e6 | −0.296909 | ||||||||
\(879\) | −4.20564e7 | −1.83595 | ||||||||
\(880\) | 1.22223e7i | 0.532041i | ||||||||
\(881\) | −2.67472e7 | −1.16102 | −0.580509 | − | 0.814254i | \(-0.697146\pi\) | ||||
−0.580509 | + | 0.814254i | \(0.697146\pi\) | |||||||
\(882\) | 1.36800e6i | 0.0592128i | ||||||||
\(883\) | − | 1.30359e7i | − | 0.562652i | −0.959612 | − | 0.281326i | \(-0.909226\pi\) | ||
0.959612 | − | 0.281326i | \(-0.0907742\pi\) | |||||||
\(884\) | −790927. | −0.0340413 | ||||||||
\(885\) | 2.71720e7 | 1.16617 | ||||||||
\(886\) | − | 1.90988e6i | − | 0.0817375i | ||||||
\(887\) | 3.76423e7 | 1.60645 | 0.803225 | − | 0.595675i | \(-0.203115\pi\) | ||||
0.803225 | + | 0.595675i | \(0.203115\pi\) | |||||||
\(888\) | 3.72418e6 | + | 1.00546e7i | 0.158489 | + | 0.427889i | ||||
\(889\) | 3.62266e6 | 0.153735 | ||||||||
\(890\) | 1.08965e7i | 0.461117i | ||||||||
\(891\) | −1.12634e7 | −0.475307 | ||||||||
\(892\) | −3.05568e7 | −1.28587 | ||||||||
\(893\) | 3.66114e7i | 1.53634i | ||||||||
\(894\) | 1.35040e6i | 0.0565091i | ||||||||
\(895\) | −6.67938e7 | −2.78727 | ||||||||
\(896\) | 1.09135e7i | 0.454143i | ||||||||
\(897\) | −724043. | −0.0300458 | ||||||||
\(898\) | −3.75227e6 | −0.155276 | ||||||||
\(899\) | 2.87768e7 | 1.18752 | ||||||||
\(900\) | −1.91478e7 | −0.787975 | ||||||||
\(901\) | − | 2.55937e7i | − | 1.05032i | ||||||
\(902\) | − | 1.82418e6i | − | 0.0746536i | ||||||
\(903\) | − | 1.39923e7i | − | 0.571043i | ||||||
\(904\) | 1.29306e6 | 0.0526257 | ||||||||
\(905\) | − | 1.89779e7i | − | 0.770242i | ||||||
\(906\) | − | 1.95371e6i | − | 0.0790753i | ||||||
\(907\) | − | 3.29270e7i | − | 1.32903i | −0.747275 | − | 0.664514i | \(-0.768638\pi\) | ||
0.747275 | − | 0.664514i | \(-0.231362\pi\) | |||||||
\(908\) | 3.28986e7i | 1.32423i | ||||||||
\(909\) | 1.45284e7 | 0.583186 | ||||||||
\(910\) | 216819.i | 0.00867950i | ||||||||
\(911\) | − | 2.83567e7i | − | 1.13203i | −0.824394 | − | 0.566017i | \(-0.808484\pi\) | ||
0.824394 | − | 0.566017i | \(-0.191516\pi\) | |||||||
\(912\) | − | 4.97060e7i | − | 1.97889i | ||||||
\(913\) | 1.24910e7 | 0.495930 | ||||||||
\(914\) | −3.09476e6 | −0.122535 | ||||||||
\(915\) | −7.63393e7 | −3.01436 | ||||||||
\(916\) | 1.35314e7 | 0.532848 | ||||||||
\(917\) | 1.45821e7i | 0.572659i | ||||||||
\(918\) | 1.90958e6 | 0.0747878 | ||||||||
\(919\) | 4.60773e6i | 0.179969i | 0.995943 | + | 0.0899846i | \(0.0286818\pi\) | ||||
−0.995943 | + | 0.0899846i | \(0.971318\pi\) | |||||||
\(920\) | − | 7.57789e6i | − | 0.295174i | ||||||
\(921\) | −2.65500e7 | −1.03137 | ||||||||
\(922\) | 283162. | 0.0109700 | ||||||||
\(923\) | 517639.i | 0.0199997i | ||||||||
\(924\) | −8.11349e6 | −0.312628 | ||||||||
\(925\) | 3.39863e7 | − | 1.25884e7i | 1.30602 | − | 0.483746i | ||||
\(926\) | −5.71281e6 | −0.218939 | ||||||||
\(927\) | 2.74880e7i | 1.05061i | ||||||||
\(928\) | 2.18643e7 | 0.833422 | ||||||||
\(929\) | 2.22109e7 | 0.844360 | 0.422180 | − | 0.906512i | \(-0.361265\pi\) | ||||
0.422180 | + | 0.906512i | \(0.361265\pi\) | |||||||
\(930\) | − | 7.12538e6i | − | 0.270147i | ||||||
\(931\) | 2.53526e7i | 0.958623i | ||||||||
\(932\) | −3.13010e7 | −1.18037 | ||||||||
\(933\) | 7.29915e6i | 0.274516i | ||||||||
\(934\) | −376704. | −0.0141297 | ||||||||
\(935\) | 1.23006e7 | 0.460147 | ||||||||
\(936\) | −257735. | −0.00961575 | ||||||||
\(937\) | −2.95907e7 | −1.10105 | −0.550523 | − | 0.834820i | \(-0.685572\pi\) | ||||
−0.550523 | + | 0.834820i | \(0.685572\pi\) | |||||||
\(938\) | − | 4.16180e6i | − | 0.154445i | ||||||
\(939\) | 2.50908e7i | 0.928647i | ||||||||
\(940\) | − | 3.55882e7i | − | 1.31367i | ||||||
\(941\) | 2.05391e7 | 0.756148 | 0.378074 | − | 0.925775i | \(-0.376586\pi\) | ||||
0.378074 | + | 0.925775i | \(0.376586\pi\) | |||||||
\(942\) | − | 5.95061e6i | − | 0.218491i | ||||||
\(943\) | − | 1.52281e7i | − | 0.557657i | ||||||
\(944\) | − | 1.47406e7i | − | 0.538377i | ||||||
\(945\) | 1.48863e7i | 0.542259i | ||||||||
\(946\) | 1.30965e6 | 0.0475801 | ||||||||
\(947\) | 4.21333e7i | 1.52669i | 0.645991 | + | 0.763345i | \(0.276444\pi\) | ||||
−0.645991 | + | 0.763345i | \(0.723556\pi\) | |||||||
\(948\) | − | 4.24259e7i | − | 1.53324i | ||||||
\(949\) | 182626.i | 0.00658259i | ||||||||
\(950\) | 1.24786e7 | 0.448598 | ||||||||
\(951\) | −1.74314e7 | −0.625000 | ||||||||
\(952\) | 5.29507e6 | 0.189356 | ||||||||
\(953\) | 4.48612e7 | 1.60007 | 0.800034 | − | 0.599954i | \(-0.204815\pi\) | ||||
0.800034 | + | 0.599954i | \(0.204815\pi\) | |||||||
\(954\) | − | 4.09799e6i | − | 0.145781i | ||||||
\(955\) | 1.03132e7 | 0.365920 | ||||||||
\(956\) | − | 8.85255e6i | − | 0.313274i | ||||||
\(957\) | 2.15355e7i | 0.760109i | ||||||||
\(958\) | 6.67092e6 | 0.234840 | ||||||||
\(959\) | 2.84806e7 | 1.00001 | ||||||||
\(960\) | 4.46021e7i | 1.56199i | ||||||||
\(961\) | 1.24185e7 | 0.433773 | ||||||||
\(962\) | 224781. | − | 83258.0i | 0.00783107 | − | 0.00290060i | ||||
\(963\) | 1.72036e7 | 0.597798 | ||||||||
\(964\) | 1.15199e7i | 0.399262i | ||||||||
\(965\) | 5.24130e7 | 1.81184 | ||||||||
\(966\) | 2.38177e6 | 0.0821216 | ||||||||
\(967\) | − | 1.77799e7i | − | 0.611453i | −0.952119 | − | 0.305727i | \(-0.901101\pi\) | ||
0.952119 | − | 0.305727i | \(-0.0988994\pi\) | |||||||
\(968\) | 9.01853e6i | 0.309348i | ||||||||
\(969\) | −5.00246e7 | −1.71149 | ||||||||
\(970\) | − | 538267.i | − | 0.0183683i | ||||||
\(971\) | 1.29448e7 | 0.440603 | 0.220302 | − | 0.975432i | \(-0.429296\pi\) | ||||
0.220302 | + | 0.975432i | \(0.429296\pi\) | |||||||
\(972\) | −2.96803e7 | −1.00763 | ||||||||
\(973\) | −5.45804e6 | −0.184822 | ||||||||
\(974\) | −5.58049e6 | −0.188484 | ||||||||
\(975\) | 2.35870e6i | 0.0794622i | ||||||||
\(976\) | 4.14136e7i | 1.39161i | ||||||||
\(977\) | 4.56506e7i | 1.53007i | 0.643990 | + | 0.765034i | \(0.277278\pi\) | ||||
−0.643990 | + | 0.765034i | \(0.722722\pi\) | |||||||
\(978\) | −1.06936e7 | −0.357500 | ||||||||
\(979\) | 1.85520e7i | 0.618634i | ||||||||
\(980\) | − | 2.46440e7i | − | 0.819684i | ||||||
\(981\) | − | 2.18890e7i | − | 0.726194i | ||||||
\(982\) | 6.38049e6i | 0.211142i | ||||||||
\(983\) | −5.14288e7 | −1.69755 | −0.848775 | − | 0.528755i | \(-0.822659\pi\) | ||||
−0.848775 | + | 0.528755i | \(0.822659\pi\) | |||||||
\(984\) | − | 1.46762e7i | − | 0.483199i | ||||||
\(985\) | − | 4.23694e6i | − | 0.139143i | ||||||
\(986\) | − | 6.90590e6i | − | 0.226218i | ||||||
\(987\) | 2.27645e7 | 0.743815 | ||||||||
\(988\) | −2.34697e6 | −0.0764919 | ||||||||
\(989\) | 1.09328e7 | 0.355420 | ||||||||
\(990\) | 1.96953e6 | 0.0638668 | ||||||||
\(991\) | − | 2.27943e6i | − | 0.0737295i | −0.999320 | − | 0.0368648i | \(-0.988263\pi\) | ||
0.999320 | − | 0.0368648i | \(-0.0117371\pi\) | |||||||
\(992\) | −1.23166e7 | −0.397386 | ||||||||
\(993\) | 2.21902e7i | 0.714149i | ||||||||
\(994\) | − | 1.70280e6i | − | 0.0546635i | ||||||
\(995\) | −3.47580e7 | −1.11300 | ||||||||
\(996\) | 4.93792e7 | 1.57723 | ||||||||
\(997\) | 2.09171e7i | 0.666444i | 0.942848 | + | 0.333222i | \(0.108136\pi\) | ||||
−0.942848 | + | 0.333222i | \(0.891864\pi\) | |||||||
\(998\) | −9.55349e6 | −0.303624 | ||||||||
\(999\) | 1.54329e7 | − | 5.71629e6i | 0.489253 | − | 0.181218i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 37.6.b.a.36.8 | ✓ | 16 | |
3.2 | odd | 2 | 333.6.c.d.73.9 | 16 | |||
4.3 | odd | 2 | 592.6.g.c.369.4 | 16 | |||
37.36 | even | 2 | inner | 37.6.b.a.36.9 | yes | 16 | |
111.110 | odd | 2 | 333.6.c.d.73.8 | 16 | |||
148.147 | odd | 2 | 592.6.g.c.369.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.6.b.a.36.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
37.6.b.a.36.9 | yes | 16 | 37.36 | even | 2 | inner | |
333.6.c.d.73.8 | 16 | 111.110 | odd | 2 | |||
333.6.c.d.73.9 | 16 | 3.2 | odd | 2 | |||
592.6.g.c.369.3 | 16 | 148.147 | odd | 2 | |||
592.6.g.c.369.4 | 16 | 4.3 | odd | 2 |