Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(19,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (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: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.18 | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.7.f.a.19.17 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.294917 | + | 7.99456i | −0.0368646 | + | 0.999320i | ||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | −63.8260 | − | 4.71546i | −0.997282 | − | 0.0736790i | ||||
\(5\) | 71.1255 | + | 102.792i | 0.569004 | + | 0.822335i | ||||
\(6\) | −4.59730 | + | 124.623i | −0.0212838 | + | 0.576958i | ||||
\(7\) | 496.078 | 1.44629 | 0.723146 | − | 0.690695i | \(-0.242695\pi\) | ||||
0.723146 | + | 0.690695i | \(0.242695\pi\) | |||||||
\(8\) | 56.5214 | − | 508.871i | 0.110393 | − | 0.993888i | ||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | −842.752 | + | 538.302i | −0.842752 | + | 0.538302i | ||||
\(11\) | 561.571i | 0.421917i | 0.977495 | + | 0.210958i | \(0.0676585\pi\) | ||||
−0.977495 | + | 0.210958i | \(0.932342\pi\) | |||||||
\(12\) | −994.950 | − | 73.5067i | −0.575781 | − | 0.0425386i | ||||
\(13\) | 1584.68i | 0.721294i | 0.932702 | + | 0.360647i | \(0.117444\pi\) | ||||
−0.932702 | + | 0.360647i | \(0.882556\pi\) | |||||||
\(14\) | −146.302 | + | 3965.93i | −0.0533169 | + | 1.44531i | ||||
\(15\) | 1108.74 | + | 1602.37i | 0.328515 | + | 0.474775i | ||||
\(16\) | 4051.53 | + | 601.938i | 0.989143 | + | 0.146958i | ||||
\(17\) | − | 4503.06i | − | 0.916561i | −0.888808 | − | 0.458281i | \(-0.848465\pi\) | ||
0.888808 | − | 0.458281i | \(-0.151535\pi\) | |||||||
\(18\) | −71.6647 | + | 1942.68i | −0.0122882 | + | 0.333107i | ||||
\(19\) | 10102.8i | 1.47293i | 0.676478 | + | 0.736463i | \(0.263505\pi\) | ||||
−0.676478 | + | 0.736463i | \(0.736495\pi\) | |||||||
\(20\) | −4054.95 | − | 6896.19i | −0.506869 | − | 0.862023i | ||||
\(21\) | 7733.09 | 0.835017 | ||||||||
\(22\) | −4489.52 | − | 165.617i | −0.421630 | − | 0.0155538i | ||||
\(23\) | −16192.2 | −1.33083 | −0.665417 | − | 0.746472i | \(-0.731746\pi\) | ||||
−0.665417 | + | 0.746472i | \(0.731746\pi\) | |||||||
\(24\) | 881.081 | − | 7932.51i | 0.0637356 | − | 0.573821i | ||||
\(25\) | −5507.32 | + | 14622.2i | −0.352469 | + | 0.935824i | ||||
\(26\) | −12668.8 | − | 467.349i | −0.720803 | − | 0.0265902i | ||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | −31662.7 | − | 2339.24i | −1.44236 | − | 0.106561i | ||||
\(29\) | 2001.00 | 0.0820451 | 0.0410225 | − | 0.999158i | \(-0.486938\pi\) | ||||
0.0410225 | + | 0.999158i | \(0.486938\pi\) | |||||||
\(30\) | −13137.2 | + | 8391.30i | −0.486563 | + | 0.310789i | ||||
\(31\) | 7380.01i | 0.247726i | 0.992299 | + | 0.123863i | \(0.0395284\pi\) | ||||
−0.992299 | + | 0.123863i | \(0.960472\pi\) | |||||||
\(32\) | −6007.10 | + | 32212.7i | −0.183322 | + | 0.983053i | ||||
\(33\) | 8754.03i | 0.243594i | ||||||||
\(34\) | 36000.0 | + | 1328.03i | 0.915938 | + | 0.0337886i | ||||
\(35\) | 35283.8 | + | 50992.8i | 0.822946 | + | 1.18934i | ||||
\(36\) | −15509.7 | − | 1145.86i | −0.332427 | − | 0.0245597i | ||||
\(37\) | − | 66699.3i | − | 1.31679i | −0.752674 | − | 0.658394i | \(-0.771236\pi\) | ||
0.752674 | − | 0.658394i | \(-0.228764\pi\) | |||||||
\(38\) | −80767.5 | − | 2979.48i | −1.47192 | − | 0.0542988i | ||||
\(39\) | 24702.8i | 0.416439i | ||||||||
\(40\) | 56327.9 | − | 30383.7i | 0.880123 | − | 0.474746i | ||||
\(41\) | −97191.8 | −1.41019 | −0.705095 | − | 0.709113i | \(-0.749096\pi\) | ||||
−0.705095 | + | 0.709113i | \(0.749096\pi\) | |||||||
\(42\) | −2280.62 | + | 61822.7i | −0.0307826 | + | 0.834449i | ||||
\(43\) | 112822. | 1.41902 | 0.709512 | − | 0.704693i | \(-0.248915\pi\) | ||||
0.709512 | + | 0.704693i | \(0.248915\pi\) | |||||||
\(44\) | 2648.07 | − | 35842.9i | 0.0310864 | − | 0.420770i | ||||
\(45\) | 17283.5 | + | 24978.4i | 0.189668 | + | 0.274112i | ||||
\(46\) | 4775.36 | − | 129450.i | 0.0490606 | − | 1.32993i | ||||
\(47\) | 196416. | 1.89183 | 0.945916 | − | 0.324412i | \(-0.105167\pi\) | ||||
0.945916 | + | 0.324412i | \(0.105167\pi\) | |||||||
\(48\) | 63157.1 | + | 9383.29i | 0.571082 | + | 0.0848460i | ||||
\(49\) | 128445. | 1.09176 | ||||||||
\(50\) | −115274. | − | 48341.0i | −0.922194 | − | 0.386728i | ||||
\(51\) | − | 70195.8i | − | 0.529177i | ||||||
\(52\) | 7472.50 | − | 101144.i | 0.0531442 | − | 0.719333i | ||||
\(53\) | − | 72076.9i | − | 0.484137i | −0.970259 | − | 0.242069i | \(-0.922174\pi\) | ||
0.970259 | − | 0.242069i | \(-0.0778260\pi\) | |||||||
\(54\) | −1117.14 | + | 30283.4i | −0.00709459 | + | 0.192319i | ||||
\(55\) | −57724.9 | + | 39942.0i | −0.346957 | + | 0.240072i | ||||
\(56\) | 28039.0 | − | 252440.i | 0.159661 | − | 1.43745i | ||||
\(57\) | 157487.i | 0.850394i | ||||||||
\(58\) | −590.128 | + | 15997.1i | −0.00302456 | + | 0.0819893i | ||||
\(59\) | 141896.i | 0.690898i | 0.938438 | + | 0.345449i | \(0.112273\pi\) | ||||
−0.938438 | + | 0.345449i | \(0.887727\pi\) | |||||||
\(60\) | −63210.4 | − | 107501.i | −0.292641 | − | 0.497689i | ||||
\(61\) | 201436. | 0.887457 | 0.443728 | − | 0.896161i | \(-0.353656\pi\) | ||||
0.443728 | + | 0.896161i | \(0.353656\pi\) | |||||||
\(62\) | −59000.0 | − | 2176.49i | −0.247558 | − | 0.00913233i | ||||
\(63\) | 120547. | 0.482097 | ||||||||
\(64\) | −255755. | − | 57524.2i | −0.975627 | − | 0.219437i | ||||
\(65\) | −162892. | + | 112711.i | −0.593145 | + | 0.410419i | ||||
\(66\) | −69984.6 | − | 2581.71i | −0.243428 | − | 0.00897998i | ||||
\(67\) | 216637. | 0.720293 | 0.360146 | − | 0.932896i | \(-0.382727\pi\) | ||||
0.360146 | + | 0.932896i | \(0.382727\pi\) | |||||||
\(68\) | −21234.0 | + | 287413.i | −0.0675313 | + | 0.914070i | ||||
\(69\) | −252412. | −0.768357 | ||||||||
\(70\) | −418071. | + | 267040.i | −1.21887 | + | 0.778542i | ||||
\(71\) | − | 358449.i | − | 1.00150i | −0.865591 | − | 0.500751i | \(-0.833057\pi\) | ||
0.865591 | − | 0.500751i | \(-0.166943\pi\) | |||||||
\(72\) | 13734.7 | − | 123656.i | 0.0367978 | − | 0.331296i | ||||
\(73\) | − | 411536.i | − | 1.05789i | −0.848657 | − | 0.528944i | \(-0.822588\pi\) | ||
0.848657 | − | 0.528944i | \(-0.177412\pi\) | |||||||
\(74\) | 533231. | + | 19670.7i | 1.31589 | + | 0.0485428i | ||||
\(75\) | −85850.7 | + | 227938.i | −0.203498 | + | 0.540298i | ||||
\(76\) | 47639.3 | − | 644822.i | 0.108524 | − | 1.46892i | ||||
\(77\) | 278583.i | 0.610215i | ||||||||
\(78\) | −197488. | − | 7285.25i | −0.416156 | − | 0.0153519i | ||||
\(79\) | − | 272036.i | − | 0.551754i | −0.961193 | − | 0.275877i | \(-0.911032\pi\) | ||
0.961193 | − | 0.275877i | \(-0.0889683\pi\) | |||||||
\(80\) | 226293. | + | 459277.i | 0.441978 | + | 0.897026i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 28663.5 | − | 777005.i | 0.0519861 | − | 1.40923i | ||||
\(83\) | −252398. | −0.441419 | −0.220709 | − | 0.975340i | \(-0.570837\pi\) | ||||
−0.220709 | + | 0.975340i | \(0.570837\pi\) | |||||||
\(84\) | −493573. | − | 36465.1i | −0.832748 | − | 0.0615233i | ||||
\(85\) | 462878. | − | 320283.i | 0.753720 | − | 0.521527i | ||||
\(86\) | −33273.2 | + | 901965.i | −0.0523117 | + | 1.41806i | ||||
\(87\) | 31192.5 | 0.0473688 | ||||||||
\(88\) | 285767. | + | 31740.8i | 0.419338 | + | 0.0465768i | ||||
\(89\) | −87241.6 | −0.123752 | −0.0618762 | − | 0.998084i | \(-0.519708\pi\) | ||||
−0.0618762 | + | 0.998084i | \(0.519708\pi\) | |||||||
\(90\) | −204789. | + | 130807.i | −0.280917 | + | 0.179434i | ||||
\(91\) | 786126.i | 1.04320i | ||||||||
\(92\) | 1.03349e6 | + | 76353.9i | 1.32722 | + | 0.0980545i | ||||
\(93\) | 115043.i | 0.143025i | ||||||||
\(94\) | −57926.2 | + | 1.57026e6i | −0.0697416 | + | 1.89055i | ||||
\(95\) | −1.03849e6 | + | 718567.i | −1.21124 | + | 0.838101i | ||||
\(96\) | −93641.4 | + | 502146.i | −0.105841 | + | 0.567566i | ||||
\(97\) | 130653.i | 0.143154i | 0.997435 | + | 0.0715771i | \(0.0228032\pi\) | ||||
−0.997435 | + | 0.0715771i | \(0.977197\pi\) | |||||||
\(98\) | −37880.4 | + | 1.02686e6i | −0.0402473 | + | 1.09102i | ||||
\(99\) | 136462.i | 0.140639i | ||||||||
\(100\) | 420461. | − | 907310.i | 0.420461 | − | 0.907310i | ||||
\(101\) | −1.08656e6 | −1.05460 | −0.527300 | − | 0.849679i | \(-0.676796\pi\) | ||||
−0.527300 | + | 0.849679i | \(0.676796\pi\) | |||||||
\(102\) | 561185. | + | 20701.9i | 0.528817 | + | 0.0195079i | ||||
\(103\) | −1.78249e6 | −1.63123 | −0.815616 | − | 0.578594i | \(-0.803602\pi\) | ||||
−0.815616 | + | 0.578594i | \(0.803602\pi\) | |||||||
\(104\) | 806398. | + | 89568.5i | 0.716885 | + | 0.0796260i | ||||
\(105\) | 550020. | + | 794899.i | 0.475128 | + | 0.686664i | ||||
\(106\) | 576224. | + | 21256.7i | 0.483808 | + | 0.0178475i | ||||
\(107\) | 558410. | 0.455829 | 0.227915 | − | 0.973681i | \(-0.426809\pi\) | ||||
0.227915 | + | 0.973681i | \(0.426809\pi\) | |||||||
\(108\) | −241773. | − | 17862.1i | −0.191927 | − | 0.0141795i | ||||
\(109\) | −453156. | −0.349920 | −0.174960 | − | 0.984576i | \(-0.555980\pi\) | ||||
−0.174960 | + | 0.984576i | \(0.555980\pi\) | |||||||
\(110\) | −302295. | − | 473265.i | −0.227119 | − | 0.355571i | ||||
\(111\) | − | 1.03974e6i | − | 0.760248i | ||||||
\(112\) | 2.00987e6 | + | 298608.i | 1.43059 | + | 0.212544i | ||||
\(113\) | − | 1.83286e6i | − | 1.27026i | −0.772403 | − | 0.635132i | \(-0.780946\pi\) | ||
0.772403 | − | 0.635132i | \(-0.219054\pi\) | |||||||
\(114\) | −1.25904e6 | − | 46445.6i | −0.849816 | − | 0.0313494i | ||||
\(115\) | −1.15168e6 | − | 1.66443e6i | −0.757250 | − | 1.09439i | ||||
\(116\) | −127716. | − | 9435.62i | −0.0818221 | − | 0.00604500i | ||||
\(117\) | 385078.i | 0.240431i | ||||||||
\(118\) | −1.13440e6 | − | 41847.4i | −0.690428 | − | 0.0254696i | ||||
\(119\) | − | 2.23387e6i | − | 1.32562i | ||||||
\(120\) | 878064. | − | 473636.i | 0.508139 | − | 0.274095i | ||||
\(121\) | 1.45620e6 | 0.821986 | ||||||||
\(122\) | −59406.8 | + | 1.61039e6i | −0.0327157 | + | 0.886853i | ||||
\(123\) | −1.51507e6 | −0.814174 | ||||||||
\(124\) | 34800.2 | − | 471037.i | 0.0182522 | − | 0.247053i | ||||
\(125\) | −1.89476e6 | + | 473907.i | −0.970116 | + | 0.242640i | ||||
\(126\) | −35551.3 | + | 963720.i | −0.0177723 | + | 0.481770i | ||||
\(127\) | 1.99686e6 | 0.974847 | 0.487423 | − | 0.873166i | \(-0.337937\pi\) | ||||
0.487423 | + | 0.873166i | \(0.337937\pi\) | |||||||
\(128\) | 535307. | − | 2.02768e6i | 0.255254 | − | 0.966874i | ||||
\(129\) | 1.75873e6 | 0.819274 | ||||||||
\(130\) | −853038. | − | 1.33549e6i | −0.388274 | − | 0.607872i | ||||
\(131\) | 596204.i | 0.265205i | 0.991169 | + | 0.132602i | \(0.0423333\pi\) | ||||
−0.991169 | + | 0.132602i | \(0.957667\pi\) | |||||||
\(132\) | 41279.3 | − | 558735.i | 0.0179478 | − | 0.242932i | ||||
\(133\) | 5.01178e6i | 2.13028i | ||||||||
\(134\) | −63890.0 | + | 1.73192e6i | −0.0265533 | + | 0.719803i | ||||
\(135\) | 269423. | + | 389375.i | 0.109505 | + | 0.158258i | ||||
\(136\) | −2.29148e6 | − | 254519.i | −0.910959 | − | 0.101182i | ||||
\(137\) | − | 4.42870e6i | − | 1.72232i | −0.508332 | − | 0.861161i | \(-0.669738\pi\) | ||
0.508332 | − | 0.861161i | \(-0.330262\pi\) | |||||||
\(138\) | 74440.6 | − | 2.01792e6i | 0.0283252 | − | 0.767835i | ||||
\(139\) | − | 5.04455e6i | − | 1.87836i | −0.343431 | − | 0.939178i | \(-0.611589\pi\) | ||
0.343431 | − | 0.939178i | \(-0.388411\pi\) | |||||||
\(140\) | −2.01157e6 | − | 3.42105e6i | −0.733080 | − | 1.24674i | ||||
\(141\) | 3.06182e6 | 1.09225 | ||||||||
\(142\) | 2.86564e6 | + | 105713.i | 1.00082 | + | 0.0369200i | ||||
\(143\) | −889912. | −0.304326 | ||||||||
\(144\) | 984522. | + | 146271.i | 0.329714 | + | 0.0489859i | ||||
\(145\) | 142322. | + | 205686.i | 0.0466840 | + | 0.0674685i | ||||
\(146\) | 3.29005e6 | + | 121369.i | 1.05717 | + | 0.0389986i | ||||
\(147\) | 2.00225e6 | 0.630328 | ||||||||
\(148\) | −314518. | + | 4.25715e6i | −0.0970197 | + | 1.31321i | ||||
\(149\) | −2.31618e6 | −0.700185 | −0.350093 | − | 0.936715i | \(-0.613850\pi\) | ||||
−0.350093 | + | 0.936715i | \(0.613850\pi\) | |||||||
\(150\) | −1.79695e6 | − | 753561.i | −0.532429 | − | 0.223277i | ||||
\(151\) | 5.72844e6i | 1.66382i | 0.554912 | + | 0.831909i | \(0.312752\pi\) | ||||
−0.554912 | + | 0.831909i | \(0.687248\pi\) | |||||||
\(152\) | 5.14102e6 | + | 571024.i | 1.46392 | + | 0.162601i | ||||
\(153\) | − | 1.09424e6i | − | 0.305520i | ||||||
\(154\) | −2.22715e6 | − | 82158.8i | −0.609800 | − | 0.0224953i | ||||
\(155\) | −758605. | + | 524907.i | −0.203714 | + | 0.140957i | ||||
\(156\) | 116485. | − | 1.57668e6i | 0.0306828 | − | 0.415307i | ||||
\(157\) | 214345.i | 0.0553879i | 0.999616 | + | 0.0276940i | \(0.00881639\pi\) | ||||
−0.999616 | + | 0.0276940i | \(0.991184\pi\) | |||||||
\(158\) | 2.17481e6 | + | 80228.0i | 0.551379 | + | 0.0203402i | ||||
\(159\) | − | 1.12357e6i | − | 0.279517i | ||||||
\(160\) | −3.73846e6 | + | 1.67366e6i | −0.912710 | + | 0.408609i | ||||
\(161\) | −8.03262e6 | −1.92477 | ||||||||
\(162\) | −17414.5 | + | 472071.i | −0.00409606 | + | 0.111036i | ||||
\(163\) | 5.13155e6 | 1.18491 | 0.592456 | − | 0.805603i | \(-0.298158\pi\) | ||||
0.592456 | + | 0.805603i | \(0.298158\pi\) | |||||||
\(164\) | 6.20337e6 | + | 458304.i | 1.40636 | + | 0.103902i | ||||
\(165\) | −899843. | + | 622635.i | −0.200316 | + | 0.138606i | ||||
\(166\) | 74436.2 | − | 2.01781e6i | 0.0162727 | − | 0.441119i | ||||
\(167\) | 3.05651e6 | 0.656260 | 0.328130 | − | 0.944633i | \(-0.393582\pi\) | ||||
0.328130 | + | 0.944633i | \(0.393582\pi\) | |||||||
\(168\) | 437085. | − | 3.93514e6i | 0.0921803 | − | 0.829913i | ||||
\(169\) | 2.31559e6 | 0.479735 | ||||||||
\(170\) | 2.42401e6 | + | 3.79497e6i | 0.493387 | + | 0.772434i | ||||
\(171\) | 2.45498e6i | 0.490975i | ||||||||
\(172\) | −7.20100e6 | − | 532009.i | −1.41517 | − | 0.104552i | ||||
\(173\) | − | 5.15201e6i | − | 0.995034i | −0.867454 | − | 0.497517i | \(-0.834245\pi\) | ||
0.867454 | − | 0.497517i | \(-0.165755\pi\) | |||||||
\(174\) | −9199.18 | + | 249370.i | −0.00174623 | + | 0.0473366i | ||||
\(175\) | −2.73206e6 | + | 7.25378e6i | −0.509773 | + | 1.35347i | ||||
\(176\) | −338031. | + | 2.27522e6i | −0.0620039 | + | 0.417336i | ||||
\(177\) | 2.21194e6i | 0.398890i | ||||||||
\(178\) | 25729.0 | − | 697459.i | 0.00456208 | − | 0.123668i | ||||
\(179\) | − | 1.97052e6i | − | 0.343576i | −0.985134 | − | 0.171788i | \(-0.945046\pi\) | ||
0.985134 | − | 0.171788i | \(-0.0549543\pi\) | |||||||
\(180\) | −985353. | − | 1.67577e6i | −0.168956 | − | 0.287341i | ||||
\(181\) | 2.34636e6 | 0.395694 | 0.197847 | − | 0.980233i | \(-0.436605\pi\) | ||||
0.197847 | + | 0.980233i | \(0.436605\pi\) | |||||||
\(182\) | −6.28474e6 | − | 231842.i | −1.04249 | − | 0.0384572i | ||||
\(183\) | 3.14007e6 | 0.512373 | ||||||||
\(184\) | −915208. | + | 8.23976e6i | −0.146915 | + | 1.32270i | ||||
\(185\) | 6.85614e6 | − | 4.74402e6i | 1.08284 | − | 0.749258i | ||||
\(186\) | −919719. | − | 33928.1i | −0.142928 | − | 0.00527255i | ||||
\(187\) | 2.52879e6 | 0.386713 | ||||||||
\(188\) | −1.25364e7 | − | 926190.i | −1.88669 | − | 0.139388i | ||||
\(189\) | 1.87914e6 | 0.278339 | ||||||||
\(190\) | −5.43836e6 | − | 8.51415e6i | −0.792879 | − | 1.24131i | ||||
\(191\) | 9.12751e6i | 1.30994i | 0.755654 | + | 0.654971i | \(0.227319\pi\) | ||||
−0.755654 | + | 0.654971i | \(0.772681\pi\) | |||||||
\(192\) | −3.98682e6 | − | 896713.i | −0.563278 | − | 0.126692i | ||||
\(193\) | 1.21768e7i | 1.69379i | 0.531758 | + | 0.846896i | \(0.321532\pi\) | ||||
−0.531758 | + | 0.846896i | \(0.678468\pi\) | |||||||
\(194\) | −1.04451e6 | − | 38531.7i | −0.143057 | − | 0.00527732i | ||||
\(195\) | −2.53924e6 | + | 1.75700e6i | −0.342452 | + | 0.236956i | ||||
\(196\) | −8.19811e6 | − | 605675.i | −1.08879 | − | 0.0804399i | ||||
\(197\) | 5.33007e6i | 0.697162i | 0.937279 | + | 0.348581i | \(0.113336\pi\) | ||||
−0.937279 | + | 0.348581i | \(0.886664\pi\) | |||||||
\(198\) | −1.09095e6 | − | 40244.9i | −0.140543 | − | 0.00518459i | ||||
\(199\) | 1.70499e6i | 0.216353i | 0.994132 | + | 0.108177i | \(0.0345012\pi\) | ||||
−0.994132 | + | 0.108177i | \(0.965499\pi\) | |||||||
\(200\) | 7.12955e6 | + | 3.62899e6i | 0.891194 | + | 0.453623i | ||||
\(201\) | 3.37704e6 | 0.415861 | ||||||||
\(202\) | 320444. | − | 8.68654e6i | 0.0388774 | − | 1.05388i | ||||
\(203\) | 992651. | 0.118661 | ||||||||
\(204\) | −331006. | + | 4.48032e6i | −0.0389892 | + | 0.527739i | ||||
\(205\) | −6.91281e6 | − | 9.99052e6i | −0.802404 | − | 1.15965i | ||||
\(206\) | 525686. | − | 1.42502e7i | 0.0601347 | − | 1.63012i | ||||
\(207\) | −3.93472e6 | −0.443611 | ||||||||
\(208\) | −953881. | + | 6.42039e6i | −0.106000 | + | 0.713463i | ||||
\(209\) | −5.67344e6 | −0.621452 | ||||||||
\(210\) | −6.51708e6 | + | 4.16274e6i | −0.703712 | + | 0.449492i | ||||
\(211\) | − | 1.25661e7i | − | 1.33768i | −0.743407 | − | 0.668840i | \(-0.766791\pi\) | ||
0.743407 | − | 0.668840i | \(-0.233209\pi\) | |||||||
\(212\) | −339876. | + | 4.60039e6i | −0.0356708 | + | 0.482822i | ||||
\(213\) | − | 5.58766e6i | − | 0.578218i | ||||||
\(214\) | −164685. | + | 4.46425e6i | −0.0168040 | + | 0.455519i | ||||
\(215\) | 8.02455e6 | + | 1.15972e7i | 0.807430 | + | 1.16691i | ||||
\(216\) | 214103. | − | 1.92760e6i | 0.0212452 | − | 0.191274i | ||||
\(217\) | 3.66106e6i | 0.358285i | ||||||||
\(218\) | 133643. | − | 3.62279e6i | 0.0128997 | − | 0.349682i | ||||
\(219\) | − | 6.41521e6i | − | 0.610771i | ||||||
\(220\) | 3.87270e6 | − | 2.27714e6i | 0.363702 | − | 0.213856i | ||||
\(221\) | 7.13593e6 | 0.661110 | ||||||||
\(222\) | 8.31225e6 | + | 306636.i | 0.759731 | + | 0.0280262i | ||||
\(223\) | −4.78645e6 | −0.431617 | −0.215809 | − | 0.976436i | \(-0.569239\pi\) | ||||
−0.215809 | + | 0.976436i | \(0.569239\pi\) | |||||||
\(224\) | −2.97999e6 | + | 1.59800e7i | −0.265137 | + | 1.42178i | ||||
\(225\) | −1.33828e6 | + | 3.55321e6i | −0.117490 | + | 0.311941i | ||||
\(226\) | 1.46529e7 | + | 540541.i | 1.26940 | + | 0.0468278i | ||||
\(227\) | −178099. | −0.0152259 | −0.00761296 | − | 0.999971i | \(-0.502423\pi\) | ||||
−0.00761296 | + | 0.999971i | \(0.502423\pi\) | |||||||
\(228\) | 742624. | − | 1.00518e7i | 0.0626562 | − | 0.848083i | ||||
\(229\) | −1.01777e6 | −0.0847505 | −0.0423753 | − | 0.999102i | \(-0.513493\pi\) | ||||
−0.0423753 | + | 0.999102i | \(0.513493\pi\) | |||||||
\(230\) | 1.36460e7 | − | 8.71632e6i | 1.12156 | − | 0.716391i | ||||
\(231\) | 4.34268e6i | 0.352308i | ||||||||
\(232\) | 113099. | − | 1.01825e6i | 0.00905723 | − | 0.0815436i | ||||
\(233\) | 2.23582e6i | 0.176754i | 0.996087 | + | 0.0883769i | \(0.0281680\pi\) | ||||
−0.996087 | + | 0.0883769i | \(0.971832\pi\) | |||||||
\(234\) | −3.07853e6 | − | 113566.i | −0.240268 | − | 0.00886340i | ||||
\(235\) | 1.39702e7 | + | 2.01899e7i | 1.07646 | + | 1.55572i | ||||
\(236\) | 669104. | − | 9.05665e6i | 0.0509047 | − | 0.689020i | ||||
\(237\) | − | 4.24063e6i | − | 0.318555i | ||||||
\(238\) | 1.78588e7 | + | 658806.i | 1.32471 | + | 0.0488682i | ||||
\(239\) | − | 2.49242e7i | − | 1.82569i | −0.408305 | − | 0.912846i | \(-0.633880\pi\) | ||
0.408305 | − | 0.912846i | \(-0.366120\pi\) | |||||||
\(240\) | 3.52755e6 | + | 7.15942e6i | 0.255176 | + | 0.517898i | ||||
\(241\) | −5.64081e6 | −0.402986 | −0.201493 | − | 0.979490i | \(-0.564579\pi\) | ||||
−0.201493 | + | 0.979490i | \(0.564579\pi\) | |||||||
\(242\) | −429457. | + | 1.16417e7i | −0.0303022 | + | 0.821428i | ||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | −1.28569e7 | − | 949862.i | −0.885045 | − | 0.0653870i | ||||
\(245\) | 9.13568e6 | + | 1.32031e7i | 0.621216 | + | 0.897793i | ||||
\(246\) | 446819. | − | 1.21123e7i | 0.0300142 | − | 0.813621i | ||||
\(247\) | −1.60097e7 | −1.06241 | ||||||||
\(248\) | 3.75547e6 | + | 417129.i | 0.246212 | + | 0.0273473i | ||||
\(249\) | −3.93449e6 | −0.254853 | ||||||||
\(250\) | −3.22988e6 | − | 1.52875e7i | −0.206712 | − | 0.978402i | ||||
\(251\) | − | 8.24054e6i | − | 0.521116i | −0.965458 | − | 0.260558i | \(-0.916093\pi\) | ||
0.965458 | − | 0.260558i | \(-0.0839066\pi\) | |||||||
\(252\) | −7.69404e6 | − | 568434.i | −0.480787 | − | 0.0355205i | ||||
\(253\) | − | 9.09310e6i | − | 0.561501i | ||||||
\(254\) | −588907. | + | 1.59640e7i | −0.0359373 | + | 0.974184i | ||||
\(255\) | 7.21556e6 | − | 4.99271e6i | 0.435160 | − | 0.301104i | ||||
\(256\) | 1.60526e7 | + | 4.87754e6i | 0.956807 | + | 0.290724i | ||||
\(257\) | − | 1.29601e7i | − | 0.763501i | −0.924265 | − | 0.381750i | \(-0.875321\pi\) | ||
0.924265 | − | 0.381750i | \(-0.124679\pi\) | |||||||
\(258\) | −518678. | + | 1.40602e7i | −0.0302022 | + | 0.818717i | ||||
\(259\) | − | 3.30880e7i | − | 1.90446i | ||||||
\(260\) | 1.09283e7 | − | 6.42581e6i | 0.621772 | − | 0.365601i | ||||
\(261\) | 486242. | 0.0273484 | ||||||||
\(262\) | −4.76639e6 | − | 175830.i | −0.265024 | − | 0.00977665i | ||||
\(263\) | −6.15939e6 | −0.338587 | −0.169294 | − | 0.985566i | \(-0.554149\pi\) | ||||
−0.169294 | + | 0.985566i | \(0.554149\pi\) | |||||||
\(264\) | 4.45467e6 | + | 494790.i | 0.242105 | + | 0.0268911i | ||||
\(265\) | 7.40892e6 | − | 5.12651e6i | 0.398123 | − | 0.275476i | ||||
\(266\) | −4.00670e7 | − | 1.47806e6i | −2.12883 | − | 0.0785319i | ||||
\(267\) | −1.35996e6 | −0.0714485 | ||||||||
\(268\) | −1.38271e7 | − | 1.02154e6i | −0.718335 | − | 0.0530705i | ||||
\(269\) | 2.56743e6 | 0.131899 | 0.0659494 | − | 0.997823i | \(-0.478992\pi\) | ||||
0.0659494 | + | 0.997823i | \(0.478992\pi\) | |||||||
\(270\) | −3.19234e6 | + | 2.03909e6i | −0.162188 | + | 0.103596i | ||||
\(271\) | − | 9.66745e6i | − | 0.485740i | −0.970059 | − | 0.242870i | \(-0.921911\pi\) | ||
0.970059 | − | 0.242870i | \(-0.0780888\pi\) | |||||||
\(272\) | 2.71057e6 | − | 1.82443e7i | 0.134696 | − | 0.906610i | ||||
\(273\) | 1.22545e7i | 0.602293i | ||||||||
\(274\) | 3.54055e7 | + | 1.30610e6i | 1.72115 | + | 0.0634927i | ||||
\(275\) | −8.21143e6 | − | 3.09275e6i | −0.394840 | − | 0.148712i | ||||
\(276\) | 1.61105e7 | + | 1.19024e6i | 0.766269 | + | 0.0566118i | ||||
\(277\) | − | 1.59611e7i | − | 0.750972i | −0.926828 | − | 0.375486i | \(-0.877476\pi\) | ||
0.926828 | − | 0.375486i | \(-0.122524\pi\) | |||||||
\(278\) | 4.03290e7 | + | 1.48772e6i | 1.87708 | + | 0.0692448i | ||||
\(279\) | 1.79334e6i | 0.0825754i | ||||||||
\(280\) | 2.79430e7 | − | 1.50727e7i | 1.27291 | − | 0.686621i | ||||
\(281\) | −4.28821e7 | −1.93267 | −0.966334 | − | 0.257290i | \(-0.917170\pi\) | ||||
−0.966334 | + | 0.257290i | \(0.917170\pi\) | |||||||
\(282\) | −902981. | + | 2.44779e7i | −0.0402653 | + | 1.09151i | ||||
\(283\) | 6.36296e6 | 0.280737 | 0.140369 | − | 0.990099i | \(-0.455171\pi\) | ||||
0.140369 | + | 0.990099i | \(0.455171\pi\) | |||||||
\(284\) | −1.69025e6 | + | 2.28784e7i | −0.0737898 | + | 0.998781i | ||||
\(285\) | −1.61884e7 | + | 1.12013e7i | −0.699309 | + | 0.483878i | ||||
\(286\) | 262450. | − | 7.11446e6i | 0.0112188 | − | 0.304119i | ||||
\(287\) | −4.82147e7 | −2.03955 | ||||||||
\(288\) | −1.45972e6 | + | 7.82768e6i | −0.0611073 | + | 0.327684i | ||||
\(289\) | 3.85998e6 | 0.159916 | ||||||||
\(290\) | −1.68634e6 | + | 1.07714e6i | −0.0691437 | + | 0.0441651i | ||||
\(291\) | 2.03668e6i | 0.0826501i | ||||||||
\(292\) | −1.94058e6 | + | 2.62667e7i | −0.0779441 | + | 1.05501i | ||||
\(293\) | 1.17997e7i | 0.469102i | 0.972104 | + | 0.234551i | \(0.0753620\pi\) | ||||
−0.972104 | + | 0.234551i | \(0.924638\pi\) | |||||||
\(294\) | −590497. | + | 1.60071e7i | −0.0232368 | + | 0.629900i | ||||
\(295\) | −1.45857e7 | + | 1.00924e7i | −0.568149 | + | 0.393124i | ||||
\(296\) | −3.39413e7 | − | 3.76993e6i | −1.30874 | − | 0.145365i | ||||
\(297\) | 2.12723e6i | 0.0811979i | ||||||||
\(298\) | 683079. | − | 1.85168e7i | 0.0258120 | − | 0.699709i | ||||
\(299\) | − | 2.56596e7i | − | 0.959922i | ||||||
\(300\) | 6.55434e6 | − | 1.41436e7i | 0.242753 | − | 0.523836i | ||||
\(301\) | 5.59687e7 | 2.05232 | ||||||||
\(302\) | −4.57964e7 | − | 1.68941e6i | −1.66269 | − | 0.0613359i | ||||
\(303\) | −1.69377e7 | −0.608874 | ||||||||
\(304\) | −6.08126e6 | + | 4.09318e7i | −0.216458 | + | 1.45693i | ||||
\(305\) | 1.43272e7 | + | 2.07060e7i | 0.504966 | + | 0.729786i | ||||
\(306\) | 8.74801e6 | + | 322711.i | 0.305313 | + | 0.0112629i | ||||
\(307\) | −3.47430e7 | −1.20075 | −0.600374 | − | 0.799719i | \(-0.704982\pi\) | ||||
−0.600374 | + | 0.799719i | \(0.704982\pi\) | |||||||
\(308\) | 1.31365e6 | − | 1.77809e7i | 0.0449600 | − | 0.608556i | ||||
\(309\) | −2.77863e7 | −0.941792 | ||||||||
\(310\) | −3.97268e6 | − | 6.21952e6i | −0.133352 | − | 0.208772i | ||||
\(311\) | 5.00149e7i | 1.66272i | 0.555737 | + | 0.831358i | \(0.312436\pi\) | ||||
−0.555737 | + | 0.831358i | \(0.687564\pi\) | |||||||
\(312\) | 1.25705e7 | + | 1.39623e6i | 0.413894 | + | 0.0459721i | ||||
\(313\) | − | 5.15834e7i | − | 1.68220i | −0.540882 | − | 0.841099i | \(-0.681909\pi\) | ||
0.540882 | − | 0.841099i | \(-0.318091\pi\) | |||||||
\(314\) | −1.71360e6 | − | 63214.0i | −0.0553503 | − | 0.00204185i | ||||
\(315\) | 8.57397e6 | + | 1.23912e7i | 0.274315 | + | 0.396445i | ||||
\(316\) | −1.28278e6 | + | 1.73630e7i | −0.0406527 | + | 0.550254i | ||||
\(317\) | 4.05089e7i | 1.27166i | 0.771827 | + | 0.635832i | \(0.219343\pi\) | ||||
−0.771827 | + | 0.635832i | \(0.780657\pi\) | |||||||
\(318\) | 8.98244e6 | + | 331359.i | 0.279327 | + | 0.0103043i | ||||
\(319\) | 1.12370e6i | 0.0346162i | ||||||||
\(320\) | −1.22777e7 | − | 3.03809e7i | −0.374685 | − | 0.927152i | ||||
\(321\) | 8.70476e6 | 0.263173 | ||||||||
\(322\) | 2.36895e6 | − | 6.42173e7i | 0.0709560 | − | 1.92347i | ||||
\(323\) | 4.54936e7 | 1.35003 | ||||||||
\(324\) | −3.76886e6 | − | 278443.i | −0.110809 | − | 0.00818656i | ||||
\(325\) | −2.31716e7 | − | 8.72736e6i | −0.675004 | − | 0.254234i | ||||
\(326\) | −1.51338e6 | + | 4.10245e7i | −0.0436813 | + | 1.18411i | ||||
\(327\) | −7.06401e6 | −0.202026 | ||||||||
\(328\) | −5.49341e6 | + | 4.94580e7i | −0.155676 | + | 1.40157i | ||||
\(329\) | 9.74375e7 | 2.73614 | ||||||||
\(330\) | −4.71231e6 | − | 7.37747e6i | −0.131127 | − | 0.205289i | ||||
\(331\) | 4.67744e7i | 1.28981i | 0.764264 | + | 0.644903i | \(0.223102\pi\) | ||||
−0.764264 | + | 0.644903i | \(0.776898\pi\) | |||||||
\(332\) | 1.61095e7 | + | 1.19017e6i | 0.440219 | + | 0.0325233i | ||||
\(333\) | − | 1.62079e7i | − | 0.438929i | ||||||
\(334\) | −901415. | + | 2.44354e7i | −0.0241928 | + | 0.655814i | ||||
\(335\) | 1.54084e7 | + | 2.22686e7i | 0.409850 | + | 0.592322i | ||||
\(336\) | 3.13309e7 | + | 4.65484e6i | 0.825951 | + | 0.122712i | ||||
\(337\) | 4.77282e7i | 1.24705i | 0.781802 | + | 0.623527i | \(0.214301\pi\) | ||||
−0.781802 | + | 0.623527i | \(0.785699\pi\) | |||||||
\(338\) | −682906. | + | 1.85121e7i | −0.0176852 | + | 0.479409i | ||||
\(339\) | − | 2.85715e7i | − | 0.733388i | ||||||
\(340\) | −3.10540e7 | + | 1.82597e7i | −0.790097 | + | 0.464576i | ||||
\(341\) | −4.14440e6 | −0.104520 | ||||||||
\(342\) | −1.96265e7 | − | 724015.i | −0.490642 | − | 0.0180996i | ||||
\(343\) | 5.35543e6 | 0.132713 | ||||||||
\(344\) | 6.37688e6 | − | 5.74120e7i | 0.156651 | − | 1.41035i | ||||
\(345\) | −1.79529e7 | − | 2.59459e7i | −0.437198 | − | 0.631847i | ||||
\(346\) | 4.11880e7 | + | 1.51941e6i | 0.994358 | + | 0.0366815i | ||||
\(347\) | 3.93322e7 | 0.941368 | 0.470684 | − | 0.882302i | \(-0.344007\pi\) | ||||
0.470684 | + | 0.882302i | \(0.344007\pi\) | |||||||
\(348\) | −1.99089e6 | − | 147087.i | −0.0472400 | − | 0.00349008i | ||||
\(349\) | −7.65808e7 | −1.80154 | −0.900769 | − | 0.434299i | \(-0.856996\pi\) | ||||
−0.900769 | + | 0.434299i | \(0.856996\pi\) | |||||||
\(350\) | −5.71850e7 | − | 2.39809e7i | −1.33376 | − | 0.559321i | ||||
\(351\) | 6.00277e6i | 0.138813i | ||||||||
\(352\) | −1.80897e7 | − | 3.37341e6i | −0.414767 | − | 0.0773466i | ||||
\(353\) | 1.22834e7i | 0.279250i | 0.990204 | + | 0.139625i | \(0.0445897\pi\) | ||||
−0.990204 | + | 0.139625i | \(0.955410\pi\) | |||||||
\(354\) | −1.76835e7 | − | 652337.i | −0.398619 | − | 0.0147049i | ||||
\(355\) | 3.68456e7 | − | 2.54949e7i | 0.823570 | − | 0.569859i | ||||
\(356\) | 5.56829e6 | + | 411384.i | 0.123416 | + | 0.00911796i | ||||
\(357\) | − | 3.48226e7i | − | 0.765344i | ||||||
\(358\) | 1.57535e7 | + | 581140.i | 0.343342 | + | 0.0126658i | ||||
\(359\) | 1.10395e7i | 0.238598i | 0.992858 | + | 0.119299i | \(0.0380647\pi\) | ||||
−0.992858 | + | 0.119299i | \(0.961935\pi\) | |||||||
\(360\) | 1.36877e7 | − | 7.38325e6i | 0.293374 | − | 0.158249i | ||||
\(361\) | −5.50207e7 | −1.16951 | ||||||||
\(362\) | −691982. | + | 1.87582e7i | −0.0145871 | + | 0.395425i | ||||
\(363\) | 2.26999e7 | 0.474574 | ||||||||
\(364\) | 3.70695e6 | − | 5.01753e7i | 0.0768621 | − | 1.04037i | ||||
\(365\) | 4.23025e7 | − | 2.92707e7i | 0.869937 | − | 0.601942i | ||||
\(366\) | −926060. | + | 2.51035e7i | −0.0188884 | + | 0.512025i | ||||
\(367\) | 5.87412e7 | 1.18835 | 0.594175 | − | 0.804336i | \(-0.297479\pi\) | ||||
0.594175 | + | 0.804336i | \(0.297479\pi\) | |||||||
\(368\) | −6.56034e7 | − | 9.74673e6i | −1.31638 | − | 0.195576i | ||||
\(369\) | −2.36176e7 | −0.470064 | ||||||||
\(370\) | 3.59044e7 | + | 5.62109e7i | 0.708830 | + | 1.10973i | ||||
\(371\) | − | 3.57558e7i | − | 0.700204i | ||||||
\(372\) | 542481. | − | 7.34274e6i | 0.0105379 | − | 0.142636i | ||||
\(373\) | − | 1.24158e7i | − | 0.239247i | −0.992819 | − | 0.119624i | \(-0.961831\pi\) | ||
0.992819 | − | 0.119624i | \(-0.0381688\pi\) | |||||||
\(374\) | −745783. | + | 2.02166e7i | −0.0142560 | + | 0.386450i | ||||
\(375\) | −2.95364e7 | + | 7.38747e6i | −0.560097 | + | 0.140088i | ||||
\(376\) | 1.11017e7 | − | 9.99501e7i | 0.208846 | − | 1.88027i | ||||
\(377\) | 3.17095e6i | 0.0591786i | ||||||||
\(378\) | −554190. | + | 1.50229e7i | −0.0102609 | + | 0.278150i | ||||
\(379\) | − | 4.18480e7i | − | 0.768701i | −0.923187 | − | 0.384350i | \(-0.874425\pi\) | ||
0.923187 | − | 0.384350i | \(-0.125575\pi\) | |||||||
\(380\) | 6.96708e7 | − | 4.09663e7i | 1.26970 | − | 0.746580i | ||||
\(381\) | 3.11280e7 | 0.562828 | ||||||||
\(382\) | −7.29704e7 | − | 2.69185e6i | −1.30905 | − | 0.0482905i | ||||
\(383\) | −5.12412e7 | −0.912058 | −0.456029 | − | 0.889965i | \(-0.650729\pi\) | ||||
−0.456029 | + | 0.889965i | \(0.650729\pi\) | |||||||
\(384\) | 8.34461e6 | − | 3.16084e7i | 0.147371 | − | 0.558225i | ||||
\(385\) | −2.86361e7 | + | 1.98144e7i | −0.501801 | + | 0.347215i | ||||
\(386\) | −9.73480e7 | − | 3.59113e6i | −1.69264 | − | 0.0624410i | ||||
\(387\) | 2.74158e7 | 0.473008 | ||||||||
\(388\) | 616089. | − | 8.33906e6i | 0.0105475 | − | 0.142765i | ||||
\(389\) | 4.98250e7 | 0.846444 | 0.423222 | − | 0.906026i | \(-0.360899\pi\) | ||||
0.423222 | + | 0.906026i | \(0.360899\pi\) | |||||||
\(390\) | −1.32975e7 | − | 2.08183e7i | −0.224170 | − | 0.350955i | ||||
\(391\) | 7.29147e7i | 1.21979i | ||||||||
\(392\) | 7.25986e6 | − | 6.53617e7i | 0.120523 | − | 1.08509i | ||||
\(393\) | 9.29390e6i | 0.153116i | ||||||||
\(394\) | −4.26115e7 | − | 1.57193e6i | −0.696688 | − | 0.0257006i | ||||
\(395\) | 2.79631e7 | − | 1.93487e7i | 0.453727 | − | 0.313950i | ||||
\(396\) | 643480. | − | 8.70982e6i | 0.0103621 | − | 0.140257i | ||||
\(397\) | 3.92214e7i | 0.626832i | 0.949616 | + | 0.313416i | \(0.101473\pi\) | ||||
−0.949616 | + | 0.313416i | \(0.898527\pi\) | |||||||
\(398\) | −1.36307e7 | − | 502831.i | −0.216206 | − | 0.00797578i | ||||
\(399\) | 7.81259e7i | 1.22992i | ||||||||
\(400\) | −3.11148e7 | + | 5.59274e7i | −0.486168 | + | 0.873865i | ||||
\(401\) | −5.63354e6 | −0.0873671 | −0.0436836 | − | 0.999045i | \(-0.513909\pi\) | ||||
−0.0436836 | + | 0.999045i | \(0.513909\pi\) | |||||||
\(402\) | −995946. | + | 2.69980e7i | −0.0153306 | + | 0.415579i | ||||
\(403\) | −1.16950e7 | −0.178683 | ||||||||
\(404\) | 6.93506e7 | + | 5.12361e6i | 1.05173 | + | 0.0777020i | ||||
\(405\) | 4.19989e6 | + | 6.06976e6i | 0.0632227 | + | 0.0913705i | ||||
\(406\) | −292749. | + | 7.93581e6i | −0.00437439 | + | 0.118581i | ||||
\(407\) | 3.74564e7 | 0.555575 | ||||||||
\(408\) | −3.57206e7 | − | 3.96757e6i | −0.525942 | − | 0.0584176i | ||||
\(409\) | −2.95973e7 | −0.432596 | −0.216298 | − | 0.976327i | \(-0.569398\pi\) | ||||
−0.216298 | + | 0.976327i | \(0.569398\pi\) | |||||||
\(410\) | 8.19085e7 | − | 5.23185e7i | 1.18844 | − | 0.759109i | ||||
\(411\) | − | 6.90366e7i | − | 0.994384i | ||||||
\(412\) | 1.13769e8 | + | 8.40526e6i | 1.62680 | + | 0.120188i | ||||
\(413\) | 7.03914e7i | 0.999240i | ||||||||
\(414\) | 1.16041e6 | − | 3.14563e7i | 0.0163535 | − | 0.443310i | ||||
\(415\) | −1.79519e7 | − | 2.59444e7i | −0.251169 | − | 0.362994i | ||||
\(416\) | −5.10469e7 | − | 9.51934e6i | −0.709070 | − | 0.132229i | ||||
\(417\) | − | 7.86367e7i | − | 1.08447i | ||||||
\(418\) | 1.67319e6 | − | 4.53567e7i | 0.0229096 | − | 0.621030i | ||||
\(419\) | − | 1.15258e7i | − | 0.156686i | −0.996926 | − | 0.0783428i | \(-0.975037\pi\) | ||
0.996926 | − | 0.0783428i | \(-0.0249629\pi\) | |||||||
\(420\) | −3.13573e7 | − | 5.33289e7i | −0.423244 | − | 0.719804i | ||||
\(421\) | 3.57459e7 | 0.479049 | 0.239525 | − | 0.970890i | \(-0.423008\pi\) | ||||
0.239525 | + | 0.970890i | \(0.423008\pi\) | |||||||
\(422\) | 1.00460e8 | + | 3.70594e6i | 1.33677 | + | 0.0493130i | ||||
\(423\) | 4.77290e7 | 0.630611 | ||||||||
\(424\) | −3.66778e7 | − | 4.07389e6i | −0.481178 | − | 0.0534456i | ||||
\(425\) | 6.58449e7 | + | 2.47998e7i | 0.857740 | + | 0.323059i | ||||
\(426\) | 4.46709e7 | + | 1.64790e6i | 0.577825 | + | 0.0213158i | ||||
\(427\) | 9.99279e7 | 1.28352 | ||||||||
\(428\) | −3.56411e7 | − | 2.63316e6i | −0.454590 | − | 0.0335851i | ||||
\(429\) | −1.38724e7 | −0.175703 | ||||||||
\(430\) | −9.50812e7 | + | 6.07325e7i | −1.19588 | + | 0.763864i | ||||
\(431\) | − | 8.20839e6i | − | 0.102524i | −0.998685 | − | 0.0512621i | \(-0.983676\pi\) | ||
0.998685 | − | 0.0512621i | \(-0.0163244\pi\) | |||||||
\(432\) | 1.53472e7 | + | 2.28014e6i | 0.190361 | + | 0.0282820i | ||||
\(433\) | − | 4.37930e7i | − | 0.539437i | −0.962939 | − | 0.269719i | \(-0.913069\pi\) | ||
0.962939 | − | 0.269719i | \(-0.0869307\pi\) | |||||||
\(434\) | −2.92686e7 | − | 1.07971e6i | −0.358041 | − | 0.0132080i | ||||
\(435\) | 2.21858e6 | + | 3.20633e6i | 0.0269530 | + | 0.0389530i | ||||
\(436\) | 2.89232e7 | + | 2.13684e6i | 0.348969 | + | 0.0257818i | ||||
\(437\) | − | 1.63587e8i | − | 1.96022i | ||||||
\(438\) | 5.12868e7 | + | 1.89195e6i | 0.610356 | + | 0.0225158i | ||||
\(439\) | 9.07805e7i | 1.07300i | 0.843901 | + | 0.536499i | \(0.180254\pi\) | ||||
−0.843901 | + | 0.536499i | \(0.819746\pi\) | |||||||
\(440\) | 1.70626e7 | + | 3.16321e7i | 0.200303 | + | 0.371339i | ||||
\(441\) | 3.12120e7 | 0.363920 | ||||||||
\(442\) | −2.10450e6 | + | 5.70486e7i | −0.0243715 | + | 0.660660i | ||||
\(443\) | 4.40997e6 | 0.0507253 | 0.0253626 | − | 0.999678i | \(-0.491926\pi\) | ||||
0.0253626 | + | 0.999678i | \(0.491926\pi\) | |||||||
\(444\) | −4.90284e6 | + | 6.63624e7i | −0.0560143 | + | 0.758181i | ||||
\(445\) | −6.20511e6 | − | 8.96773e6i | −0.0704156 | − | 0.101766i | ||||
\(446\) | 1.41160e6 | − | 3.82655e7i | 0.0159114 | − | 0.431324i | ||||
\(447\) | −3.61056e7 | −0.404252 | ||||||||
\(448\) | −1.26874e8 | − | 2.85365e7i | −1.41104 | − | 0.317370i | ||||
\(449\) | −7.74897e7 | −0.856062 | −0.428031 | − | 0.903764i | \(-0.640793\pi\) | ||||
−0.428031 | + | 0.903764i | \(0.640793\pi\) | |||||||
\(450\) | −2.80116e7 | − | 1.17469e7i | −0.307398 | − | 0.128909i | ||||
\(451\) | − | 5.45801e7i | − | 0.594983i | ||||||
\(452\) | −8.64278e6 | + | 1.16984e8i | −0.0935919 | + | 1.26681i | ||||
\(453\) | 8.92976e7i | 0.960606i | ||||||||
\(454\) | 52524.3 | − | 1.42382e6i | 0.000561297 | − | 0.0152156i | ||||
\(455\) | −8.08074e7 | + | 5.59136e7i | −0.857861 | + | 0.593586i | ||||
\(456\) | 8.01405e7 | + | 8.90139e6i | 0.845197 | + | 0.0938779i | ||||
\(457\) | 1.64079e8i | 1.71911i | 0.511045 | + | 0.859554i | \(0.329259\pi\) | ||||
−0.511045 | + | 0.859554i | \(0.670741\pi\) | |||||||
\(458\) | 300157. | − | 8.13661e6i | 0.00312429 | − | 0.0846929i | ||||
\(459\) | − | 1.70576e7i | − | 0.176392i | ||||||
\(460\) | 6.56588e7 | + | 1.11665e8i | 0.674558 | + | 1.14721i | ||||
\(461\) | −1.26212e8 | −1.28824 | −0.644121 | − | 0.764924i | \(-0.722777\pi\) | ||||
−0.644121 | + | 0.764924i | \(0.722777\pi\) | |||||||
\(462\) | −3.47178e7 | − | 1.28073e6i | −0.352068 | − | 0.0129877i | ||||
\(463\) | −3.21664e7 | −0.324085 | −0.162043 | − | 0.986784i | \(-0.551808\pi\) | ||||
−0.162043 | + | 0.986784i | \(0.551808\pi\) | |||||||
\(464\) | 8.10710e6 | + | 1.20448e6i | 0.0811543 | + | 0.0120571i | ||||
\(465\) | −1.18255e7 | + | 8.18249e6i | −0.117614 | + | 0.0813817i | ||||
\(466\) | −1.78744e7 | − | 659380.i | −0.176634 | − | 0.00651596i | ||||
\(467\) | 1.95660e7 | 0.192110 | 0.0960551 | − | 0.995376i | \(-0.469377\pi\) | ||||
0.0960551 | + | 0.995376i | \(0.469377\pi\) | |||||||
\(468\) | 1.81582e6 | − | 2.45780e7i | 0.0177147 | − | 0.239778i | ||||
\(469\) | 1.07469e8 | 1.04175 | ||||||||
\(470\) | −1.65530e8 | + | 1.05731e8i | −1.59434 | + | 1.01838i | ||||
\(471\) | 3.34131e6i | 0.0319782i | ||||||||
\(472\) | 7.22066e7 | + | 8.02015e6i | 0.686675 | + | 0.0762705i | ||||
\(473\) | 6.33578e7i | 0.598710i | ||||||||
\(474\) | 3.39020e7 | + | 1.25063e6i | 0.318339 | + | 0.0117434i | ||||
\(475\) | −1.47726e8 | − | 5.56394e7i | −1.37840 | − | 0.519160i | ||||
\(476\) | −1.05337e7 | + | 1.42579e8i | −0.0976700 | + | 1.32201i | ||||
\(477\) | − | 1.75147e7i | − | 0.161379i | ||||||
\(478\) | 1.99258e8 | + | 7.35056e6i | 1.82445 | + | 0.0673033i | ||||
\(479\) | 1.93927e8i | 1.76454i | 0.470743 | + | 0.882270i | \(0.343986\pi\) | ||||
−0.470743 | + | 0.882270i | \(0.656014\pi\) | |||||||
\(480\) | −5.82768e7 | + | 2.60898e7i | −0.526953 | + | 0.235911i | ||||
\(481\) | 1.05697e8 | 0.949791 | ||||||||
\(482\) | 1.66357e6 | − | 4.50958e7i | 0.0148559 | − | 0.402712i | ||||
\(483\) | −1.25216e8 | −1.11127 | ||||||||
\(484\) | −9.29434e7 | − | 6.86665e6i | −0.819752 | − | 0.0605632i | ||||
\(485\) | −1.34301e7 | + | 9.29276e6i | −0.117721 | + | 0.0814553i | ||||
\(486\) | −271466. | + | 7.35886e6i | −0.00236486 | + | 0.0641064i | ||||
\(487\) | −1.62572e8 | −1.40754 | −0.703768 | − | 0.710430i | \(-0.748500\pi\) | ||||
−0.703768 | + | 0.710430i | \(0.748500\pi\) | |||||||
\(488\) | 1.13854e7 | − | 1.02505e8i | 0.0979693 | − | 0.882033i | ||||
\(489\) | 7.99930e7 | 0.684109 | ||||||||
\(490\) | −1.08247e8 | + | 6.91420e7i | −0.920083 | + | 0.587697i | ||||
\(491\) | − | 1.55899e8i | − | 1.31704i | −0.752564 | − | 0.658519i | \(-0.771183\pi\) | ||
0.752564 | − | 0.658519i | \(-0.228817\pi\) | |||||||
\(492\) | 9.67009e7 | + | 7.14425e6i | 0.811961 | + | 0.0599876i | ||||
\(493\) | − | 9.01062e6i | − | 0.0751993i | ||||||
\(494\) | 4.72154e6 | − | 1.27991e8i | 0.0391654 | − | 1.06169i | ||||
\(495\) | −1.40272e7 | + | 9.70592e6i | −0.115652 | + | 0.0800241i | ||||
\(496\) | −4.44231e6 | + | 2.99003e7i | −0.0364053 | + | 0.245037i | ||||
\(497\) | − | 1.77819e8i | − | 1.44847i | ||||||
\(498\) | 1.16035e6 | − | 3.14545e7i | 0.00939506 | − | 0.254680i | ||||
\(499\) | 5.34345e7i | 0.430051i | 0.976608 | + | 0.215026i | \(0.0689835\pi\) | ||||
−0.976608 | + | 0.215026i | \(0.931017\pi\) | |||||||
\(500\) | 1.23170e8 | − | 2.13129e7i | 0.985357 | − | 0.170503i | ||||
\(501\) | 4.76462e7 | 0.378892 | ||||||||
\(502\) | 6.58795e7 | + | 2.43027e6i | 0.520762 | + | 0.0192107i | ||||
\(503\) | −1.13337e8 | −0.890565 | −0.445283 | − | 0.895390i | \(-0.646897\pi\) | ||||
−0.445283 | + | 0.895390i | \(0.646897\pi\) | |||||||
\(504\) | 6.81348e6 | − | 6.13428e7i | 0.0532203 | − | 0.479151i | ||||
\(505\) | −7.72819e7 | − | 1.11689e8i | −0.600072 | − | 0.867235i | ||||
\(506\) | 7.26954e7 | + | 2.68171e6i | 0.561119 | + | 0.0206995i | ||||
\(507\) | 3.60965e7 | 0.276975 | ||||||||
\(508\) | −1.27452e8 | − | 9.41611e6i | −0.972197 | − | 0.0718258i | ||||
\(509\) | −1.55905e8 | −1.18224 | −0.591120 | − | 0.806584i | \(-0.701314\pi\) | ||||
−0.591120 | + | 0.806584i | \(0.701314\pi\) | |||||||
\(510\) | 3.77866e7 | + | 5.91577e7i | 0.284857 | + | 0.445965i | ||||
\(511\) | − | 2.04154e8i | − | 1.53001i | ||||||
\(512\) | −4.37280e7 | + | 1.26895e8i | −0.325799 | + | 0.945439i | ||||
\(513\) | 3.82694e7i | 0.283465i | ||||||||
\(514\) | 1.03610e8 | + | 3.82215e6i | 0.762982 | + | 0.0281461i | ||||
\(515\) | −1.26781e8 | − | 1.83226e8i | −0.928178 | − | 1.34142i | ||||
\(516\) | −1.12253e8 | − | 8.29320e6i | −0.817047 | − | 0.0603633i | ||||
\(517\) | 1.10301e8i | 0.798195i | ||||||||
\(518\) | 2.64524e8 | + | 9.75821e6i | 1.90317 | + | 0.0702071i | ||||
\(519\) | − | 8.03118e7i | − | 0.574483i | ||||||
\(520\) | 4.81486e7 | + | 8.92618e7i | 0.342431 | + | 0.634827i | ||||
\(521\) | −1.28940e8 | −0.911750 | −0.455875 | − | 0.890044i | \(-0.650674\pi\) | ||||
−0.455875 | + | 0.890044i | \(0.650674\pi\) | |||||||
\(522\) | −143401. | + | 3.88730e6i | −0.00100819 | + | 0.0273298i | ||||
\(523\) | −5.74458e7 | −0.401562 | −0.200781 | − | 0.979636i | \(-0.564348\pi\) | ||||
−0.200781 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(524\) | 2.81137e6 | − | 3.80533e7i | 0.0195400 | − | 0.264484i | ||||
\(525\) | −4.25886e7 | + | 1.13075e8i | −0.294317 | + | 0.781429i | ||||
\(526\) | 1.81651e6 | − | 4.92416e7i | 0.0124819 | − | 0.338357i | ||||
\(527\) | 3.32327e7 | 0.227056 | ||||||||
\(528\) | −5.26938e6 | + | 3.54672e7i | −0.0357979 | + | 0.240949i | ||||
\(529\) | 1.14153e8 | 0.771117 | ||||||||
\(530\) | 3.87992e7 | + | 6.07430e7i | 0.260612 | + | 0.408008i | ||||
\(531\) | 3.44807e7i | 0.230299i | ||||||||
\(532\) | 2.36328e7 | − | 3.19882e8i | 0.156957 | − | 2.12449i | ||||
\(533\) | − | 1.54018e8i | − | 1.01716i | ||||||
\(534\) | 401076. | − | 1.08723e7i | 0.00263392 | − | 0.0713999i | ||||
\(535\) | 3.97172e7 | + | 5.74000e7i | 0.259369 | + | 0.374844i | ||||
\(536\) | 1.22446e7 | − | 1.10240e8i | 0.0795155 | − | 0.715890i | ||||
\(537\) | − | 3.07174e7i | − | 0.198363i | ||||||
\(538\) | −757177. | + | 2.05254e7i | −0.00486240 | + | 0.131809i | ||||
\(539\) | 7.21308e7i | 0.460632i | ||||||||
\(540\) | −1.53601e7 | − | 2.61227e7i | −0.0975469 | − | 0.165896i | ||||
\(541\) | −8.81969e7 | −0.557008 | −0.278504 | − | 0.960435i | \(-0.589839\pi\) | ||||
−0.278504 | + | 0.960435i | \(0.589839\pi\) | |||||||
\(542\) | 7.72870e7 | + | 2.85109e6i | 0.485410 | + | 0.0179066i | ||||
\(543\) | 3.65762e7 | 0.228454 | ||||||||
\(544\) | 1.45056e8 | + | 2.70503e7i | 0.901028 | + | 0.168026i | ||||
\(545\) | −3.22310e7 | − | 4.65808e7i | −0.199106 | − | 0.287751i | ||||
\(546\) | −9.79693e7 | − | 3.61406e6i | −0.601883 | − | 0.0222033i | ||||
\(547\) | 2.52994e8 | 1.54578 | 0.772892 | − | 0.634538i | \(-0.218810\pi\) | ||||
0.772892 | + | 0.634538i | \(0.218810\pi\) | |||||||
\(548\) | −2.08834e7 | + | 2.82666e8i | −0.126899 | + | 1.71764i | ||||
\(549\) | 4.89489e7 | 0.295819 | ||||||||
\(550\) | 2.71469e7 | − | 6.47347e7i | 0.163167 | − | 0.389089i | ||||
\(551\) | 2.02157e7i | 0.120846i | ||||||||
\(552\) | −1.42667e7 | + | 1.28445e8i | −0.0848215 | + | 0.763661i | ||||
\(553\) | − | 1.34951e8i | − | 0.797998i | ||||||
\(554\) | 1.27602e8 | + | 4.70720e6i | 0.750462 | + | 0.0276843i | ||||
\(555\) | 1.06877e8 | − | 7.39519e7i | 0.625178 | − | 0.432584i | ||||
\(556\) | −2.37874e7 | + | 3.21974e8i | −0.138395 | + | 1.87325i | ||||
\(557\) | 2.32228e8i | 1.34384i | 0.740622 | + | 0.671922i | \(0.234531\pi\) | ||||
−0.740622 | + | 0.671922i | \(0.765469\pi\) | |||||||
\(558\) | −1.43370e7 | − | 528887.i | −0.0825193 | − | 0.00304411i | ||||
\(559\) | 1.78788e8i | 1.02353i | ||||||||
\(560\) | 1.12259e8 | + | 2.27837e8i | 0.639229 | + | 1.29736i | ||||
\(561\) | 3.94200e7 | 0.223269 | ||||||||
\(562\) | 1.26467e7 | − | 3.42824e8i | 0.0712470 | − | 1.93135i | ||||
\(563\) | 2.04220e8 | 1.14439 | 0.572193 | − | 0.820119i | \(-0.306093\pi\) | ||||
0.572193 | + | 0.820119i | \(0.306093\pi\) | |||||||
\(564\) | −1.95424e8 | − | 1.44379e7i | −1.08928 | − | 0.0804759i | ||||
\(565\) | 1.88403e8 | − | 1.30363e8i | 1.04458 | − | 0.722786i | ||||
\(566\) | −1.87654e6 | + | 5.08691e7i | −0.0103493 | + | 0.280547i | ||||
\(567\) | 2.92929e7 | 0.160699 | ||||||||
\(568\) | −1.82404e8 | − | 2.02600e7i | −0.995382 | − | 0.110559i | ||||
\(569\) | 1.10819e8 | 0.601558 | 0.300779 | − | 0.953694i | \(-0.402753\pi\) | ||||
0.300779 | + | 0.953694i | \(0.402753\pi\) | |||||||
\(570\) | −8.47756e7 | − | 1.32723e8i | −0.457769 | − | 0.716671i | ||||
\(571\) | − | 1.80433e8i | − | 0.969186i | −0.874740 | − | 0.484593i | \(-0.838968\pi\) | ||
0.874740 | − | 0.484593i | \(-0.161032\pi\) | |||||||
\(572\) | 5.67996e7 | + | 4.19634e6i | 0.303499 | + | 0.0224224i | ||||
\(573\) | 1.42284e8i | 0.756295i | ||||||||
\(574\) | 1.42193e7 | − | 3.85455e8i | 0.0751871 | − | 2.03816i | ||||
\(575\) | 8.91760e7 | − | 2.36767e8i | 0.469077 | − | 1.24543i | ||||
\(576\) | −6.21484e7 | − | 1.39784e7i | −0.325209 | − | 0.0731457i | ||||
\(577\) | 1.16278e8i | 0.605297i | 0.953102 | + | 0.302648i | \(0.0978708\pi\) | ||||
−0.953102 | + | 0.302648i | \(0.902129\pi\) | |||||||
\(578\) | −1.13837e6 | + | 3.08588e7i | −0.00589523 | + | 0.159807i | ||||
\(579\) | 1.89817e8i | 0.977912i | ||||||||
\(580\) | −8.11395e6 | − | 1.37993e7i | −0.0415861 | − | 0.0707248i | ||||
\(581\) | −1.25209e8 | −0.638421 | ||||||||
\(582\) | −1.62824e7 | − | 600650.i | −0.0825939 | − | 0.00304686i | ||||
\(583\) | 4.04763e7 | 0.204266 | ||||||||
\(584\) | −2.09419e8 | − | 2.32606e7i | −1.05142 | − | 0.116784i | ||||
\(585\) | −3.95829e7 | + | 2.73889e7i | −0.197715 | + | 0.136806i | ||||
\(586\) | −9.43332e7 | − | 3.47992e6i | −0.468783 | − | 0.0172932i | ||||
\(587\) | −8.67855e7 | −0.429075 | −0.214537 | − | 0.976716i | \(-0.568824\pi\) | ||||
−0.214537 | + | 0.976716i | \(0.568824\pi\) | |||||||
\(588\) | −1.27796e8 | − | 9.44154e6i | −0.628615 | − | 0.0464420i | ||||
\(589\) | −7.45588e7 | −0.364882 | ||||||||
\(590\) | −7.63829e7 | − | 1.19583e8i | −0.371912 | − | 0.582255i | ||||
\(591\) | 8.30875e7i | 0.402507i | ||||||||
\(592\) | 4.01488e7 | − | 2.70234e8i | 0.193512 | − | 1.30249i | ||||
\(593\) | 1.04689e8i | 0.502038i | 0.967982 | + | 0.251019i | \(0.0807657\pi\) | ||||
−0.967982 | + | 0.251019i | \(0.919234\pi\) | |||||||
\(594\) | −1.70063e7 | − | 627355.i | −0.0811427 | − | 0.00299333i | ||||
\(595\) | 2.29624e8 | − | 1.58885e8i | 1.09010 | − | 0.754280i | ||||
\(596\) | 1.47832e8 | + | 1.09218e7i | 0.698282 | + | 0.0515890i | ||||
\(597\) | 2.65782e7i | 0.124912i | ||||||||
\(598\) | 2.05137e8 | + | 7.56743e6i | 0.959269 | + | 0.0353871i | ||||
\(599\) | − | 6.77750e7i | − | 0.315347i | −0.987491 | − | 0.157674i | \(-0.949601\pi\) | ||
0.987491 | − | 0.157674i | \(-0.0503994\pi\) | |||||||
\(600\) | 1.11139e8 | + | 5.65703e7i | 0.514531 | + | 0.261899i | ||||
\(601\) | 2.94031e8 | 1.35447 | 0.677236 | − | 0.735766i | \(-0.263177\pi\) | ||||
0.677236 | + | 0.735766i | \(0.263177\pi\) | |||||||
\(602\) | −1.65061e7 | + | 4.47445e8i | −0.0756580 | + | 2.05093i | ||||
\(603\) | 5.26429e7 | 0.240098 | ||||||||
\(604\) | 2.70122e7 | − | 3.65624e8i | 0.122588 | − | 1.65930i | ||||
\(605\) | 1.03573e8 | + | 1.49685e8i | 0.467714 | + | 0.675948i | ||||
\(606\) | 4.99522e6 | − | 1.35410e8i | 0.0224459 | − | 0.608460i | ||||
\(607\) | −1.77492e8 | −0.793618 | −0.396809 | − | 0.917901i | \(-0.629882\pi\) | ||||
−0.396809 | + | 0.917901i | \(0.629882\pi\) | |||||||
\(608\) | −3.25438e8 | − | 6.06885e7i | −1.44796 | − | 0.270020i | ||||
\(609\) | 1.54739e7 | 0.0685091 | ||||||||
\(610\) | −1.69760e8 | + | 1.08433e8i | −0.747906 | + | 0.477720i | ||||
\(611\) | 3.11256e8i | 1.36457i | ||||||||
\(612\) | −5.15987e6 | + | 6.98413e7i | −0.0225104 | + | 0.304690i | ||||
\(613\) | − | 1.82426e8i | − | 0.791962i | −0.918259 | − | 0.395981i | \(-0.870405\pi\) | ||
0.918259 | − | 0.395981i | \(-0.129595\pi\) | |||||||
\(614\) | 1.02463e7 | − | 2.77755e8i | 0.0442651 | − | 1.19993i | ||||
\(615\) | −1.07760e8 | − | 1.55737e8i | −0.463268 | − | 0.669524i | ||||
\(616\) | 1.41763e8 | + | 1.57459e7i | 0.606485 | + | 0.0673637i | ||||
\(617\) | − | 2.51870e8i | − | 1.07231i | −0.844119 | − | 0.536156i | \(-0.819876\pi\) | ||
0.844119 | − | 0.536156i | \(-0.180124\pi\) | |||||||
\(618\) | 8.19464e6 | − | 2.22139e8i | 0.0347188 | − | 0.941152i | ||||
\(619\) | 2.50301e8i | 1.05534i | 0.849450 | + | 0.527669i | \(0.176934\pi\) | ||||
−0.849450 | + | 0.527669i | \(0.823066\pi\) | |||||||
\(620\) | 5.08939e7 | − | 2.99256e7i | 0.213546 | − | 0.125565i | ||||
\(621\) | −6.13362e7 | −0.256119 | ||||||||
\(622\) | −3.99847e8 | − | 1.47502e7i | −1.66159 | − | 0.0612953i | ||||
\(623\) | −4.32787e7 | −0.178982 | ||||||||
\(624\) | −1.48695e7 | + | 1.00084e8i | −0.0611989 | + | 0.411918i | ||||
\(625\) | −1.83479e8 | − | 1.61059e8i | −0.751532 | − | 0.659697i | ||||
\(626\) | 4.12387e8 | + | 1.52128e7i | 1.68105 | + | 0.0620135i | ||||
\(627\) | −8.84402e7 | −0.358796 | ||||||||
\(628\) | 1.01074e6 | − | 1.36808e7i | 0.00408093 | − | 0.0552374i | ||||
\(629\) | −3.00351e8 | −1.20692 | ||||||||
\(630\) | −1.01591e8 | + | 6.48907e7i | −0.406288 | + | 0.259514i | ||||
\(631\) | 2.44022e8i | 0.971272i | 0.874161 | + | 0.485636i | \(0.161412\pi\) | ||||
−0.874161 | + | 0.485636i | \(0.838588\pi\) | |||||||
\(632\) | −1.38431e8 | − | 1.53759e7i | −0.548382 | − | 0.0609100i | ||||
\(633\) | − | 1.95886e8i | − | 0.772309i | ||||||
\(634\) | −3.23851e8 | − | 1.19467e7i | −1.27080 | − | 0.0468794i | ||||
\(635\) | 1.42028e8 | + | 2.05261e8i | 0.554692 | + | 0.801650i | ||||
\(636\) | −5.29814e6 | + | 7.17129e7i | −0.0205945 | + | 0.278757i | ||||
\(637\) | 2.03544e8i | 0.787480i | ||||||||
\(638\) | −8.98351e6 | − | 331399.i | −0.0345927 | − | 0.00127611i | ||||
\(639\) | − | 8.71031e7i | − | 0.333834i | ||||||
\(640\) | 2.46503e8 | − | 8.91947e7i | 0.940335 | − | 0.340251i | ||||
\(641\) | 2.17104e8 | 0.824317 | 0.412159 | − | 0.911112i | \(-0.364775\pi\) | ||||
0.412159 | + | 0.911112i | \(0.364775\pi\) | |||||||
\(642\) | −2.56718e6 | + | 6.95907e7i | −0.00970177 | + | 0.262994i | ||||
\(643\) | −7.06668e7 | −0.265817 | −0.132908 | − | 0.991128i | \(-0.542432\pi\) | ||||
−0.132908 | + | 0.991128i | \(0.542432\pi\) | |||||||
\(644\) | 5.12690e8 | + | 3.78775e7i | 1.91954 | + | 0.141815i | ||||
\(645\) | 1.25090e8 | + | 1.80783e8i | 0.466170 | + | 0.673717i | ||||
\(646\) | −1.34168e7 | + | 3.63701e8i | −0.0497682 | + | 1.34911i | ||||
\(647\) | 1.10253e8 | 0.407077 | 0.203539 | − | 0.979067i | \(-0.434756\pi\) | ||||
0.203539 | + | 0.979067i | \(0.434756\pi\) | |||||||
\(648\) | 3.33753e6 | − | 3.00483e7i | 0.0122659 | − | 0.110432i | ||||
\(649\) | −7.96846e7 | −0.291501 | ||||||||
\(650\) | 7.66051e7 | − | 1.82673e8i | 0.278944 | − | 0.665173i | ||||
\(651\) | 5.70703e7i | 0.206856i | ||||||||
\(652\) | −3.27527e8 | − | 2.41976e7i | −1.18169 | − | 0.0873032i | ||||
\(653\) | − | 2.64139e8i | − | 0.948622i | −0.880357 | − | 0.474311i | \(-0.842697\pi\) | ||
0.880357 | − | 0.474311i | \(-0.157303\pi\) | |||||||
\(654\) | 2.08329e6 | − | 5.64737e7i | 0.00744762 | − | 0.201889i | ||||
\(655\) | −6.12849e7 | + | 4.24053e7i | −0.218087 | + | 0.150902i | ||||
\(656\) | −3.93775e8 | − | 5.85034e7i | −1.39488 | − | 0.207238i | ||||
\(657\) | − | 1.00003e8i | − | 0.352629i | ||||||
\(658\) | −2.87359e7 | + | 7.78970e8i | −0.100867 | + | 2.73428i | ||||
\(659\) | 3.71991e8i | 1.29980i | 0.760020 | + | 0.649900i | \(0.225189\pi\) | ||||
−0.760020 | + | 0.649900i | \(0.774811\pi\) | |||||||
\(660\) | 6.03694e7 | − | 3.54971e7i | 0.209983 | − | 0.123470i | ||||
\(661\) | 8.07649e6 | 0.0279652 | 0.0139826 | − | 0.999902i | \(-0.495549\pi\) | ||||
0.0139826 | + | 0.999902i | \(0.495549\pi\) | |||||||
\(662\) | −3.73941e8 | − | 1.37946e7i | −1.28893 | − | 0.0475482i | ||||
\(663\) | 1.11238e8 | 0.381692 | ||||||||
\(664\) | −1.42659e7 | + | 1.28438e8i | −0.0487297 | + | 0.438721i | ||||
\(665\) | −5.15170e8 | + | 3.56465e8i | −1.75180 | + | 1.21214i | ||||
\(666\) | 1.29575e8 | + | 4.77999e6i | 0.438631 | + | 0.0161809i | ||||
\(667\) | −3.24007e7 | −0.109188 | ||||||||
\(668\) | −1.95085e8 | − | 1.44128e7i | −0.654476 | − | 0.0483526i | ||||
\(669\) | −7.46133e7 | −0.249194 | ||||||||
\(670\) | −1.82572e8 | + | 1.16616e8i | −0.607028 | + | 0.387735i | ||||
\(671\) | 1.13121e8i | 0.374433i | ||||||||
\(672\) | −4.64534e7 | + | 2.49104e8i | −0.153077 | + | 0.820866i | ||||
\(673\) | 4.68686e8i | 1.53758i | 0.639504 | + | 0.768788i | \(0.279140\pi\) | ||||
−0.639504 | + | 0.768788i | \(0.720860\pi\) | |||||||
\(674\) | −3.81566e8 | − | 1.40758e7i | −1.24621 | − | 0.0459721i | ||||
\(675\) | −2.08617e7 | + | 5.53890e7i | −0.0678326 | + | 0.180099i | ||||
\(676\) | −1.47795e8 | − | 1.09191e7i | −0.478431 | − | 0.0353464i | ||||
\(677\) | − | 4.87718e8i | − | 1.57182i | −0.618340 | − | 0.785911i | \(-0.712195\pi\) | ||
0.618340 | − | 0.785911i | \(-0.287805\pi\) | |||||||
\(678\) | 2.28416e8 | + | 8.42620e6i | 0.732889 | + | 0.0270360i | ||||
\(679\) | 6.48141e7i | 0.207043i | ||||||||
\(680\) | −1.36820e8 | − | 2.53648e8i | −0.435134 | − | 0.806686i | ||||
\(681\) | −2.77629e6 | −0.00879069 | ||||||||
\(682\) | 1.22225e6 | − | 3.31327e7i | 0.00385308 | − | 0.104449i | ||||
\(683\) | 1.37472e8 | 0.431473 | 0.215736 | − | 0.976452i | \(-0.430785\pi\) | ||||
0.215736 | + | 0.976452i | \(0.430785\pi\) | |||||||
\(684\) | 1.15764e7 | − | 1.56692e8i | 0.0361746 | − | 0.489641i | ||||
\(685\) | 4.55234e8 | − | 3.14994e8i | 1.41633 | − | 0.980009i | ||||
\(686\) | −1.57941e6 | + | 4.28143e7i | −0.00489239 | + | 0.132622i | ||||
\(687\) | −1.58654e7 | −0.0489307 | ||||||||
\(688\) | 4.57103e8 | + | 6.79121e7i | 1.40362 | + | 0.208536i | ||||
\(689\) | 1.14219e8 | 0.349205 | ||||||||
\(690\) | 2.12721e8 | − | 1.35874e8i | 0.647534 | − | 0.413608i | ||||
\(691\) | − | 3.91195e7i | − | 0.118566i | −0.998241 | − | 0.0592829i | \(-0.981119\pi\) | ||
0.998241 | − | 0.0592829i | \(-0.0188814\pi\) | |||||||
\(692\) | −2.42941e7 | + | 3.28832e8i | −0.0733132 | + | 0.992330i | ||||
\(693\) | 6.76957e7i | 0.203405i | ||||||||
\(694\) | −1.15997e7 | + | 3.14443e8i | −0.0347031 | + | 0.940728i | ||||
\(695\) | 5.18538e8 | − | 3.58796e8i | 1.54464 | − | 1.06879i | ||||
\(696\) | 1.76304e6 | − | 1.58729e7i | 0.00522920 | − | 0.0470792i | ||||
\(697\) | 4.37661e8i | 1.29253i | ||||||||
\(698\) | 2.25849e7 | − | 6.12230e8i | 0.0664129 | − | 1.80031i | ||||
\(699\) | 3.48530e7i | 0.102049i | ||||||||
\(700\) | 2.08582e8 | − | 4.50097e8i | 0.608110 | − | 1.31224i | ||||
\(701\) | 7.90495e7 | 0.229480 | 0.114740 | − | 0.993396i | \(-0.463396\pi\) | ||||
0.114740 | + | 0.993396i | \(0.463396\pi\) | |||||||
\(702\) | −4.79895e7 | − | 1.77032e6i | −0.138719 | − | 0.00511728i | ||||
\(703\) | 6.73849e8 | 1.93953 | ||||||||
\(704\) | 3.23039e7 | − | 1.43624e8i | 0.0925843 | − | 0.411633i | ||||
\(705\) | 2.17773e8 | + | 3.14730e8i | 0.621494 | + | 0.898195i | ||||
\(706\) | −9.82002e7 | − | 3.62257e6i | −0.279060 | − | 0.0102944i | ||||
\(707\) | −5.39017e8 | −1.52526 | ||||||||
\(708\) | 1.04303e7 | − | 1.41179e8i | 0.0293898 | − | 0.397806i | ||||
\(709\) | 3.79297e8 | 1.06424 | 0.532121 | − | 0.846668i | \(-0.321395\pi\) | ||||
0.532121 | + | 0.846668i | \(0.321395\pi\) | |||||||
\(710\) | 1.92954e8 | + | 3.02083e8i | 0.539111 | + | 0.844018i | ||||
\(711\) | − | 6.61048e7i | − | 0.183918i | ||||||
\(712\) | −4.93102e6 | + | 4.43947e7i | −0.0136614 | + | 0.122996i | ||||
\(713\) | − | 1.19499e8i | − | 0.329682i | ||||||
\(714\) | 2.78392e8 | + | 1.02698e7i | 0.764824 | + | 0.0282141i | ||||
\(715\) | −6.32954e7 | − | 9.14757e7i | −0.173163 | − | 0.250258i | ||||
\(716\) | −9.29192e6 | + | 1.25771e8i | −0.0253143 | + | 0.342642i | ||||
\(717\) | − | 3.88530e8i | − | 1.05406i | ||||||
\(718\) | −8.82560e7 | − | 3.25573e6i | −0.238436 | − | 0.00879581i | ||||
\(719\) | 9.42836e7i | 0.253659i | 0.991925 | + | 0.126829i | \(0.0404801\pi\) | ||||
−0.991925 | + | 0.126829i | \(0.959520\pi\) | |||||||
\(720\) | 5.49891e7 | + | 1.11604e8i | 0.147326 | + | 0.299009i | ||||
\(721\) | −8.84255e8 | −2.35924 | ||||||||
\(722\) | 1.62265e7 | − | 4.39866e8i | 0.0431135 | − | 1.16872i | ||||
\(723\) | −8.79315e7 | −0.232664 | ||||||||
\(724\) | −1.49759e8 | − | 1.10642e7i | −0.394619 | − | 0.0291544i | ||||
\(725\) | −1.10201e7 | + | 2.92591e7i | −0.0289183 | + | 0.0767797i | ||||
\(726\) | −6.69458e6 | + | 1.81476e8i | −0.0174950 | + | 0.474251i | ||||
\(727\) | −3.70399e8 | −0.963977 | −0.481988 | − | 0.876178i | \(-0.660085\pi\) | ||||
−0.481988 | + | 0.876178i | \(0.660085\pi\) | |||||||
\(728\) | 4.00037e8 | + | 4.44330e7i | 1.03683 | + | 0.115162i | ||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 2.21531e8 | + | 3.46823e8i | 0.569463 | + | 0.891536i | ||||
\(731\) | − | 5.08046e8i | − | 1.30062i | ||||||
\(732\) | −2.00418e8 | − | 1.48069e7i | −0.510981 | − | 0.0377512i | ||||
\(733\) | − | 2.70421e8i | − | 0.686639i | −0.939219 | − | 0.343320i | \(-0.888449\pi\) | ||
0.939219 | − | 0.343320i | \(-0.111551\pi\) | |||||||
\(734\) | −1.73238e7 | + | 4.69610e8i | −0.0438080 | + | 1.18754i | ||||
\(735\) | 1.42411e8 | + | 2.05815e8i | 0.358659 | + | 0.518341i | ||||
\(736\) | 9.72684e7 | − | 5.21596e8i | 0.243971 | − | 1.30828i | ||||
\(737\) | 1.21657e8i | 0.303904i | ||||||||
\(738\) | 6.96522e6 | − | 1.88812e8i | 0.0173287 | − | 0.469744i | ||||
\(739\) | − | 1.34877e8i | − | 0.334199i | −0.985940 | − | 0.167099i | \(-0.946560\pi\) | ||
0.985940 | − | 0.167099i | \(-0.0534400\pi\) | |||||||
\(740\) | −4.59970e8 | + | 2.70462e8i | −1.13510 | + | 0.667439i | ||||
\(741\) | −2.49567e8 | −0.613384 | ||||||||
\(742\) | 2.85852e8 | + | 1.05450e7i | 0.699728 | + | 0.0258127i | ||||
\(743\) | −3.91308e8 | −0.954008 | −0.477004 | − | 0.878901i | \(-0.658277\pi\) | ||||
−0.477004 | + | 0.878901i | \(0.658277\pi\) | |||||||
\(744\) | 5.85420e7 | + | 6.50239e6i | 0.142151 | + | 0.0157890i | ||||
\(745\) | −1.64739e8 | − | 2.38084e8i | −0.398408 | − | 0.575787i | ||||
\(746\) | 9.92586e7 | + | 3.66161e6i | 0.239085 | + | 0.00881975i | ||||
\(747\) | −6.13326e7 | −0.147140 | ||||||||
\(748\) | −1.61403e8 | − | 1.19244e7i | −0.385661 | − | 0.0284926i | ||||
\(749\) | 2.77015e8 | 0.659262 | ||||||||
\(750\) | −5.03488e7 | − | 2.38309e8i | −0.119345 | − | 0.564881i | ||||
\(751\) | − | 2.95353e8i | − | 0.697303i | −0.937253 | − | 0.348651i | \(-0.886640\pi\) | ||
0.937253 | − | 0.348651i | \(-0.113360\pi\) | |||||||
\(752\) | 7.95784e8 | + | 1.18230e8i | 1.87129 | + | 0.278019i | ||||
\(753\) | − | 1.28457e8i | − | 0.300867i | ||||||
\(754\) | −2.53503e7 | − | 935165.i | −0.0591384 | − | 0.00218159i | ||||
\(755\) | −5.88837e8 | + | 4.07438e8i | −1.36821 | + | 0.946719i | ||||
\(756\) | −1.19938e8 | − | 8.86102e6i | −0.277583 | − | 0.0205078i | ||||
\(757\) | 4.40767e8i | 1.01607i | 0.861338 | + | 0.508033i | \(0.169627\pi\) | ||||
−0.861338 | + | 0.508033i | \(0.830373\pi\) | |||||||
\(758\) | 3.34557e8 | + | 1.23417e7i | 0.768178 | + | 0.0283378i | ||||
\(759\) | − | 1.41747e8i | − | 0.324183i | ||||||
\(760\) | 3.06961e8 | + | 5.69069e8i | 0.699266 | + | 1.29636i | ||||
\(761\) | 8.11422e8 | 1.84117 | 0.920583 | − | 0.390548i | \(-0.127714\pi\) | ||||
0.920583 | + | 0.390548i | \(0.127714\pi\) | |||||||
\(762\) | −9.18015e6 | + | 2.48854e8i | −0.0207484 | + | 0.562445i | ||||
\(763\) | −2.24801e8 | −0.506086 | ||||||||
\(764\) | 4.30404e7 | − | 5.82573e8i | 0.0965153 | − | 1.30638i | ||||
\(765\) | 1.12479e8 | − | 7.78287e7i | 0.251240 | − | 0.173842i | ||||
\(766\) | 1.51119e7 | − | 4.09651e8i | 0.0336226 | − | 0.911438i | ||||
\(767\) | −2.24860e8 | −0.498340 | ||||||||
\(768\) | 2.50235e8 | + | 7.60333e7i | 0.552413 | + | 0.167850i | ||||
\(769\) | −4.57333e8 | −1.00567 | −0.502833 | − | 0.864383i | \(-0.667709\pi\) | ||||
−0.502833 | + | 0.864383i | \(0.667709\pi\) | |||||||
\(770\) | −1.49962e8 | − | 2.34777e8i | −0.328480 | − | 0.514260i | ||||
\(771\) | − | 2.02028e8i | − | 0.440807i | ||||||
\(772\) | 5.74191e7 | − | 7.77195e8i | 0.124797 | − | 1.68919i | ||||
\(773\) | 7.52735e8i | 1.62969i | 0.579682 | + | 0.814843i | \(0.303177\pi\) | ||||
−0.579682 | + | 0.814843i | \(0.696823\pi\) | |||||||
\(774\) | −8.08538e6 | + | 2.19178e8i | −0.0174372 | + | 0.472686i | ||||
\(775\) | −1.07912e8 | − | 4.06441e7i | −0.231828 | − | 0.0873158i | ||||
\(776\) | 6.64855e7 | + | 7.38469e6i | 0.142279 | + | 0.0158033i | ||||
\(777\) | − | 5.15792e8i | − | 1.09954i | ||||||
\(778\) | −1.46942e7 | + | 3.98329e8i | −0.0312038 | + | 0.845869i | ||||
\(779\) | − | 9.81909e8i | − | 2.07711i | ||||||
\(780\) | 1.70355e8 | − | 1.00168e8i | 0.358980 | − | 0.211080i | ||||
\(781\) | 2.01295e8 | 0.422551 | ||||||||
\(782\) | −5.82921e8 | − | 2.15038e7i | −1.21896 | − | 0.0449670i | ||||
\(783\) | 7.57977e6 | 0.0157896 | ||||||||
\(784\) | 5.20397e8 | + | 7.73157e7i | 1.07991 | + | 0.160442i | ||||
\(785\) | −2.20330e7 | + | 1.52454e7i | −0.0455474 | + | 0.0315160i | ||||
\(786\) | −7.43007e7 | − | 2.74093e6i | −0.153012 | − | 0.00564455i | ||||
\(787\) | −2.11025e8 | −0.432921 | −0.216461 | − | 0.976291i | \(-0.569451\pi\) | ||||
−0.216461 | + | 0.976291i | \(0.569451\pi\) | |||||||
\(788\) | 2.51337e7 | − | 3.40197e8i | 0.0513663 | − | 0.695267i | ||||
\(789\) | −9.60154e7 | −0.195483 | ||||||||
\(790\) | 1.46438e8 | + | 2.29259e8i | 0.297011 | + | 0.464992i | ||||
\(791\) | − | 9.09242e8i | − | 1.83717i | ||||||
\(792\) | 6.94414e7 | + | 7.71301e6i | 0.139779 | + | 0.0155256i | ||||
\(793\) | 3.19212e8i | 0.640117i | ||||||||
\(794\) | −3.13558e8 | − | 1.15670e7i | −0.626406 | − | 0.0231079i | ||||
\(795\) | 1.15494e8 | − | 7.99144e7i | 0.229856 | − | 0.159046i | ||||
\(796\) | 8.03983e6 | − | 1.08823e8i | 0.0159407 | − | 0.215765i | ||||
\(797\) | 2.07292e8i | 0.409456i | 0.978819 | + | 0.204728i | \(0.0656310\pi\) | ||||
−0.978819 | + | 0.204728i | \(0.934369\pi\) | |||||||
\(798\) | −6.24582e8 | − | 2.30406e7i | −1.22908 | − | 0.0453404i | ||||
\(799\) | − | 8.84472e8i | − | 1.73398i | ||||||
\(800\) | −4.37939e8 | − | 2.65243e8i | −0.855349 | − | 0.518052i | ||||
\(801\) | −2.11997e7 | −0.0412508 | ||||||||
\(802\) | 1.66142e6 | − | 4.50377e7i | 0.00322075 | − | 0.0873078i | ||||
\(803\) | 2.31107e8 | 0.446340 | ||||||||
\(804\) | −2.15543e8 | − | 1.59243e7i | −0.414731 | − | 0.0306403i | ||||
\(805\) | −5.71324e8 | − | 8.25688e8i | −1.09520 | − | 1.58281i | ||||
\(806\) | 3.44904e6 | − | 9.34962e7i | 0.00658709 | − | 0.178562i | ||||
\(807\) | 4.00222e7 | 0.0761518 | ||||||||
\(808\) | −6.14137e7 | + | 5.52917e8i | −0.116421 | + | 1.04816i | ||||
\(809\) | 4.26907e8 | 0.806283 | 0.403142 | − | 0.915138i | \(-0.367918\pi\) | ||||
0.403142 | + | 0.915138i | \(0.367918\pi\) | |||||||
\(810\) | −4.97637e7 | + | 3.17862e7i | −0.0936391 | + | 0.0598114i | ||||
\(811\) | 6.62743e8i | 1.24246i | 0.783628 | + | 0.621230i | \(0.213367\pi\) | ||||
−0.783628 | + | 0.621230i | \(0.786633\pi\) | |||||||
\(812\) | −6.33570e7 | − | 4.68081e6i | −0.118339 | − | 0.00874284i | ||||
\(813\) | − | 1.50701e8i | − | 0.280442i | ||||||
\(814\) | −1.10465e7 | + | 2.99447e8i | −0.0204810 | + | 0.555197i | ||||
\(815\) | 3.64984e8 | + | 5.27482e8i | 0.674220 | + | 0.974394i | ||||
\(816\) | 4.22536e7 | − | 2.84400e8i | 0.0777665 | − | 0.523431i | ||||
\(817\) | 1.13982e9i | 2.09012i | ||||||||
\(818\) | 8.72874e6 | − | 2.36617e8i | 0.0159475 | − | 0.432302i | ||||
\(819\) | 1.91029e8i | 0.347734i | ||||||||
\(820\) | 3.94108e8 | + | 6.70252e8i | 0.714781 | + | 1.21562i | ||||
\(821\) | 5.73913e8 | 1.03709 | 0.518545 | − | 0.855050i | \(-0.326474\pi\) | ||||
0.518545 | + | 0.855050i | \(0.326474\pi\) | |||||||
\(822\) | 5.51917e8 | + | 2.03600e7i | 0.993708 | + | 0.0366575i | ||||
\(823\) | −5.19180e8 | −0.931362 | −0.465681 | − | 0.884953i | \(-0.654191\pi\) | ||||
−0.465681 | + | 0.884953i | \(0.654191\pi\) | |||||||
\(824\) | −1.00749e8 | + | 9.07058e8i | −0.180077 | + | 1.62126i | ||||
\(825\) | −1.28004e8 | − | 4.82113e7i | −0.227961 | − | 0.0858592i | ||||
\(826\) | −5.62749e8 | − | 2.07596e7i | −0.998560 | − | 0.0368366i | ||||
\(827\) | 4.62996e8 | 0.818580 | 0.409290 | − | 0.912404i | \(-0.365776\pi\) | ||||
0.409290 | + | 0.912404i | \(0.365776\pi\) | |||||||
\(828\) | 2.51137e8 | + | 1.85540e7i | 0.442405 | + | 0.0326848i | ||||
\(829\) | −7.20209e8 | −1.26414 | −0.632069 | − | 0.774912i | \(-0.717794\pi\) | ||||
−0.632069 | + | 0.774912i | \(0.717794\pi\) | |||||||
\(830\) | 2.12709e8 | − | 1.35866e8i | 0.372007 | − | 0.237617i | ||||
\(831\) | − | 2.48809e8i | − | 0.433574i | ||||||
\(832\) | 9.11575e7 | − | 4.05290e8i | 0.158279 | − | 0.703713i | ||||
\(833\) | − | 5.78394e8i | − | 1.00067i | ||||||
\(834\) | 6.28666e8 | + | 2.31913e7i | 1.08373 | + | 0.0399785i | ||||
\(835\) | 2.17396e8 | + | 3.14184e8i | 0.373415 | + | 0.539665i | ||||
\(836\) | 3.62113e8 | + | 2.67529e7i | 0.619763 | + | 0.0457880i | ||||
\(837\) | 2.79555e7i | 0.0476749i | ||||||||
\(838\) | 9.21438e7 | + | 3.39915e6i | 0.156579 | + | 0.00577615i | ||||
\(839\) | 3.84875e8i | 0.651680i | 0.945425 | + | 0.325840i | \(0.105647\pi\) | ||||
−0.945425 | + | 0.325840i | \(0.894353\pi\) | |||||||
\(840\) | 4.35589e8 | − | 2.34960e8i | 0.734918 | − | 0.396421i | ||||
\(841\) | −5.90819e8 | −0.993269 | ||||||||
\(842\) | −1.05421e7 | + | 2.85773e8i | −0.0176599 | + | 0.478723i | ||||
\(843\) | −6.68466e8 | −1.11583 | ||||||||
\(844\) | −5.92548e7 | + | 8.02042e8i | −0.0985589 | + | 1.33404i | ||||
\(845\) | 1.64698e8 | + | 2.38024e8i | 0.272971 | + | 0.394503i | ||||
\(846\) | −1.40761e7 | + | 3.81572e8i | −0.0232472 | + | 0.630182i | ||||
\(847\) | 7.22388e8 | 1.18883 | ||||||||
\(848\) | 4.33859e7 | − | 2.92022e8i | 0.0711477 | − | 0.478881i | ||||
\(849\) | 9.91888e7 | 0.162084 | ||||||||
\(850\) | −2.17683e8 | + | 5.19087e8i | −0.354460 | + | 0.845247i | ||||
\(851\) | 1.08001e9i | 1.75243i | ||||||||
\(852\) | −2.63484e7 | + | 3.56639e8i | −0.0426025 | + | 0.576646i | ||||
\(853\) | − | 5.38061e8i | − | 0.866931i | −0.901170 | − | 0.433466i | \(-0.857291\pi\) | ||
0.901170 | − | 0.433466i | \(-0.142709\pi\) | |||||||
\(854\) | −2.94704e7 | + | 7.98880e8i | −0.0473165 | + | 1.28265i | ||||
\(855\) | −2.52352e8 | + | 1.74612e8i | −0.403746 | + | 0.279367i | ||||
\(856\) | 3.15621e7 | − | 2.84159e8i | 0.0503205 | − | 0.453043i | ||||
\(857\) | − | 3.71687e8i | − | 0.590521i | −0.955417 | − | 0.295261i | \(-0.904594\pi\) | ||
0.955417 | − | 0.295261i | \(-0.0954065\pi\) | |||||||
\(858\) | 4.09119e6 | − | 1.10903e8i | 0.00647721 | − | 0.175583i | ||||
\(859\) | − | 3.70545e7i | − | 0.0584603i | −0.999573 | − | 0.0292302i | \(-0.990694\pi\) | ||
0.999573 | − | 0.0292302i | \(-0.00930557\pi\) | |||||||
\(860\) | −4.57489e8 | − | 7.78044e8i | −0.719259 | − | 1.22323i | ||||
\(861\) | −7.51593e8 | −1.17753 | ||||||||
\(862\) | 6.56225e7 | + | 2.42079e6i | 0.102454 | + | 0.00377951i | ||||
\(863\) | 2.37470e7 | 0.0369468 | 0.0184734 | − | 0.999829i | \(-0.494119\pi\) | ||||
0.0184734 | + | 0.999829i | \(0.494119\pi\) | |||||||
\(864\) | −2.27548e7 | + | 1.22021e8i | −0.0352803 | + | 0.189189i | ||||
\(865\) | 5.29584e8 | − | 3.66439e8i | 0.818251 | − | 0.566178i | ||||
\(866\) | 3.50106e8 | + | 1.29153e7i | 0.539071 | + | 0.0198861i | ||||
\(867\) | 6.01711e7 | 0.0923274 | ||||||||
\(868\) | 1.72636e7 | − | 2.33671e8i | 0.0263981 | − | 0.357311i | ||||
\(869\) | 1.52768e8 | 0.232794 | ||||||||
\(870\) | −2.62875e7 | + | 1.67910e7i | −0.0399201 | + | 0.0254987i | ||||
\(871\) | 3.43302e8i | 0.519543i | ||||||||
\(872\) | −2.56130e7 | + | 2.30598e8i | −0.0386288 | + | 0.347781i | ||||
\(873\) | 3.17487e7i | 0.0477181i | ||||||||
\(874\) | 1.30781e9 | + | 4.82445e7i | 1.95889 | + | 0.0722626i | ||||
\(875\) | −9.39948e8 | + | 2.35095e8i | −1.40307 | + | 0.350929i | ||||
\(876\) | −3.02507e7 | + | 4.09458e8i | −0.0450011 | + | 0.609111i | ||||
\(877\) | − | 9.70223e8i | − | 1.43838i | −0.694815 | − | 0.719189i | \(-0.744514\pi\) | ||
0.694815 | − | 0.719189i | \(-0.255486\pi\) | |||||||
\(878\) | −7.25751e8 | − | 2.67727e7i | −1.07227 | − | 0.0395556i | ||||
\(879\) | 1.83939e8i | 0.270836i | ||||||||
\(880\) | −2.57917e8 | + | 1.27079e8i | −0.378470 | + | 0.186478i | ||||
\(881\) | 3.34234e8 | 0.488791 | 0.244396 | − | 0.969676i | \(-0.421410\pi\) | ||||
0.244396 | + | 0.969676i | \(0.421410\pi\) | |||||||
\(882\) | −9.20494e6 | + | 2.49526e8i | −0.0134158 | + | 0.363673i | ||||
\(883\) | −1.04292e9 | −1.51485 | −0.757426 | − | 0.652921i | \(-0.773543\pi\) | ||||
−0.757426 | + | 0.652921i | \(0.773543\pi\) | |||||||
\(884\) | −4.55458e8 | − | 3.36492e7i | −0.659313 | − | 0.0487099i | ||||
\(885\) | −2.27369e8 | + | 1.57325e8i | −0.328021 | + | 0.226970i | ||||
\(886\) | −1.30057e6 | + | 3.52558e7i | −0.00186997 | + | 0.0506908i | ||||
\(887\) | 2.82542e8 | 0.404867 | 0.202434 | − | 0.979296i | \(-0.435115\pi\) | ||||
0.202434 | + | 0.979296i | \(0.435115\pi\) | |||||||
\(888\) | −5.29092e8 | − | 5.87675e7i | −0.755601 | − | 0.0839263i | ||||
\(889\) | 9.90598e8 | 1.40991 | ||||||||
\(890\) | 7.35230e7 | − | 4.69624e7i | 0.104293 | − | 0.0666162i | ||||
\(891\) | 3.31602e7i | 0.0468796i | ||||||||
\(892\) | 3.05500e8 | + | 2.25703e7i | 0.430444 | + | 0.0318011i | ||||
\(893\) | 1.98435e9i | 2.78653i | ||||||||
\(894\) | 1.06481e7 | − | 2.88649e8i | 0.0149026 | − | 0.403977i | ||||
\(895\) | 2.02554e8 | − | 1.40154e8i | 0.282534 | − | 0.195496i | ||||
\(896\) | 2.65554e8 | − | 1.00589e9i | 0.369172 | − | 1.39838i | ||||
\(897\) | − | 3.99993e8i | − | 0.554211i | ||||||
\(898\) | 2.28530e7 | − | 6.19497e8i | 0.0315584 | − | 0.855480i | ||||
\(899\) | 1.47674e7i | 0.0203247i | ||||||||
\(900\) | 1.02172e8 | − | 2.20476e8i | 0.140154 | − | 0.302437i | ||||
\(901\) | −3.24567e8 | −0.443742 | ||||||||
\(902\) | 4.36344e8 | + | 1.60966e7i | 0.594579 | + | 0.0219338i | ||||
\(903\) | 8.72466e8 | 1.18491 | ||||||||
\(904\) | −9.32689e8 | − | 1.03596e8i | −1.26250 | − | 0.140229i | ||||
\(905\) | 1.66886e8 | + | 2.41187e8i | 0.225152 | + | 0.325393i | ||||
\(906\) | −7.13895e8 | − | 2.63353e7i | −0.959953 | − | 0.0354123i | ||||
\(907\) | 6.77657e7 | 0.0908214 | 0.0454107 | − | 0.998968i | \(-0.485540\pi\) | ||||
0.0454107 | + | 0.998968i | \(0.485540\pi\) | |||||||
\(908\) | 1.13673e7 | + | 839818.i | 0.0151845 | + | 0.00112183i | ||||
\(909\) | −2.64033e8 | −0.351534 | ||||||||
\(910\) | −4.23174e8 | − | 6.62509e8i | −0.561558 | − | 0.879160i | ||||
\(911\) | 9.61421e7i | 0.127162i | 0.997977 | + | 0.0635812i | \(0.0202522\pi\) | ||||
−0.997977 | + | 0.0635812i | \(0.979748\pi\) | |||||||
\(912\) | −9.47975e7 | + | 6.38063e8i | −0.124972 | + | 0.841161i | ||||
\(913\) | − | 1.41739e8i | − | 0.186242i | ||||||
\(914\) | −1.31174e9 | − | 4.83895e7i | −1.71794 | − | 0.0633742i | ||||
\(915\) | 2.23339e8 | + | 3.22774e8i | 0.291543 | + | 0.421342i | ||||
\(916\) | 6.49601e7 | + | 4.79924e6i | 0.0845202 | + | 0.00624434i | ||||
\(917\) | 2.95764e8i | 0.383563i | ||||||||
\(918\) | 1.36368e8 | + | 5.03057e6i | 0.176272 | + | 0.00650263i | ||||
\(919\) | − | 5.40889e8i | − | 0.696885i | −0.937330 | − | 0.348443i | \(-0.886711\pi\) | ||
0.937330 | − | 0.348443i | \(-0.113289\pi\) | |||||||
\(920\) | −9.12075e8 | + | 4.91981e8i | −1.17130 | + | 0.631808i | ||||
\(921\) | −5.41590e8 | −0.693253 | ||||||||
\(922\) | 3.72220e7 | − | 1.00901e9i | 0.0474905 | − | 1.28737i | ||||
\(923\) | 5.68028e8 | 0.722378 | ||||||||
\(924\) | 2.04777e7 | − | 2.77176e8i | 0.0259577 | − | 0.351350i | ||||
\(925\) | 9.75293e8 | + | 3.67334e8i | 1.23228 | + | 0.464127i | ||||
\(926\) | 9.48641e6 | − | 2.57156e8i | 0.0119473 | − | 0.323865i | ||||
\(927\) | −4.33145e8 | −0.543744 | ||||||||
\(928\) | −1.20202e7 | + | 6.44575e7i | −0.0150407 | + | 0.0806547i | ||||
\(929\) | −1.21327e9 | −1.51325 | −0.756626 | − | 0.653848i | \(-0.773154\pi\) | ||||
−0.756626 | + | 0.653848i | \(0.773154\pi\) | |||||||
\(930\) | −6.19279e7 | − | 9.69527e7i | −0.0769906 | − | 0.120534i | ||||
\(931\) | 1.29765e9i | 1.60808i | ||||||||
\(932\) | 1.05429e7 | − | 1.42703e8i | 0.0130231 | − | 0.176273i | ||||
\(933\) | 7.79655e8i | 0.959970i | ||||||||
\(934\) | −5.77033e6 | + | 1.56421e8i | −0.00708207 | + | 0.191980i | ||||
\(935\) | 1.79862e8 | + | 2.59939e8i | 0.220041 | + | 0.318007i | ||||
\(936\) | 1.95955e8 | + | 2.17651e7i | 0.238962 | + | 0.0265420i | ||||
\(937\) | − | 4.32441e8i | − | 0.525663i | −0.964842 | − | 0.262832i | \(-0.915344\pi\) | ||
0.964842 | − | 0.262832i | \(-0.0846564\pi\) | |||||||
\(938\) | −3.16944e7 | + | 8.59168e8i | −0.0384038 | + | 1.04105i | ||||
\(939\) | − | 8.04106e8i | − | 0.971217i | ||||||
\(940\) | −7.96455e8 | − | 1.35452e9i | −0.958910 | − | 1.63080i | ||||
\(941\) | 1.21123e9 | 1.45364 | 0.726821 | − | 0.686827i | \(-0.240997\pi\) | ||||
0.726821 | + | 0.686827i | \(0.240997\pi\) | |||||||
\(942\) | −2.67123e7 | − | 985409.i | −0.0319565 | − | 0.00117886i | ||||
\(943\) | 1.57375e9 | 1.87673 | ||||||||
\(944\) | −8.54125e7 | + | 5.74895e8i | −0.101533 | + | 0.683396i | ||||
\(945\) | 1.33655e8 | + | 1.93160e8i | 0.158376 | + | 0.228888i | ||||
\(946\) | −5.06518e8 | − | 1.86853e7i | −0.598303 | − | 0.0220712i | ||||
\(947\) | 6.93040e8 | 0.816034 | 0.408017 | − | 0.912974i | \(-0.366220\pi\) | ||||
0.408017 | + | 0.912974i | \(0.366220\pi\) | |||||||
\(948\) | −1.99965e7 | + | 2.70662e8i | −0.0234709 | + | 0.317690i | ||||
\(949\) | 6.52154e8 | 0.763047 | ||||||||
\(950\) | 4.88379e8 | − | 1.16459e9i | 0.569622 | − | 1.35832i | ||||
\(951\) | 6.31471e8i | 0.734196i | ||||||||
\(952\) | −1.13675e9 | − | 1.26262e8i | −1.31751 | − | 0.146339i | ||||
\(953\) | − | 3.68416e8i | − | 0.425657i | −0.977090 | − | 0.212828i | \(-0.931732\pi\) | ||
0.977090 | − | 0.212828i | \(-0.0682675\pi\) | |||||||
\(954\) | 1.40022e8 | + | 5.16538e6i | 0.161269 | + | 0.00594918i | ||||
\(955\) | −9.38233e8 | + | 6.49198e8i | −1.07721 | + | 0.745362i | ||||
\(956\) | −1.17529e8 | + | 1.59081e9i | −0.134515 | + | 1.82073i | ||||
\(957\) | 1.75168e7i | 0.0199857i | ||||||||
\(958\) | −1.55036e9 | − | 5.71923e7i | −1.76334 | − | 0.0650490i | ||||
\(959\) | − | 2.19698e9i | − | 2.49098i | ||||||
\(960\) | −1.91390e8 | − | 4.73592e8i | −0.216324 | − | 0.535292i | ||||
\(961\) | 8.33039e8 | 0.938632 | ||||||||
\(962\) | −3.11718e7 | + | 8.45002e8i | −0.0350136 | + | 0.949145i | ||||
\(963\) | 1.35694e8 | 0.151943 | ||||||||
\(964\) | 3.60031e8 | + | 2.65990e7i | 0.401891 | + | 0.0296916i | ||||
\(965\) | −1.25167e9 | + | 8.66079e8i | −1.39286 | + | 0.963775i | ||||
\(966\) | 3.69283e7 | − | 1.00105e9i | 0.0409664 | − | 1.11051i | ||||
\(967\) | 1.15287e9 | 1.27497 | 0.637485 | − | 0.770463i | \(-0.279975\pi\) | ||||
0.637485 | + | 0.770463i | \(0.279975\pi\) | |||||||
\(968\) | 8.23064e7 | − | 7.41017e8i | 0.0907418 | − | 0.816962i | ||||
\(969\) | 7.09174e8 | 0.779438 | ||||||||
\(970\) | −7.03308e7 | − | 1.10108e8i | −0.0770602 | − | 0.120643i | ||||
\(971\) | 4.34130e8i | 0.474201i | 0.971485 | + | 0.237100i | \(0.0761971\pi\) | ||||
−0.971485 | + | 0.237100i | \(0.923803\pi\) | |||||||
\(972\) | −5.87508e7 | − | 4.34050e6i | −0.0639757 | − | 0.00472651i | ||||
\(973\) | − | 2.50249e9i | − | 2.71665i | ||||||
\(974\) | 4.79452e7 | − | 1.29969e9i | 0.0518882 | − | 1.40658i | ||||
\(975\) | −3.61210e8 | − | 1.36046e8i | −0.389714 | − | 0.146782i | ||||
\(976\) | 8.16123e8 | + | 1.21252e8i | 0.877821 | + | 0.130418i | ||||
\(977\) | − | 1.16648e9i | − | 1.25082i | −0.780297 | − | 0.625410i | \(-0.784932\pi\) | ||
0.780297 | − | 0.625410i | \(-0.215068\pi\) | |||||||
\(978\) | −2.35913e7 | + | 6.39509e8i | −0.0252194 | + | 0.683644i | ||||
\(979\) | − | 4.89924e7i | − | 0.0522132i | ||||||
\(980\) | −5.20836e8 | − | 8.85777e8i | −0.553379 | − | 0.941123i | ||||
\(981\) | −1.10117e8 | −0.116640 | ||||||||
\(982\) | 1.24634e9 | + | 4.59771e7i | 1.31614 | + | 0.0485520i | ||||
\(983\) | −4.61997e8 | −0.486384 | −0.243192 | − | 0.969978i | \(-0.578194\pi\) | ||||
−0.243192 | + | 0.969978i | \(0.578194\pi\) | |||||||
\(984\) | −8.56338e7 | + | 7.70974e8i | −0.0898794 | + | 0.809198i | ||||
\(985\) | −5.47887e8 | + | 3.79104e8i | −0.573301 | + | 0.396688i | ||||
\(986\) | 7.20360e7 | + | 2.65738e6i | 0.0751482 | + | 0.00277219i | ||||
\(987\) | 1.51890e9 | 1.57971 | ||||||||
\(988\) | 1.02184e9 | + | 7.54932e7i | 1.05952 | + | 0.0782775i | ||||
\(989\) | −1.82685e9 | −1.88848 | ||||||||
\(990\) | −7.34577e7 | − | 1.15003e8i | −0.0757063 | − | 0.118524i | ||||
\(991\) | − | 1.16310e9i | − | 1.19508i | −0.801841 | − | 0.597538i | \(-0.796146\pi\) | ||
0.801841 | − | 0.597538i | \(-0.203854\pi\) | |||||||
\(992\) | −2.37730e8 | − | 4.43324e7i | −0.243528 | − | 0.0454137i | ||||
\(993\) | 7.29141e8i | 0.744670i | ||||||||
\(994\) | 1.42158e9 | + | 5.24417e7i | 1.44748 | + | 0.0533971i | ||||
\(995\) | −1.75259e8 | + | 1.21269e8i | −0.177915 | + | 0.123106i | ||||
\(996\) | 2.51123e8 | + | 1.85529e7i | 0.254161 | + | 0.0187773i | ||||
\(997\) | 1.47436e9i | 1.48771i | 0.668343 | + | 0.743853i | \(0.267004\pi\) | ||||
−0.668343 | + | 0.743853i | \(0.732996\pi\) | |||||||
\(998\) | −4.27185e8 | − | 1.57587e7i | −0.429759 | − | 0.0158537i | ||||
\(999\) | − | 2.52656e8i | − | 0.253416i |
(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 | 60.7.f.a.19.18 | yes | 36 | |
3.2 | odd | 2 | 180.7.f.g.19.19 | 36 | |||
4.3 | odd | 2 | inner | 60.7.f.a.19.20 | yes | 36 | |
5.4 | even | 2 | inner | 60.7.f.a.19.19 | yes | 36 | |
12.11 | even | 2 | 180.7.f.g.19.17 | 36 | |||
15.14 | odd | 2 | 180.7.f.g.19.18 | 36 | |||
20.19 | odd | 2 | inner | 60.7.f.a.19.17 | ✓ | 36 | |
60.59 | even | 2 | 180.7.f.g.19.20 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.f.a.19.17 | ✓ | 36 | 20.19 | odd | 2 | inner | |
60.7.f.a.19.18 | yes | 36 | 1.1 | even | 1 | trivial | |
60.7.f.a.19.19 | yes | 36 | 5.4 | even | 2 | inner | |
60.7.f.a.19.20 | yes | 36 | 4.3 | odd | 2 | inner | |
180.7.f.g.19.17 | 36 | 12.11 | even | 2 | |||
180.7.f.g.19.18 | 36 | 15.14 | odd | 2 | |||
180.7.f.g.19.19 | 36 | 3.2 | odd | 2 | |||
180.7.f.g.19.20 | 36 | 60.59 | even | 2 |