Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(7,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.7");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 37.21 | ||
Character | \(\chi\) | \(=\) | 43.37 |
Dual form | 43.7.d.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.1507i | 1.89384i | 0.321467 | + | 0.946921i | \(0.395824\pi\) | ||||
−0.321467 | + | 0.946921i | \(0.604176\pi\) | |||||||
\(3\) | 15.3614 | + | 8.86889i | 0.568939 | + | 0.328477i | 0.756726 | − | 0.653733i | \(-0.226798\pi\) |
−0.187786 | + | 0.982210i | \(0.560131\pi\) | |||||||
\(4\) | −165.545 | −2.58664 | ||||||||
\(5\) | 63.9718 | + | 36.9341i | 0.511774 | + | 0.295473i | 0.733563 | − | 0.679622i | \(-0.237856\pi\) |
−0.221788 | + | 0.975095i | \(0.571189\pi\) | |||||||
\(6\) | −134.370 | + | 232.736i | −0.622084 | + | 1.07748i | ||||
\(7\) | −298.109 | + | 172.114i | −0.869123 | + | 0.501789i | −0.867057 | − | 0.498209i | \(-0.833991\pi\) |
−0.00206660 | + | 0.999998i | \(0.500658\pi\) | |||||||
\(8\) | − | 1538.48i | − | 3.00484i | ||||||
\(9\) | −207.186 | − | 358.856i | −0.284205 | − | 0.492258i | ||||
\(10\) | −559.579 | + | 969.219i | −0.559579 | + | 0.969219i | ||||
\(11\) | −1171.40 | −0.880094 | −0.440047 | − | 0.897975i | \(-0.645038\pi\) | ||||
−0.440047 | + | 0.897975i | \(0.645038\pi\) | |||||||
\(12\) | −2542.99 | − | 1468.20i | −1.47164 | − | 0.849651i | ||||
\(13\) | 642.173 | + | 1112.28i | 0.292295 | + | 0.506271i | 0.974352 | − | 0.225029i | \(-0.0722476\pi\) |
−0.682057 | + | 0.731299i | \(0.738914\pi\) | |||||||
\(14\) | −2607.65 | − | 4516.58i | −0.950308 | − | 1.64598i | ||||
\(15\) | 655.129 | + | 1134.72i | 0.194112 | + | 0.336212i | ||||
\(16\) | 12714.2 | 3.10405 | ||||||||
\(17\) | 1587.56 | + | 2749.73i | 0.323134 | + | 0.559684i | 0.981133 | − | 0.193335i | \(-0.0619303\pi\) |
−0.657999 | + | 0.753019i | \(0.728597\pi\) | |||||||
\(18\) | 5436.94 | − | 3139.02i | 0.932259 | − | 0.538240i | ||||
\(19\) | 5769.57 | + | 3331.06i | 0.841168 | + | 0.485648i | 0.857661 | − | 0.514216i | \(-0.171917\pi\) |
−0.0164933 | + | 0.999864i | \(0.505250\pi\) | |||||||
\(20\) | −10590.2 | − | 6114.25i | −1.32377 | − | 0.764281i | ||||
\(21\) | −6105.82 | −0.659305 | ||||||||
\(22\) | − | 17747.6i | − | 1.66676i | ||||||
\(23\) | −7350.54 | + | 12731.5i | −0.604138 | + | 1.04640i | 0.388049 | + | 0.921639i | \(0.373149\pi\) |
−0.992187 | + | 0.124759i | \(0.960184\pi\) | |||||||
\(24\) | 13644.6 | − | 23633.1i | 0.987021 | − | 1.70957i | ||||
\(25\) | −5084.24 | − | 8806.16i | −0.325391 | − | 0.563594i | ||||
\(26\) | −16851.8 | + | 9729.39i | −0.958796 | + | 0.553561i | ||||
\(27\) | − | 20280.9i | − | 1.03037i | ||||||
\(28\) | 49350.4 | − | 28492.5i | 2.24811 | − | 1.29794i | ||||
\(29\) | 3269.02 | − | 1887.37i | 0.134037 | − | 0.0773860i | −0.431482 | − | 0.902121i | \(-0.642009\pi\) |
0.565519 | + | 0.824735i | \(0.308676\pi\) | |||||||
\(30\) | −17191.8 | + | 9925.68i | −0.636733 | + | 0.367618i | ||||
\(31\) | −29197.4 | + | 50571.3i | −0.980074 | + | 1.69754i | −0.318014 | + | 0.948086i | \(0.603016\pi\) |
−0.662060 | + | 0.749451i | \(0.730318\pi\) | |||||||
\(32\) | 94166.8i | 2.87374i | ||||||||
\(33\) | −17994.4 | − | 10389.1i | −0.500720 | − | 0.289091i | ||||
\(34\) | −41660.4 | + | 24052.6i | −1.05995 | + | 0.611964i | ||||
\(35\) | −25427.4 | −0.593060 | ||||||||
\(36\) | 34298.5 | + | 59406.8i | 0.735136 | + | 1.27329i | ||||
\(37\) | −22487.0 | − | 12982.9i | −0.443941 | − | 0.256310i | 0.261327 | − | 0.965250i | \(-0.415840\pi\) |
−0.705268 | + | 0.708941i | \(0.749173\pi\) | |||||||
\(38\) | −50468.0 | + | 87413.2i | −0.919741 | + | 1.59304i | ||||
\(39\) | 22781.4i | 0.384050i | ||||||||
\(40\) | 56822.3 | − | 98419.1i | 0.887848 | − | 1.53780i | ||||
\(41\) | 26952.4 | 0.391063 | 0.195531 | − | 0.980697i | \(-0.437357\pi\) | ||||
0.195531 | + | 0.980697i | \(0.437357\pi\) | |||||||
\(42\) | − | 92507.6i | − | 1.24862i | ||||||
\(43\) | 79186.0 | + | 7137.46i | 0.995962 | + | 0.0897715i | ||||
\(44\) | 193920. | 2.27648 | ||||||||
\(45\) | − | 30608.9i | − | 0.335900i | ||||||
\(46\) | −192892. | − | 111366.i | −1.98171 | − | 1.14414i | ||||
\(47\) | −198596. | −1.91283 | −0.956416 | − | 0.292006i | \(-0.905677\pi\) | ||||
−0.956416 | + | 0.292006i | \(0.905677\pi\) | |||||||
\(48\) | 195307. | + | 112761.i | 1.76602 | + | 1.01961i | ||||
\(49\) | 421.621 | − | 730.269i | 0.00358372 | − | 0.00620719i | ||||
\(50\) | 133420. | − | 77030.0i | 1.06736 | − | 0.616240i | ||||
\(51\) | 56319.4i | 0.424568i | ||||||||
\(52\) | −106308. | − | 184131.i | −0.756062 | − | 1.30954i | ||||
\(53\) | −120372. | + | 208490.i | −0.808531 | + | 1.40042i | 0.105350 | + | 0.994435i | \(0.466404\pi\) |
−0.913881 | + | 0.405981i | \(0.866930\pi\) | |||||||
\(54\) | 307270. | 1.95137 | ||||||||
\(55\) | −74936.8 | − | 43264.8i | −0.450409 | − | 0.260044i | ||||
\(56\) | 264793. | + | 458634.i | 1.50779 | + | 2.61157i | ||||
\(57\) | 59085.6 | + | 102339.i | 0.319049 | + | 0.552609i | ||||
\(58\) | 28595.0 | + | 49528.0i | 0.146557 | + | 0.253844i | ||||
\(59\) | 163320. | 0.795213 | 0.397607 | − | 0.917556i | \(-0.369841\pi\) | ||||
0.397607 | + | 0.917556i | \(0.369841\pi\) | |||||||
\(60\) | −108453. | − | 187846.i | −0.502098 | − | 0.869659i | ||||
\(61\) | 266231. | − | 153708.i | 1.17292 | − | 0.677187i | 0.218555 | − | 0.975825i | \(-0.429866\pi\) |
0.954366 | + | 0.298638i | \(0.0965323\pi\) | |||||||
\(62\) | −766193. | − | 442362.i | −3.21487 | − | 1.85610i | ||||
\(63\) | 123528. | + | 71318.9i | 0.494019 | + | 0.285222i | ||||
\(64\) | −612988. | −2.33836 | ||||||||
\(65\) | 94872.4i | 0.345462i | ||||||||
\(66\) | 157402. | − | 272628.i | 0.547492 | − | 0.948284i | ||||
\(67\) | −145518. | + | 252044.i | −0.483828 | + | 0.838015i | −0.999827 | − | 0.0185740i | \(-0.994087\pi\) |
0.515999 | + | 0.856589i | \(0.327421\pi\) | |||||||
\(68\) | −262811. | − | 455203.i | −0.835829 | − | 1.44770i | ||||
\(69\) | −225829. | + | 130382.i | −0.687435 | + | 0.396891i | ||||
\(70\) | − | 385244.i | − | 1.12316i | ||||||
\(71\) | 500666. | − | 289060.i | 1.39886 | − | 0.807630i | 0.404583 | − | 0.914501i | \(-0.367417\pi\) |
0.994273 | + | 0.106871i | \(0.0340832\pi\) | |||||||
\(72\) | −552092. | + | 318750.i | −1.47916 | + | 0.853991i | ||||
\(73\) | 9585.49 | − | 5534.19i | 0.0246403 | − | 0.0142261i | −0.487629 | − | 0.873051i | \(-0.662138\pi\) |
0.512270 | + | 0.858825i | \(0.328805\pi\) | |||||||
\(74\) | 196700. | − | 340694.i | 0.485410 | − | 0.840755i | ||||
\(75\) | − | 180366.i | − | 0.427535i | ||||||
\(76\) | −955122. | − | 551440.i | −2.17579 | − | 1.25620i | ||||
\(77\) | 349207. | − | 201615.i | 0.764910 | − | 0.441621i | ||||
\(78\) | −345156. | −0.727329 | ||||||||
\(79\) | 348781. | + | 604107.i | 0.707411 | + | 1.22527i | 0.965814 | + | 0.259234i | \(0.0834702\pi\) |
−0.258404 | + | 0.966037i | \(0.583196\pi\) | |||||||
\(80\) | 813349. | + | 469587.i | 1.58857 | + | 0.917163i | ||||
\(81\) | 28830.2 | − | 49935.4i | 0.0542491 | − | 0.0939622i | ||||
\(82\) | 408349.i | 0.740610i | ||||||||
\(83\) | 94634.3 | − | 163911.i | 0.165506 | − | 0.286665i | −0.771329 | − | 0.636437i | \(-0.780408\pi\) |
0.936835 | + | 0.349772i | \(0.113741\pi\) | |||||||
\(84\) | 1.01079e6 | 1.70538 | ||||||||
\(85\) | 234540.i | 0.381909i | ||||||||
\(86\) | −108138. | + | 1.19973e6i | −0.170013 | + | 1.88620i | ||||
\(87\) | 66955.4 | 0.101678 | ||||||||
\(88\) | 1.80218e6i | 2.64454i | ||||||||
\(89\) | 423625. | + | 244580.i | 0.600914 | + | 0.346938i | 0.769401 | − | 0.638766i | \(-0.220555\pi\) |
−0.168487 | + | 0.985704i | \(0.553888\pi\) | |||||||
\(90\) | 463747. | 0.636142 | ||||||||
\(91\) | −382876. | − | 221053.i | −0.508082 | − | 0.293341i | ||||
\(92\) | 1.21684e6 | − | 2.10764e6i | 1.56268 | − | 2.70665i | ||||
\(93\) | −897023. | + | 517896.i | −1.11520 | + | 0.643864i | ||||
\(94\) | − | 3.00888e6i | − | 3.62260i | ||||||
\(95\) | 246060. | + | 426188.i | 0.286992 | + | 0.497085i | ||||
\(96\) | −835154. | + | 1.44653e6i | −0.943959 | + | 1.63498i | ||||
\(97\) | 895486. | 0.981169 | 0.490584 | − | 0.871394i | \(-0.336783\pi\) | ||||
0.490584 | + | 0.871394i | \(0.336783\pi\) | |||||||
\(98\) | 11064.1 | + | 6387.87i | 0.0117554 | + | 0.00678700i | ||||
\(99\) | 242698. | + | 420366.i | 0.250127 | + | 0.433233i | ||||
\(100\) | 841669. | + | 1.45781e6i | 0.841669 | + | 1.45781i | ||||
\(101\) | 496645. | + | 860215.i | 0.482039 | + | 0.834916i | 0.999787 | − | 0.0206169i | \(-0.00656304\pi\) |
−0.517749 | + | 0.855533i | \(0.673230\pi\) | |||||||
\(102\) | −853280. | −0.804065 | ||||||||
\(103\) | −621056. | − | 1.07570e6i | −0.568354 | − | 0.984419i | −0.996729 | − | 0.0808173i | \(-0.974247\pi\) |
0.428375 | − | 0.903601i | \(-0.359086\pi\) | |||||||
\(104\) | 1.71121e6 | − | 987968.i | 1.52126 | − | 0.878300i | ||||
\(105\) | −390600. | − | 225513.i | −0.337415 | − | 0.194807i | ||||
\(106\) | −3.15877e6 | − | 1.82372e6i | −2.65217 | − | 1.53123i | ||||
\(107\) | 78155.5 | 0.0637982 | 0.0318991 | − | 0.999491i | \(-0.489844\pi\) | ||||
0.0318991 | + | 0.999491i | \(0.489844\pi\) | |||||||
\(108\) | 3.35739e6i | 2.66520i | ||||||||
\(109\) | 517811. | − | 896874.i | 0.399845 | − | 0.692551i | −0.593862 | − | 0.804567i | \(-0.702397\pi\) |
0.993706 | + | 0.112016i | \(0.0357307\pi\) | |||||||
\(110\) | 655493. | − | 1.13535e6i | 0.492482 | − | 0.853004i | ||||
\(111\) | −230287. | − | 398869.i | −0.168384 | − | 0.291649i | ||||
\(112\) | −3.79022e6 | + | 2.18828e6i | −2.69780 | + | 1.55758i | ||||
\(113\) | 1.19444e6i | 0.827804i | 0.910322 | + | 0.413902i | \(0.135834\pi\) | ||||
−0.910322 | + | 0.413902i | \(0.864166\pi\) | |||||||
\(114\) | −1.55052e6 | + | 895190.i | −1.04655 | + | 0.604228i | ||||
\(115\) | −940455. | + | 542972.i | −0.618364 | + | 0.357013i | ||||
\(116\) | −541169. | + | 312444.i | −0.346704 | + | 0.200170i | ||||
\(117\) | 266098. | − | 460896.i | 0.166144 | − | 0.287770i | ||||
\(118\) | 2.47442e6i | 1.50601i | ||||||||
\(119\) | −946530. | − | 546479.i | −0.561686 | − | 0.324290i | ||||
\(120\) | 1.74574e6 | − | 1.00790e6i | 1.01026 | − | 0.583276i | ||||
\(121\) | −399373. | −0.225435 | ||||||||
\(122\) | 2.32880e6 | + | 4.03359e6i | 1.28248 | + | 2.22133i | ||||
\(123\) | 414026. | + | 239038.i | 0.222491 | + | 0.128455i | ||||
\(124\) | 4.83347e6 | − | 8.37182e6i | 2.53509 | − | 4.39091i | ||||
\(125\) | − | 1.90532e6i | − | 0.975523i | ||||||
\(126\) | −1.08053e6 | + | 1.87154e6i | −0.540166 | + | 0.935594i | ||||
\(127\) | −2.33602e6 | −1.14042 | −0.570211 | − | 0.821498i | \(-0.693139\pi\) | ||||
−0.570211 | + | 0.821498i | \(0.693139\pi\) | |||||||
\(128\) | − | 3.26054e6i | − | 1.55475i | ||||||
\(129\) | 1.15310e6 | + | 811932.i | 0.537154 | + | 0.378225i | ||||
\(130\) | −1.43739e6 | −0.654250 | ||||||||
\(131\) | − | 239232.i | − | 0.106416i | −0.998583 | − | 0.0532078i | \(-0.983055\pi\) | ||
0.998583 | − | 0.0532078i | \(-0.0169446\pi\) | |||||||
\(132\) | 2.97887e6 | + | 1.71985e6i | 1.29518 | + | 0.747772i | ||||
\(133\) | −2.29328e6 | −0.974771 | ||||||||
\(134\) | −3.81865e6 | − | 2.20470e6i | −1.58707 | − | 0.916294i | ||||
\(135\) | 749056. | − | 1.29740e6i | 0.304448 | − | 0.527319i | ||||
\(136\) | 4.23039e6 | − | 2.44242e6i | 1.68176 | − | 0.970964i | ||||
\(137\) | 1.36946e6i | 0.532582i | 0.963893 | + | 0.266291i | \(0.0857981\pi\) | ||||
−0.963893 | + | 0.266291i | \(0.914202\pi\) | |||||||
\(138\) | −1.97539e6 | − | 3.42147e6i | −0.751649 | − | 1.30189i | ||||
\(139\) | 569254. | − | 985977.i | 0.211964 | − | 0.367132i | −0.740365 | − | 0.672205i | \(-0.765347\pi\) |
0.952329 | + | 0.305073i | \(0.0986808\pi\) | |||||||
\(140\) | 4.20938e6 | 1.53403 | ||||||||
\(141\) | −3.05071e6 | − | 1.76133e6i | −1.08829 | − | 0.628322i | ||||
\(142\) | 4.37947e6 | + | 7.58546e6i | 1.52952 | + | 2.64921i | ||||
\(143\) | −752245. | − | 1.30293e6i | −0.257247 | − | 0.445565i | ||||
\(144\) | −2.63420e6 | − | 4.56257e6i | −0.882188 | − | 1.52799i | ||||
\(145\) | 278833. | 0.0914619 | ||||||||
\(146\) | 83847.0 | + | 145227.i | 0.0269419 | + | 0.0466648i | ||||
\(147\) | 12953.3 | − | 7478.62i | 0.00407784 | − | 0.00235434i | ||||
\(148\) | 3.72260e6 | + | 2.14924e6i | 1.14831 | + | 0.662980i | ||||
\(149\) | −734887. | − | 424287.i | −0.222158 | − | 0.128263i | 0.384791 | − | 0.923004i | \(-0.374273\pi\) |
−0.606949 | + | 0.794741i | \(0.707607\pi\) | |||||||
\(150\) | 2.73268e6 | 0.809683 | ||||||||
\(151\) | 3.95092e6i | 1.14754i | 0.819017 | + | 0.573770i | \(0.194520\pi\) | ||||
−0.819017 | + | 0.573770i | \(0.805480\pi\) | |||||||
\(152\) | 5.12476e6 | − | 8.87635e6i | 1.45929 | − | 2.52757i | ||||
\(153\) | 657838. | − | 1.13941e6i | 0.183673 | − | 0.318130i | ||||
\(154\) | 3.05461e6 | + | 5.29074e6i | 0.836360 | + | 1.44862i | ||||
\(155\) | −3.73562e6 | + | 2.15676e6i | −1.00315 | + | 0.579170i | ||||
\(156\) | − | 3.77135e6i | − | 0.993397i | ||||||
\(157\) | 677236. | − | 391002.i | 0.175001 | − | 0.101037i | −0.409941 | − | 0.912112i | \(-0.634451\pi\) |
0.584942 | + | 0.811075i | \(0.301117\pi\) | |||||||
\(158\) | −9.15266e6 | + | 5.28429e6i | −2.32047 | + | 1.33972i | ||||
\(159\) | −3.69814e6 | + | 2.13512e6i | −0.920010 | + | 0.531168i | ||||
\(160\) | −3.47797e6 | + | 6.02402e6i | −0.849113 | + | 1.47071i | ||||
\(161\) | − | 5.06051e6i | − | 1.21260i | ||||||
\(162\) | 756558. | + | 436799.i | 0.177950 | + | 0.102739i | ||||
\(163\) | 4.01220e6 | − | 2.31644e6i | 0.926445 | − | 0.534883i | 0.0407593 | − | 0.999169i | \(-0.487022\pi\) |
0.885685 | + | 0.464286i | \(0.153689\pi\) | |||||||
\(164\) | −4.46183e6 | −1.01154 | ||||||||
\(165\) | −767421. | − | 1.32921e6i | −0.170837 | − | 0.295898i | ||||
\(166\) | 2.48338e6 | + | 1.43378e6i | 0.542898 | + | 0.313443i | ||||
\(167\) | −3.84335e6 | + | 6.65688e6i | −0.825203 | + | 1.42929i | 0.0765608 | + | 0.997065i | \(0.475606\pi\) |
−0.901764 | + | 0.432229i | \(0.857727\pi\) | |||||||
\(168\) | 9.39366e6i | 1.98110i | ||||||||
\(169\) | 1.58863e6 | − | 2.75159e6i | 0.329127 | − | 0.570064i | ||||
\(170\) | −3.55345e6 | −0.723275 | ||||||||
\(171\) | − | 2.76059e6i | − | 0.552096i | ||||||
\(172\) | −1.31088e7 | − | 1.18157e6i | −2.57619 | − | 0.232206i | ||||
\(173\) | 2.74566e6 | 0.530283 | 0.265142 | − | 0.964209i | \(-0.414581\pi\) | ||||
0.265142 | + | 0.964209i | \(0.414581\pi\) | |||||||
\(174\) | 1.01442e6i | 0.192562i | ||||||||
\(175\) | 3.03132e6 | + | 1.75013e6i | 0.565611 | + | 0.326555i | ||||
\(176\) | −1.48935e7 | −2.73185 | ||||||||
\(177\) | 2.50882e6 | + | 1.44847e6i | 0.452428 | + | 0.261209i | ||||
\(178\) | −3.70557e6 | + | 6.41824e6i | −0.657045 | + | 1.13804i | ||||
\(179\) | 9.12503e6 | − | 5.26834e6i | 1.59102 | − | 0.918575i | 0.597885 | − | 0.801582i | \(-0.296008\pi\) |
0.993133 | − | 0.116993i | \(-0.0373254\pi\) | |||||||
\(180\) | 5.06714e6i | 0.868851i | ||||||||
\(181\) | −5.75180e6 | − | 9.96241e6i | −0.969991 | − | 1.68007i | −0.695560 | − | 0.718468i | \(-0.744844\pi\) |
−0.274431 | − | 0.961607i | \(-0.588490\pi\) | |||||||
\(182\) | 3.34912e6 | − | 5.80085e6i | 0.555542 | − | 0.962226i | ||||
\(183\) | 5.45289e6 | 0.889761 | ||||||||
\(184\) | 1.95871e7 | + | 1.13086e7i | 3.14425 | + | 1.81534i | ||||
\(185\) | −959020. | − | 1.66107e6i | −0.151465 | − | 0.262345i | ||||
\(186\) | −7.84651e6 | − | 1.35905e7i | −1.21938 | − | 2.11202i | ||||
\(187\) | −1.85967e6 | − | 3.22104e6i | −0.284388 | − | 0.492574i | ||||
\(188\) | 3.28765e7 | 4.94780 | ||||||||
\(189\) | 3.49061e6 | + | 6.04591e6i | 0.517030 | + | 0.895523i | ||||
\(190\) | −6.45706e6 | + | 3.72799e6i | −0.941400 | + | 0.543517i | ||||
\(191\) | 1.00169e7 | + | 5.78326e6i | 1.43758 | + | 0.829990i | 0.997682 | − | 0.0680560i | \(-0.0216796\pi\) |
0.439903 | + | 0.898046i | \(0.355013\pi\) | |||||||
\(192\) | −9.41632e6 | − | 5.43652e6i | −1.33039 | − | 0.768099i | ||||
\(193\) | 3.60963e6 | 0.502101 | 0.251050 | − | 0.967974i | \(-0.419224\pi\) | ||||
0.251050 | + | 0.967974i | \(0.419224\pi\) | |||||||
\(194\) | 1.35673e7i | 1.85818i | ||||||||
\(195\) | −841412. | + | 1.45737e6i | −0.113476 | + | 0.196547i | ||||
\(196\) | −69797.1 | + | 120892.i | −0.00926978 | + | 0.0160557i | ||||
\(197\) | −5.71614e6 | − | 9.90065e6i | −0.747661 | − | 1.29499i | −0.948941 | − | 0.315453i | \(-0.897844\pi\) |
0.201281 | − | 0.979534i | \(-0.435490\pi\) | |||||||
\(198\) | −6.36885e6 | + | 3.67706e6i | −0.820475 | + | 0.473702i | ||||
\(199\) | 5.61273e6i | 0.712221i | 0.934444 | + | 0.356110i | \(0.115897\pi\) | ||||
−0.934444 | + | 0.356110i | \(0.884103\pi\) | |||||||
\(200\) | −1.35481e7 | + | 7.82199e6i | −1.69351 | + | 0.977748i | ||||
\(201\) | −4.47070e6 | + | 2.58116e6i | −0.550538 | + | 0.317853i | ||||
\(202\) | −1.30329e7 | + | 7.52454e6i | −1.58120 | + | 0.912905i | ||||
\(203\) | −649683. | + | 1.12528e6i | −0.0776629 | + | 0.134516i | ||||
\(204\) | − | 9.32338e6i | − | 1.09820i | ||||||
\(205\) | 1.72419e6 | + | 995464.i | 0.200136 | + | 0.115548i | ||||
\(206\) | 1.62977e7 | − | 9.40946e6i | 1.86433 | − | 1.07637i | ||||
\(207\) | 6.09171e6 | 0.686797 | ||||||||
\(208\) | 8.16471e6 | + | 1.41417e7i | 0.907300 | + | 1.57149i | ||||
\(209\) | −6.75850e6 | − | 3.90202e6i | −0.740306 | − | 0.427416i | ||||
\(210\) | 3.41669e6 | − | 5.91788e6i | 0.368933 | − | 0.639011i | ||||
\(211\) | 7.60059e6i | 0.809096i | 0.914517 | + | 0.404548i | \(0.132571\pi\) | ||||
−0.914517 | + | 0.404548i | \(0.867429\pi\) | |||||||
\(212\) | 1.99269e7 | − | 3.45144e7i | 2.09138 | − | 3.62237i | ||||
\(213\) | 1.02545e7 | 1.06115 | ||||||||
\(214\) | 1.18411e6i | 0.120824i | ||||||||
\(215\) | 4.80205e6 | + | 3.38126e6i | 0.483183 | + | 0.340223i | ||||
\(216\) | −3.12016e7 | −3.09611 | ||||||||
\(217\) | − | 2.01010e7i | − | 1.96716i | ||||||
\(218\) | 1.35883e7 | + | 7.84521e6i | 1.31158 | + | 0.757243i | ||||
\(219\) | 196328. | 0.0186918 | ||||||||
\(220\) | 1.24054e7 | + | 7.16226e6i | 1.16504 | + | 0.672639i | ||||
\(221\) | −2.03897e6 | + | 3.53160e6i | −0.188901 | + | 0.327186i | ||||
\(222\) | 6.04315e6 | − | 3.48901e6i | 0.552337 | − | 0.318892i | ||||
\(223\) | 1.74335e6i | 0.157206i | 0.996906 | + | 0.0786030i | \(0.0250460\pi\) | ||||
−0.996906 | + | 0.0786030i | \(0.974954\pi\) | |||||||
\(224\) | −1.62074e7 | − | 2.80720e7i | −1.44201 | − | 2.49764i | ||||
\(225\) | −2.10676e6 | + | 3.64902e6i | −0.184956 | + | 0.320353i | ||||
\(226\) | −1.80966e7 | −1.56773 | ||||||||
\(227\) | 1.15973e6 | + | 669570.i | 0.0991469 | + | 0.0572425i | 0.548754 | − | 0.835984i | \(-0.315103\pi\) |
−0.449607 | + | 0.893227i | \(0.648436\pi\) | |||||||
\(228\) | −9.78131e6 | − | 1.69417e7i | −0.825263 | − | 1.42940i | ||||
\(229\) | −3.66746e6 | − | 6.35222e6i | −0.305393 | − | 0.528955i | 0.671956 | − | 0.740591i | \(-0.265454\pi\) |
−0.977349 | + | 0.211636i | \(0.932121\pi\) | |||||||
\(230\) | −8.22642e6 | − | 1.42486e7i | −0.676126 | − | 1.17108i | ||||
\(231\) | 7.15238e6 | 0.580250 | ||||||||
\(232\) | −2.90367e6 | − | 5.02931e6i | −0.232532 | − | 0.402758i | ||||
\(233\) | −1.02503e7 | + | 5.91799e6i | −0.810340 | + | 0.467850i | −0.847074 | − | 0.531475i | \(-0.821638\pi\) |
0.0367338 | + | 0.999325i | \(0.488305\pi\) | |||||||
\(234\) | 6.98291e6 | + | 4.03158e6i | 0.544990 | + | 0.314650i | ||||
\(235\) | −1.27045e7 | − | 7.33497e6i | −0.978939 | − | 0.565190i | ||||
\(236\) | −2.70368e7 | −2.05693 | ||||||||
\(237\) | 1.23732e7i | 0.929473i | ||||||||
\(238\) | 8.27956e6 | − | 1.43406e7i | 0.614153 | − | 1.06374i | ||||
\(239\) | −1.10330e7 | + | 1.91098e7i | −0.808167 | + | 1.39979i | 0.105966 | + | 0.994370i | \(0.466207\pi\) |
−0.914132 | + | 0.405416i | \(0.867127\pi\) | |||||||
\(240\) | 8.32943e6 | + | 1.44270e7i | 0.602534 | + | 1.04362i | ||||
\(241\) | 4.78634e6 | − | 2.76339e6i | 0.341942 | − | 0.197420i | −0.319189 | − | 0.947691i | \(-0.603410\pi\) |
0.661130 | + | 0.750271i | \(0.270077\pi\) | |||||||
\(242\) | − | 6.05079e6i | − | 0.426939i | ||||||
\(243\) | −1.19182e7 | + | 6.88099e6i | −0.830602 | + | 0.479548i | ||||
\(244\) | −4.40731e7 | + | 2.54456e7i | −3.03392 | + | 1.75164i | ||||
\(245\) | 53943.7 | − | 31144.4i | 0.00366811 | − | 0.00211779i | ||||
\(246\) | −3.62160e6 | + | 6.27279e6i | −0.243274 | + | 0.421362i | ||||
\(247\) | 8.55647e6i | 0.567811i | ||||||||
\(248\) | 7.78028e7 | + | 4.49195e7i | 5.10082 | + | 2.94496i | ||||
\(249\) | 2.90742e6 | − | 1.67860e6i | 0.188326 | − | 0.108730i | ||||
\(250\) | 2.88670e7 | 1.84749 | ||||||||
\(251\) | 1.97528e6 | + | 3.42128e6i | 0.124913 | + | 0.216356i | 0.921699 | − | 0.387906i | \(-0.126802\pi\) |
−0.796786 | + | 0.604262i | \(0.793468\pi\) | |||||||
\(252\) | −2.04494e7 | − | 1.18065e7i | −1.27785 | − | 0.737766i | ||||
\(253\) | 8.61046e6 | − | 1.49138e7i | 0.531698 | − | 0.920928i | ||||
\(254\) | − | 3.53924e7i | − | 2.15978i | ||||||
\(255\) | −2.08011e6 | + | 3.60285e6i | −0.125448 | + | 0.217283i | ||||
\(256\) | 1.01683e7 | 0.606079 | ||||||||
\(257\) | 7.57008e6i | 0.445965i | 0.974822 | + | 0.222983i | \(0.0715794\pi\) | ||||
−0.974822 | + | 0.222983i | \(0.928421\pi\) | |||||||
\(258\) | −1.23014e7 | + | 1.74704e7i | −0.716299 | + | 1.01728i | ||||
\(259\) | 8.93810e6 | 0.514453 | ||||||||
\(260\) | − | 1.57056e7i | − | 0.893584i | ||||||
\(261\) | −1.35459e6 | − | 782072.i | −0.0761878 | − | 0.0439871i | ||||
\(262\) | 3.62454e6 | 0.201534 | ||||||||
\(263\) | −8.11313e6 | − | 4.68412e6i | −0.445986 | − | 0.257490i | 0.260147 | − | 0.965569i | \(-0.416229\pi\) |
−0.706133 | + | 0.708079i | \(0.749562\pi\) | |||||||
\(264\) | −1.59833e7 | + | 2.76839e7i | −0.868670 | + | 1.50458i | ||||
\(265\) | −1.54008e7 | + | 8.89164e6i | −0.827571 | + | 0.477798i | ||||
\(266\) | − | 3.47449e7i | − | 1.84606i | ||||||
\(267\) | 4.33831e6 | + | 7.51417e6i | 0.227922 | + | 0.394773i | ||||
\(268\) | 2.40897e7 | − | 4.17245e7i | 1.25149 | − | 2.16764i | ||||
\(269\) | 3.00182e6 | 0.154215 | 0.0771077 | − | 0.997023i | \(-0.475431\pi\) | ||||
0.0771077 | + | 0.997023i | \(0.475431\pi\) | |||||||
\(270\) | 1.96566e7 | + | 1.13487e7i | 0.998659 | + | 0.576576i | ||||
\(271\) | −624680. | − | 1.08198e6i | −0.0313870 | − | 0.0543639i | 0.849905 | − | 0.526936i | \(-0.176659\pi\) |
−0.881292 | + | 0.472572i | \(0.843326\pi\) | |||||||
\(272\) | 2.01845e7 | + | 3.49605e7i | 1.00302 | + | 1.73729i | ||||
\(273\) | −3.92099e6 | − | 6.79136e6i | −0.192712 | − | 0.333787i | ||||
\(274\) | −2.07483e7 | −1.00863 | ||||||||
\(275\) | 5.95570e6 | + | 1.03156e7i | 0.286375 | + | 0.496016i | ||||
\(276\) | 3.73847e7 | − | 2.15841e7i | 1.77815 | − | 1.02661i | ||||
\(277\) | −2.91712e7 | − | 1.68420e7i | −1.37251 | − | 0.792418i | −0.381265 | − | 0.924466i | \(-0.624511\pi\) |
−0.991243 | + | 0.132048i | \(0.957845\pi\) | |||||||
\(278\) | 1.49383e7 | + | 8.62461e6i | 0.695290 | + | 0.401426i | ||||
\(279\) | 2.41971e7 | 1.11417 | ||||||||
\(280\) | 3.91195e7i | 1.78205i | ||||||||
\(281\) | 1.25507e6 | − | 2.17384e6i | 0.0565650 | − | 0.0979734i | −0.836356 | − | 0.548186i | \(-0.815319\pi\) |
0.892921 | + | 0.450213i | \(0.148652\pi\) | |||||||
\(282\) | 2.66854e7 | − | 4.62204e7i | 1.18994 | − | 2.06104i | ||||
\(283\) | −1.16382e7 | − | 2.01580e7i | −0.513484 | − | 0.889381i | −0.999878 | − | 0.0156411i | \(-0.995021\pi\) |
0.486393 | − | 0.873740i | \(-0.338312\pi\) | |||||||
\(284\) | −8.28826e7 | + | 4.78523e7i | −3.61833 | + | 2.08905i | ||||
\(285\) | 8.72910e6i | 0.377081i | ||||||||
\(286\) | 1.97403e7 | − | 1.13971e7i | 0.843830 | − | 0.487186i | ||||
\(287\) | −8.03477e6 | + | 4.63888e6i | −0.339882 | + | 0.196231i | ||||
\(288\) | 3.37923e7 | − | 1.95100e7i | 1.41462 | − | 0.816733i | ||||
\(289\) | 7.02812e6 | − | 1.21731e7i | 0.291169 | − | 0.504320i | ||||
\(290\) | 4.22453e6i | 0.173214i | ||||||||
\(291\) | 1.37559e7 | + | 7.94197e6i | 0.558225 | + | 0.322292i | ||||
\(292\) | −1.58683e6 | + | 916155.i | −0.0637355 | + | 0.0367977i | ||||
\(293\) | 1.78262e7 | 0.708691 | 0.354345 | − | 0.935115i | \(-0.384704\pi\) | ||||
0.354345 | + | 0.935115i | \(0.384704\pi\) | |||||||
\(294\) | 113307. | + | 196253.i | 0.00445875 | + | 0.00772278i | ||||
\(295\) | 1.04479e7 | + | 6.03208e6i | 0.406970 | + | 0.234964i | ||||
\(296\) | −1.99738e7 | + | 3.45957e7i | −0.770169 | + | 1.33397i | ||||
\(297\) | 2.37571e7i | 0.906826i | ||||||||
\(298\) | 6.42826e6 | − | 1.11341e7i | 0.242910 | − | 0.420732i | ||||
\(299\) | −1.88813e7 | −0.706347 | ||||||||
\(300\) | 2.98587e7i | 1.10588i | ||||||||
\(301\) | −2.48345e7 | + | 1.15012e7i | −0.910661 | + | 0.421740i | ||||
\(302\) | −5.98594e7 | −2.17326 | ||||||||
\(303\) | 1.76188e7i | 0.633355i | ||||||||
\(304\) | 7.33554e7 | + | 4.23518e7i | 2.61103 | + | 1.50748i | ||||
\(305\) | 2.27084e7 | 0.800361 | ||||||||
\(306\) | 1.72629e7 | + | 9.96672e6i | 0.602489 | + | 0.347847i | ||||
\(307\) | −1.40587e7 | + | 2.43504e7i | −0.485881 | + | 0.841571i | −0.999868 | − | 0.0162271i | \(-0.994835\pi\) |
0.513987 | + | 0.857798i | \(0.328168\pi\) | |||||||
\(308\) | −5.78093e7 | + | 3.33762e7i | −1.97854 | + | 1.14231i | ||||
\(309\) | − | 2.20323e7i | − | 0.746766i | ||||||
\(310\) | −3.26765e7 | − | 5.65973e7i | −1.09686 | − | 1.89981i | ||||
\(311\) | −2.27588e7 | + | 3.94193e7i | −0.756602 | + | 1.31047i | 0.187972 | + | 0.982174i | \(0.439809\pi\) |
−0.944574 | + | 0.328299i | \(0.893525\pi\) | |||||||
\(312\) | 3.50487e7 | 1.15401 | ||||||||
\(313\) | −2.58144e7 | − | 1.49039e7i | −0.841839 | − | 0.486036i | 0.0160500 | − | 0.999871i | \(-0.494891\pi\) |
−0.857889 | + | 0.513835i | \(0.828224\pi\) | |||||||
\(314\) | 5.92397e6 | + | 1.02606e7i | 0.191348 | + | 0.331425i | ||||
\(315\) | 5.26820e6 | + | 9.12480e6i | 0.168551 | + | 0.291939i | ||||
\(316\) | −5.77389e7 | − | 1.00007e8i | −1.82981 | − | 3.16933i | ||||
\(317\) | −5.61205e6 | −0.176175 | −0.0880873 | − | 0.996113i | \(-0.528075\pi\) | ||||
−0.0880873 | + | 0.996113i | \(0.528075\pi\) | |||||||
\(318\) | −3.23487e7 | − | 5.60296e7i | −1.00595 | − | 1.74235i | ||||
\(319\) | −3.82934e6 | + | 2.21087e6i | −0.117965 | + | 0.0681070i | ||||
\(320\) | −3.92139e7 | − | 2.26402e7i | −1.19671 | − | 0.690923i | ||||
\(321\) | 1.20057e6 | + | 693152.i | 0.0362973 | + | 0.0209562i | ||||
\(322\) | 7.66705e7 | 2.29647 | ||||||||
\(323\) | 2.11530e7i | 0.627717i | ||||||||
\(324\) | −4.77269e6 | + | 8.26654e6i | −0.140323 | + | 0.243046i | ||||
\(325\) | 6.52993e6 | − | 1.13102e7i | 0.190221 | − | 0.329472i | ||||
\(326\) | 3.50958e7 | + | 6.07877e7i | 1.01298 | + | 1.75454i | ||||
\(327\) | 1.59085e7 | − | 9.18481e6i | 0.454975 | − | 0.262680i | ||||
\(328\) | − | 4.14657e7i | − | 1.17508i | ||||||
\(329\) | 5.92033e7 | − | 3.41811e7i | 1.66249 | − | 0.959838i | ||||
\(330\) | 2.01385e7 | − | 1.16270e7i | 0.560385 | − | 0.323538i | ||||
\(331\) | −7.65746e6 | + | 4.42103e6i | −0.211155 | + | 0.121910i | −0.601848 | − | 0.798611i | \(-0.705569\pi\) |
0.390693 | + | 0.920521i | \(0.372235\pi\) | |||||||
\(332\) | −1.56662e7 | + | 2.71347e7i | −0.428104 | + | 0.741498i | ||||
\(333\) | 1.07594e7i | 0.291378i | ||||||||
\(334\) | −1.00857e8 | − | 5.82296e7i | −2.70686 | − | 1.56280i | ||||
\(335\) | −1.86180e7 | + | 1.07491e7i | −0.495222 | + | 0.285916i | ||||
\(336\) | −7.76305e7 | −2.04651 | ||||||||
\(337\) | −1.73029e7 | − | 2.99695e7i | −0.452094 | − | 0.783050i | 0.546422 | − | 0.837510i | \(-0.315990\pi\) |
−0.998516 | + | 0.0544601i | \(0.982656\pi\) | |||||||
\(338\) | 4.16886e7 | + | 2.40689e7i | 1.07961 | + | 0.623314i | ||||
\(339\) | −1.05933e7 | + | 1.83482e7i | −0.271915 | + | 0.470970i | ||||
\(340\) | − | 3.88268e7i | − | 0.987860i | ||||||
\(341\) | 3.42019e7 | − | 5.92395e7i | 0.862556 | − | 1.49399i | ||||
\(342\) | 4.18250e7 | 1.04558 | ||||||||
\(343\) | − | 4.02077e7i | − | 0.996384i | ||||||
\(344\) | 1.09808e7 | − | 1.21826e8i | 0.269749 | − | 2.99271i | ||||
\(345\) | −1.92622e7 | −0.469082 | ||||||||
\(346\) | 4.15987e7i | 1.00427i | ||||||||
\(347\) | 2.21778e7 | + | 1.28044e7i | 0.530800 | + | 0.306458i | 0.741342 | − | 0.671127i | \(-0.234190\pi\) |
−0.210542 | + | 0.977585i | \(0.567523\pi\) | |||||||
\(348\) | −1.10841e7 | −0.263005 | ||||||||
\(349\) | 2.95681e7 | + | 1.70712e7i | 0.695580 | + | 0.401593i | 0.805699 | − | 0.592325i | \(-0.201790\pi\) |
−0.110119 | + | 0.993918i | \(0.535123\pi\) | |||||||
\(350\) | −2.65158e7 | + | 4.59267e7i | −0.618444 | + | 1.07118i | ||||
\(351\) | 2.25579e7 | − | 1.30238e7i | 0.521648 | − | 0.301174i | ||||
\(352\) | − | 1.10307e8i | − | 2.52916i | ||||||
\(353\) | 2.17271e7 | + | 3.76325e7i | 0.493945 | + | 0.855538i | 0.999976 | − | 0.00697779i | \(-0.00222112\pi\) |
−0.506031 | + | 0.862515i | \(0.668888\pi\) | |||||||
\(354\) | −2.19453e7 | + | 3.80104e7i | −0.494689 | + | 0.856827i | ||||
\(355\) | 4.27047e7 | 0.954532 | ||||||||
\(356\) | −7.01290e7 | − | 4.04890e7i | −1.55434 | − | 0.897401i | ||||
\(357\) | −9.69333e6 | − | 1.67893e7i | −0.213043 | − | 0.369002i | ||||
\(358\) | 7.98192e7 | + | 1.38251e8i | 1.73963 | + | 3.01314i | ||||
\(359\) | 1.87165e7 | + | 3.24179e7i | 0.404521 | + | 0.700651i | 0.994266 | − | 0.106939i | \(-0.0341050\pi\) |
−0.589745 | + | 0.807590i | \(0.700772\pi\) | |||||||
\(360\) | −4.70911e7 | −1.00933 | ||||||||
\(361\) | −1.33099e6 | − | 2.30534e6i | −0.0282913 | − | 0.0490020i | ||||
\(362\) | 1.50938e8 | − | 8.71440e7i | 3.18180 | − | 1.83701i | ||||
\(363\) | −6.13491e6 | − | 3.54199e6i | −0.128259 | − | 0.0740504i | ||||
\(364\) | 6.33830e7 | + | 3.65942e7i | 1.31422 | + | 0.758767i | ||||
\(365\) | 817601. | 0.0168137 | ||||||||
\(366\) | 8.26153e7i | 1.68507i | ||||||||
\(367\) | 2.80728e7 | − | 4.86235e7i | 0.567920 | − | 0.983667i | −0.428851 | − | 0.903375i | \(-0.641082\pi\) |
0.996771 | − | 0.0802916i | \(-0.0255851\pi\) | |||||||
\(368\) | −9.34562e7 | + | 1.61871e8i | −1.87527 | + | 3.24807i | ||||
\(369\) | −5.58416e6 | − | 9.67204e6i | −0.111142 | − | 0.192504i | ||||
\(370\) | 2.51665e7 | − | 1.45299e7i | 0.496840 | − | 0.286851i | ||||
\(371\) | − | 8.28704e7i | − | 1.62285i | ||||||
\(372\) | 1.48497e8 | − | 8.57350e7i | 2.88463 | − | 1.66544i | ||||
\(373\) | 1.88413e7 | − | 1.08780e7i | 0.363064 | − | 0.209615i | −0.307360 | − | 0.951593i | \(-0.599446\pi\) |
0.670424 | + | 0.741978i | \(0.266112\pi\) | |||||||
\(374\) | 4.88011e7 | − | 2.81754e7i | 0.932857 | − | 0.538585i | ||||
\(375\) | 1.68981e7 | − | 2.92683e7i | 0.320437 | − | 0.555014i | ||||
\(376\) | 3.05535e8i | 5.74775i | ||||||||
\(377\) | 4.19855e6 | + | 2.42403e6i | 0.0783566 | + | 0.0452392i | ||||
\(378\) | −9.16000e7 | + | 5.28853e7i | −1.69598 | + | 0.979173i | ||||
\(379\) | −1.04980e7 | −0.192837 | −0.0964186 | − | 0.995341i | \(-0.530739\pi\) | ||||
−0.0964186 | + | 0.995341i | \(0.530739\pi\) | |||||||
\(380\) | −4.07339e7 | − | 7.05532e7i | −0.742344 | − | 1.28578i | ||||
\(381\) | −3.58845e7 | − | 2.07179e7i | −0.648831 | − | 0.374603i | ||||
\(382\) | −8.76206e7 | + | 1.51763e8i | −1.57187 | + | 2.72256i | ||||
\(383\) | − | 6.08536e7i | − | 1.08315i | −0.840651 | − | 0.541577i | \(-0.817827\pi\) | ||
0.840651 | − | 0.541577i | \(-0.182173\pi\) | |||||||
\(384\) | 2.89173e7 | − | 5.00863e7i | 0.510698 | − | 0.884555i | ||||
\(385\) | 2.97858e7 | 0.521948 | ||||||||
\(386\) | 5.46886e7i | 0.950899i | ||||||||
\(387\) | −1.38449e7 | − | 2.98952e7i | −0.238867 | − | 0.515784i | ||||
\(388\) | −1.48243e8 | −2.53793 | ||||||||
\(389\) | 6.51260e7i | 1.10638i | 0.833054 | + | 0.553192i | \(0.186590\pi\) | ||||
−0.833054 | + | 0.553192i | \(0.813410\pi\) | |||||||
\(390\) | −2.20802e7 | − | 1.27480e7i | −0.372228 | − | 0.214906i | ||||
\(391\) | −4.66776e7 | −0.780869 | ||||||||
\(392\) | −1.12350e6 | − | 648654.i | −0.0186516 | − | 0.0107685i | ||||
\(393\) | 2.12172e6 | − | 3.67493e6i | 0.0349551 | − | 0.0605440i | ||||
\(394\) | 1.50002e8 | − | 8.66038e7i | 2.45250 | − | 1.41595i | ||||
\(395\) | 5.15277e7i | 0.836083i | ||||||||
\(396\) | −4.01774e7 | − | 6.95893e7i | −0.646988 | − | 1.12062i | ||||
\(397\) | −2.72536e7 | + | 4.72047e7i | −0.435565 | + | 0.754420i | −0.997342 | − | 0.0728685i | \(-0.976785\pi\) |
0.561777 | + | 0.827289i | \(0.310118\pi\) | |||||||
\(398\) | −8.50369e7 | −1.34883 | ||||||||
\(399\) | −3.52279e7 | − | 2.03389e7i | −0.554586 | − | 0.320190i | ||||
\(400\) | −6.46420e7 | − | 1.11963e8i | −1.01003 | − | 1.74943i | ||||
\(401\) | 1.18127e7 | + | 2.04602e7i | 0.183196 | + | 0.317304i | 0.942967 | − | 0.332886i | \(-0.108022\pi\) |
−0.759771 | + | 0.650190i | \(0.774689\pi\) | |||||||
\(402\) | −3.91064e7 | − | 6.77343e7i | −0.601963 | − | 1.04263i | ||||
\(403\) | −7.49991e7 | −1.14588 | ||||||||
\(404\) | −8.22170e7 | − | 1.42404e8i | −1.24686 | − | 2.15962i | ||||
\(405\) | 3.68864e6 | − | 2.12964e6i | 0.0555266 | − | 0.0320583i | ||||
\(406\) | −1.70489e7 | − | 9.84318e6i | −0.254752 | − | 0.147081i | ||||
\(407\) | 2.63413e7 | + | 1.52082e7i | 0.390710 | + | 0.225576i | ||||
\(408\) | 8.66461e7 | 1.27576 | ||||||||
\(409\) | − | 9.77849e7i | − | 1.42923i | −0.699518 | − | 0.714615i | \(-0.746602\pi\) | ||
0.699518 | − | 0.714615i | \(-0.253398\pi\) | |||||||
\(410\) | −1.50820e7 | + | 2.61228e7i | −0.218830 | + | 0.379025i | ||||
\(411\) | −1.21455e7 | + | 2.10367e7i | −0.174941 | + | 0.303007i | ||||
\(412\) | 1.02813e8 | + | 1.78077e8i | 1.47013 | + | 2.54633i | ||||
\(413\) | −4.86872e7 | + | 2.81096e7i | −0.691138 | + | 0.399029i | ||||
\(414\) | 9.22939e7i | 1.30068i | ||||||||
\(415\) | 1.21078e7 | − | 6.99047e6i | 0.169404 | − | 0.0978052i | ||||
\(416\) | −1.04739e8 | + | 6.04714e7i | −1.45489 | + | 0.839982i | ||||
\(417\) | 1.74890e7 | − | 1.00973e7i | 0.241189 | − | 0.139251i | ||||
\(418\) | 5.91185e7 | − | 1.02396e8i | 0.809458 | − | 1.40202i | ||||
\(419\) | 2.55991e7i | 0.348003i | 0.984745 | + | 0.174001i | \(0.0556697\pi\) | ||||
−0.984745 | + | 0.174001i | \(0.944330\pi\) | |||||||
\(420\) | 6.46618e7 | + | 3.73325e7i | 0.872770 | + | 0.503894i | ||||
\(421\) | 4.52772e7 | − | 2.61408e7i | 0.606783 | − | 0.350326i | −0.164923 | − | 0.986307i | \(-0.552737\pi\) |
0.771705 | + | 0.635980i | \(0.219404\pi\) | |||||||
\(422\) | −1.15155e8 | −1.53230 | ||||||||
\(423\) | 4.11463e7 | + | 7.12674e7i | 0.543637 | + | 0.941608i | ||||
\(424\) | 3.20757e8 | + | 1.85189e8i | 4.20802 | + | 2.42950i | ||||
\(425\) | 1.61430e7 | − | 2.79605e7i | 0.210290 | − | 0.364233i | ||||
\(426\) | 1.55364e8i | 2.00965i | ||||||||
\(427\) | −5.29106e7 | + | 9.16439e7i | −0.679609 | + | 1.17712i | ||||
\(428\) | −1.29382e7 | −0.165023 | ||||||||
\(429\) | − | 2.66863e7i | − | 0.338000i | ||||||
\(430\) | −5.12286e7 | + | 7.27546e7i | −0.644328 | + | 0.915072i | ||||
\(431\) | 7.90484e7 | 0.987328 | 0.493664 | − | 0.869653i | \(-0.335657\pi\) | ||||
0.493664 | + | 0.869653i | \(0.335657\pi\) | |||||||
\(432\) | − | 2.57855e8i | − | 3.19833i | ||||||
\(433\) | −9.70713e7 | − | 5.60442e7i | −1.19571 | − | 0.690346i | −0.236117 | − | 0.971725i | \(-0.575875\pi\) |
−0.959597 | + | 0.281379i | \(0.909208\pi\) | |||||||
\(434\) | 3.04546e8 | 3.72549 | ||||||||
\(435\) | 4.28326e6 | + | 2.47294e6i | 0.0520363 | + | 0.0300432i | ||||
\(436\) | −8.57208e7 | + | 1.48473e8i | −1.03425 | + | 1.79138i | ||||
\(437\) | −8.48189e7 | + | 4.89702e7i | −1.01636 | + | 0.586797i | ||||
\(438\) | 2.97452e6i | 0.0353993i | ||||||||
\(439\) | −4.61110e7 | − | 7.98666e7i | −0.545018 | − | 0.944000i | −0.998606 | − | 0.0527878i | \(-0.983189\pi\) |
0.453587 | − | 0.891212i | \(-0.350144\pi\) | |||||||
\(440\) | −6.65619e7 | + | 1.15289e8i | −0.781390 | + | 1.35341i | ||||
\(441\) | −349416. | −0.00407405 | ||||||||
\(442\) | −5.35063e7 | − | 3.08919e7i | −0.619639 | − | 0.357749i | ||||
\(443\) | −7.03615e7 | − | 1.21870e8i | −0.809326 | − | 1.40179i | −0.913331 | − | 0.407218i | \(-0.866499\pi\) |
0.104005 | − | 0.994577i | \(-0.466834\pi\) | |||||||
\(444\) | 3.81228e7 | + | 6.60306e7i | 0.435547 | + | 0.754390i | ||||
\(445\) | 1.80667e7 | + | 3.12925e7i | 0.205021 | + | 0.355107i | ||||
\(446\) | −2.64130e7 | −0.297723 | ||||||||
\(447\) | −7.52590e6 | − | 1.30352e7i | −0.0842629 | − | 0.145948i | ||||
\(448\) | 1.82737e8 | − | 1.05503e8i | 2.03233 | − | 1.17336i | ||||
\(449\) | −5.15468e7 | − | 2.97606e7i | −0.569460 | − | 0.328778i | 0.187474 | − | 0.982270i | \(-0.439970\pi\) |
−0.756933 | + | 0.653492i | \(0.773303\pi\) | |||||||
\(450\) | −5.52854e7 | − | 3.19190e7i | −0.606698 | − | 0.350277i | ||||
\(451\) | −3.15722e7 | −0.344172 | ||||||||
\(452\) | − | 1.97732e8i | − | 2.14123i | ||||||
\(453\) | −3.50403e7 | + | 6.06915e7i | −0.376941 | + | 0.652880i | ||||
\(454\) | −1.01445e7 | + | 1.75708e7i | −0.108408 | + | 0.187769i | ||||
\(455\) | −1.63288e7 | − | 2.82824e7i | −0.173349 | − | 0.300249i | ||||
\(456\) | 1.57447e8 | − | 9.09018e7i | 1.66050 | − | 0.958690i | ||||
\(457\) | 3.35987e7i | 0.352025i | 0.984388 | + | 0.176012i | \(0.0563199\pi\) | ||||
−0.984388 | + | 0.176012i | \(0.943680\pi\) | |||||||
\(458\) | 9.62408e7 | − | 5.55647e7i | 1.00176 | − | 0.578365i | ||||
\(459\) | 5.57668e7 | − | 3.21970e7i | 0.576684 | − | 0.332949i | ||||
\(460\) | 1.55687e8 | − | 8.98861e7i | 1.59948 | − | 0.923462i | ||||
\(461\) | 1.41112e7 | − | 2.44413e7i | 0.144033 | − | 0.249472i | −0.784979 | − | 0.619522i | \(-0.787326\pi\) |
0.929012 | + | 0.370051i | \(0.120660\pi\) | |||||||
\(462\) | 1.08364e8i | 1.09890i | ||||||||
\(463\) | 1.46789e8 | + | 8.47487e7i | 1.47894 | + | 0.853867i | 0.999716 | − | 0.0238258i | \(-0.00758469\pi\) |
0.479224 | + | 0.877692i | \(0.340918\pi\) | |||||||
\(464\) | 4.15629e7 | − | 2.39964e7i | 0.416056 | − | 0.240210i | ||||
\(465\) | −7.65122e7 | −0.760977 | ||||||||
\(466\) | −8.96620e7 | − | 1.55299e8i | −0.886034 | − | 1.53466i | ||||
\(467\) | 8.43466e7 | + | 4.86975e7i | 0.828165 | + | 0.478141i | 0.853224 | − | 0.521544i | \(-0.174644\pi\) |
−0.0250587 | + | 0.999686i | \(0.507977\pi\) | |||||||
\(468\) | −4.40512e7 | + | 7.62988e7i | −0.429754 | + | 0.744356i | ||||
\(469\) | − | 1.00182e8i | − | 0.971118i | ||||||
\(470\) | 1.11130e8 | − | 1.92483e8i | 1.07038 | − | 1.85395i | ||||
\(471\) | 1.38710e7 | 0.132753 | ||||||||
\(472\) | − | 2.51264e8i | − | 2.38949i | ||||||
\(473\) | −9.27588e7 | − | 8.36085e6i | −0.876540 | − | 0.0790073i | ||||
\(474\) | −1.87463e8 | −1.76028 | ||||||||
\(475\) | − | 6.77437e7i | − | 0.632103i | ||||||
\(476\) | 1.56693e8 | + | 9.04668e7i | 1.45288 | + | 0.838819i | ||||
\(477\) | 9.97572e7 | 0.919155 | ||||||||
\(478\) | −2.89527e8 | − | 1.67158e8i | −2.65097 | − | 1.53054i | ||||
\(479\) | −9.55930e7 | + | 1.65572e8i | −0.869800 | + | 1.50654i | −0.00759931 | + | 0.999971i | \(0.502419\pi\) |
−0.862201 | + | 0.506567i | \(0.830914\pi\) | |||||||
\(480\) | −1.06853e8 | + | 6.16914e7i | −0.966188 | + | 0.557829i | ||||
\(481\) | − | 3.33490e7i | − | 0.299673i | ||||||
\(482\) | 4.18675e7 | + | 7.25166e7i | 0.373883 | + | 0.647584i | ||||
\(483\) | 4.48811e7 | − | 7.77363e7i | 0.398311 | − | 0.689895i | ||||
\(484\) | 6.61140e7 | 0.583119 | ||||||||
\(485\) | 5.72859e7 | + | 3.30740e7i | 0.502137 | + | 0.289909i | ||||
\(486\) | −1.04252e8 | − | 1.80570e8i | −0.908188 | − | 1.57303i | ||||
\(487\) | 8.46455e7 | + | 1.46610e8i | 0.732853 | + | 1.26934i | 0.955659 | + | 0.294476i | \(0.0951452\pi\) |
−0.222806 | + | 0.974863i | \(0.571521\pi\) | |||||||
\(488\) | −2.36477e8 | − | 4.09590e8i | −2.03484 | − | 3.52444i | ||||
\(489\) | 8.21771e7 | 0.702788 | ||||||||
\(490\) | 471861. | + | 817287.i | 0.00401075 | + | 0.00694682i | ||||
\(491\) | −1.42452e8 | + | 8.22450e7i | −1.20344 | + | 0.694808i | −0.961319 | − | 0.275437i | \(-0.911177\pi\) |
−0.242124 | + | 0.970245i | \(0.577844\pi\) | |||||||
\(492\) | −6.85398e7 | − | 3.95715e7i | −0.575503 | − | 0.332267i | ||||
\(493\) | 1.03795e7 | + | 5.99260e6i | 0.0866234 | + | 0.0500121i | ||||
\(494\) | −1.29637e8 | −1.07534 | ||||||||
\(495\) | 3.58554e7i | 0.295624i | ||||||||
\(496\) | −3.71221e8 | + | 6.42973e8i | −3.04220 | + | 5.26924i | ||||
\(497\) | −9.95022e7 | + | 1.72343e8i | −0.810519 | + | 1.40386i | ||||
\(498\) | 2.54320e7 | + | 4.40496e7i | 0.205917 | + | 0.356660i | ||||
\(499\) | −2.20603e6 | + | 1.27365e6i | −0.0177546 | + | 0.0102506i | −0.508851 | − | 0.860855i | \(-0.669930\pi\) |
0.491096 | + | 0.871105i | \(0.336596\pi\) | |||||||
\(500\) | 3.15416e8i | 2.52332i | ||||||||
\(501\) | −1.18078e8 | + | 6.81725e7i | −0.938981 | + | 0.542121i | ||||
\(502\) | −5.18350e7 | + | 2.99269e7i | −0.409743 | + | 0.236565i | ||||
\(503\) | −8.97203e7 | + | 5.18001e7i | −0.704996 | + | 0.407030i | −0.809206 | − | 0.587526i | \(-0.800102\pi\) |
0.104209 | + | 0.994555i | \(0.466769\pi\) | |||||||
\(504\) | 1.09723e8 | − | 1.90045e8i | 0.857046 | − | 1.48445i | ||||
\(505\) | 7.33726e7i | 0.569718i | ||||||||
\(506\) | 2.25954e8 | + | 1.30455e8i | 1.74409 | + | 1.00695i | ||||
\(507\) | 4.88071e7 | − | 2.81788e7i | 0.374506 | − | 0.216221i | ||||
\(508\) | 3.86716e8 | 2.94986 | ||||||||
\(509\) | −4.89545e7 | − | 8.47916e7i | −0.371227 | − | 0.642983i | 0.618528 | − | 0.785763i | \(-0.287729\pi\) |
−0.989755 | + | 0.142780i | \(0.954396\pi\) | |||||||
\(510\) | −5.45858e7 | − | 3.15151e7i | −0.411500 | − | 0.237579i | ||||
\(511\) | −1.90502e6 | + | 3.29959e6i | −0.0142770 | + | 0.0247284i | ||||
\(512\) | − | 5.46169e7i | − | 0.406927i | ||||||
\(513\) | 6.75568e7 | − | 1.17012e8i | 0.500400 | − | 0.866718i | ||||
\(514\) | −1.14692e8 | −0.844588 | ||||||||
\(515\) | − | 9.17527e7i | − | 0.671733i | ||||||
\(516\) | −1.90890e8 | − | 1.34411e8i | −1.38942 | − | 0.978332i | ||||
\(517\) | 2.32636e8 | 1.68347 | ||||||||
\(518\) | 1.35419e8i | 0.974293i | ||||||||
\(519\) | 4.21770e7 | + | 2.43509e7i | 0.301699 | + | 0.174186i | ||||
\(520\) | 1.45959e8 | 1.03806 | ||||||||
\(521\) | −1.33581e7 | − | 7.71230e6i | −0.0944565 | − | 0.0545345i | 0.452028 | − | 0.892004i | \(-0.350701\pi\) |
−0.546484 | + | 0.837469i | \(0.684034\pi\) | |||||||
\(522\) | 1.18490e7 | − | 2.05230e7i | 0.0833045 | − | 0.144288i | ||||
\(523\) | 3.74560e7 | − | 2.16252e7i | 0.261828 | − | 0.151167i | −0.363340 | − | 0.931657i | \(-0.618364\pi\) |
0.625168 | + | 0.780490i | \(0.285030\pi\) | |||||||
\(524\) | 3.96036e7i | 0.275258i | ||||||||
\(525\) | 3.10435e7 | + | 5.37688e7i | 0.214532 | + | 0.371580i | ||||
\(526\) | 7.09678e7 | − | 1.22920e8i | 0.487646 | − | 0.844627i | ||||
\(527\) | −1.85410e8 | −1.26678 | ||||||||
\(528\) | −2.28784e8 | − | 1.32088e8i | −1.55426 | − | 0.897352i | ||||
\(529\) | −3.40431e7 | − | 5.89643e7i | −0.229965 | − | 0.398311i | ||||
\(530\) | −1.34715e8 | − | 2.33333e8i | −0.904874 | − | 1.56729i | ||||
\(531\) | −3.38376e7 | − | 5.86084e7i | −0.226004 | − | 0.391450i | ||||
\(532\) | 3.79641e8 | 2.52138 | ||||||||
\(533\) | 1.73081e7 | + | 2.99785e7i | 0.114306 | + | 0.197983i | ||||
\(534\) | −1.13845e8 | + | 6.57286e7i | −0.747637 | + | 0.431649i | ||||
\(535\) | 4.99975e6 | + | 2.88660e6i | 0.0326503 | + | 0.0188506i | ||||
\(536\) | 3.87764e8 | + | 2.23875e8i | 2.51810 | + | 1.45383i | ||||
\(537\) | 1.86897e8 | 1.20692 | ||||||||
\(538\) | 4.54798e7i | 0.292060i | ||||||||
\(539\) | −493889. | + | 855441.i | −0.00315401 | + | 0.00546290i | ||||
\(540\) | −1.24002e8 | + | 2.14778e8i | −0.787496 | + | 1.36398i | ||||
\(541\) | 1.36950e8 | + | 2.37205e8i | 0.864911 | + | 1.49807i | 0.867135 | + | 0.498073i | \(0.165959\pi\) |
−0.00222366 | + | 0.999998i | \(0.500708\pi\) | |||||||
\(542\) | 1.63928e7 | − | 9.46436e6i | 0.102957 | − | 0.0594420i | ||||
\(543\) | − | 2.04048e8i | − | 1.27448i | ||||||
\(544\) | −2.58933e8 | + | 1.49495e8i | −1.60839 | + | 0.928603i | ||||
\(545\) | 6.62505e7 | − | 3.82498e7i | 0.409261 | − | 0.236287i | ||||
\(546\) | 1.02894e8 | − | 5.94059e7i | 0.632139 | − | 0.364966i | ||||
\(547\) | −3.66334e7 | + | 6.34509e7i | −0.223828 | + | 0.387682i | −0.955967 | − | 0.293473i | \(-0.905189\pi\) |
0.732139 | + | 0.681155i | \(0.238522\pi\) | |||||||
\(548\) | − | 2.26706e8i | − | 1.37759i | ||||||
\(549\) | −1.10319e8 | − | 6.36924e7i | −0.666701 | − | 0.384920i | ||||
\(550\) | −1.56289e8 | + | 9.02333e7i | −0.939375 | + | 0.542349i | ||||
\(551\) | 2.51478e7 | 0.150330 | ||||||||
\(552\) | 2.00590e8 | + | 3.47432e8i | 1.19259 | + | 2.06563i | ||||
\(553\) | −2.07950e8 | − | 1.20060e8i | −1.22965 | − | 0.709941i | ||||
\(554\) | 2.55169e8 | − | 4.41965e8i | 1.50071 | − | 2.59931i | ||||
\(555\) | − | 3.40218e7i | − | 0.199011i | ||||||
\(556\) | −9.42370e7 | + | 1.63223e8i | −0.548273 | + | 0.949637i | ||||
\(557\) | 1.01404e8 | 0.586799 | 0.293400 | − | 0.955990i | \(-0.405213\pi\) | ||||
0.293400 | + | 0.955990i | \(0.405213\pi\) | |||||||
\(558\) | 3.66604e8i | 2.11006i | ||||||||
\(559\) | 4.29123e7 | + | 9.26602e7i | 0.245667 | + | 0.530466i | ||||
\(560\) | −3.23289e8 | −1.84089 | ||||||||
\(561\) | − | 6.59728e7i | − | 0.373660i | ||||||
\(562\) | 3.29352e7 | + | 1.90152e7i | 0.185546 | + | 0.107125i | ||||
\(563\) | 4.67884e7 | 0.262188 | 0.131094 | − | 0.991370i | \(-0.458151\pi\) | ||||
0.131094 | + | 0.991370i | \(0.458151\pi\) | |||||||
\(564\) | 5.05028e8 | + | 2.91578e8i | 2.81500 | + | 1.62524i | ||||
\(565\) | −4.41154e7 | + | 7.64102e7i | −0.244594 | + | 0.423649i | ||||
\(566\) | 3.05408e8 | − | 1.76328e8i | 1.68435 | − | 0.972458i | ||||
\(567\) | 1.98483e7i | 0.108886i | ||||||||
\(568\) | −4.44712e8 | − | 7.70263e8i | −2.42680 | − | 4.20334i | ||||
\(569\) | −4.07982e7 | + | 7.06646e7i | −0.221465 | + | 0.383588i | −0.955253 | − | 0.295790i | \(-0.904417\pi\) |
0.733788 | + | 0.679378i | \(0.237750\pi\) | |||||||
\(570\) | −1.32252e8 | −0.714132 | ||||||||
\(571\) | 1.97450e8 | + | 1.13998e8i | 1.06059 | + | 0.612333i | 0.925596 | − | 0.378513i | \(-0.123564\pi\) |
0.134996 | + | 0.990846i | \(0.456898\pi\) | |||||||
\(572\) | 1.24530e8 | + | 2.15692e8i | 0.665405 | + | 1.15252i | ||||
\(573\) | 1.02582e8 | + | 1.77677e8i | 0.545265 | + | 0.944427i | ||||
\(574\) | −7.02824e7 | − | 1.21733e8i | −0.371630 | − | 0.643682i | ||||
\(575\) | 1.49488e8 | 0.786325 | ||||||||
\(576\) | 1.27002e8 | + | 2.19974e8i | 0.664575 | + | 1.15108i | ||||
\(577\) | 1.63107e8 | − | 9.41701e7i | 0.849075 | − | 0.490214i | −0.0112636 | − | 0.999937i | \(-0.503585\pi\) |
0.860339 | + | 0.509723i | \(0.170252\pi\) | |||||||
\(578\) | 1.84431e8 | + | 1.06481e8i | 0.955102 | + | 0.551429i | ||||
\(579\) | 5.54488e7 | + | 3.20134e7i | 0.285665 | + | 0.164929i | ||||
\(580\) | −4.61594e7 | −0.236579 | ||||||||
\(581\) | 6.51514e7i | 0.332197i | ||||||||
\(582\) | −1.20327e8 | + | 2.08412e8i | −0.610369 | + | 1.05719i | ||||
\(583\) | 1.41004e8 | − | 2.44226e8i | 0.711583 | − | 1.23250i | ||||
\(584\) | −8.51422e6 | − | 1.47471e7i | −0.0427471 | − | 0.0740401i | ||||
\(585\) | 3.40456e7 | − | 1.96562e7i | 0.170056 | − | 0.0981821i | ||||
\(586\) | 2.70080e8i | 1.34215i | ||||||||
\(587\) | 3.75175e7 | − | 2.16607e7i | 0.185490 | − | 0.107092i | −0.404380 | − | 0.914591i | \(-0.632513\pi\) |
0.589869 | + | 0.807499i | \(0.299179\pi\) | |||||||
\(588\) | −2.14436e6 | + | 1.23805e6i | −0.0105479 | + | 0.00608982i | ||||
\(589\) | −3.36912e8 | + | 1.94517e8i | −1.64881 | + | 0.951942i | ||||
\(590\) | −9.13905e7 | + | 1.58293e8i | −0.444985 | + | 0.770736i | ||||
\(591\) | − | 2.02783e8i | − | 0.982358i | ||||||
\(592\) | −2.85903e8 | − | 1.65066e8i | −1.37802 | − | 0.795598i | ||||
\(593\) | 7.99031e6 | − | 4.61321e6i | 0.0383177 | − | 0.0221227i | −0.480719 | − | 0.876875i | \(-0.659624\pi\) |
0.519036 | + | 0.854752i | \(0.326291\pi\) | |||||||
\(594\) | −3.59937e8 | −1.71738 | ||||||||
\(595\) | −4.03675e7 | − | 6.99185e7i | −0.191638 | − | 0.331926i | ||||
\(596\) | 1.21657e8 | + | 7.02385e7i | 0.574641 | + | 0.331769i | ||||
\(597\) | −4.97786e7 | + | 8.62191e7i | −0.233948 | + | 0.405210i | ||||
\(598\) | − | 2.86065e8i | − | 1.33771i | ||||||
\(599\) | −3.94924e7 | + | 6.84028e7i | −0.183752 | + | 0.318268i | −0.943155 | − | 0.332352i | \(-0.892158\pi\) |
0.759403 | + | 0.650620i | \(0.225491\pi\) | |||||||
\(600\) | −2.77489e8 | −1.28467 | ||||||||
\(601\) | 82367.9i | 0.000379432i | 1.00000 | 0.000189716i | \(6.03885e-5\pi\) | |||||
−1.00000 | 0.000189716i | \(0.999940\pi\) | ||||||||
\(602\) | −1.74252e8 | − | 3.76261e8i | −0.798709 | − | 1.72465i | ||||
\(603\) | 1.20597e8 | 0.550026 | ||||||||
\(604\) | − | 6.54054e8i | − | 2.96827i | ||||||
\(605\) | −2.55486e7 | − | 1.47505e7i | −0.115372 | − | 0.0666101i | ||||
\(606\) | −2.66937e8 | −1.19947 | ||||||||
\(607\) | −1.09940e7 | − | 6.34736e6i | −0.0491573 | − | 0.0283810i | 0.475220 | − | 0.879867i | \(-0.342368\pi\) |
−0.524377 | + | 0.851486i | \(0.675702\pi\) | |||||||
\(608\) | −3.13675e8 | + | 5.43302e8i | −1.39563 | + | 2.41730i | ||||
\(609\) | −1.99600e7 | + | 1.15239e7i | −0.0883709 | + | 0.0510210i | ||||
\(610\) | 3.44048e8i | 1.51576i | ||||||||
\(611\) | −1.27533e8 | − | 2.20894e8i | −0.559112 | − | 0.968411i | ||||
\(612\) | −1.08902e8 | + | 1.88623e8i | −0.475094 | + | 0.822887i | ||||
\(613\) | 5.50832e7 | 0.239132 | 0.119566 | − | 0.992826i | \(-0.461850\pi\) | ||||
0.119566 | + | 0.992826i | \(0.461850\pi\) | |||||||
\(614\) | −3.68926e8 | − | 2.13000e8i | −1.59380 | − | 0.920182i | ||||
\(615\) | 1.76573e7 | + | 3.05834e7i | 0.0759100 | + | 0.131480i | ||||
\(616\) | −3.10179e8 | − | 5.37246e8i | −1.32700 | − | 2.29843i | ||||
\(617\) | 2.17210e8 | + | 3.76218e8i | 0.924748 | + | 1.60171i | 0.791965 | + | 0.610566i | \(0.209058\pi\) |
0.132783 | + | 0.991145i | \(0.457609\pi\) | |||||||
\(618\) | 3.33806e8 | 1.41426 | ||||||||
\(619\) | −5.37800e7 | − | 9.31497e7i | −0.226751 | − | 0.392744i | 0.730092 | − | 0.683348i | \(-0.239477\pi\) |
−0.956843 | + | 0.290604i | \(0.906144\pi\) | |||||||
\(620\) | 6.18411e8 | − | 3.57040e8i | 2.59479 | − | 1.49810i | ||||
\(621\) | 2.58206e8 | + | 1.49075e8i | 1.07818 | + | 0.622488i | ||||
\(622\) | −5.97232e8 | − | 3.44812e8i | −2.48183 | − | 1.43288i | ||||
\(623\) | −1.68382e8 | −0.696357 | ||||||||
\(624\) | 2.89648e8i | 1.19211i | ||||||||
\(625\) | −9.06997e6 | + | 1.57096e7i | −0.0371506 | + | 0.0643467i | ||||
\(626\) | 2.25806e8 | − | 3.91107e8i | 0.920475 | − | 1.59431i | ||||
\(627\) | −6.92132e7 | − | 1.19881e8i | −0.280793 | − | 0.486347i | ||||
\(628\) | −1.12113e8 | + | 6.47284e7i | −0.452665 | + | 0.261346i | ||||
\(629\) | − | 8.24440e7i | − | 0.331289i | ||||||
\(630\) | −1.38247e8 | + | 7.98172e7i | −0.552886 | + | 0.319209i | ||||
\(631\) | −1.07504e8 | + | 6.20672e7i | −0.427893 | + | 0.247044i | −0.698448 | − | 0.715660i | \(-0.746126\pi\) |
0.270556 | + | 0.962704i | \(0.412793\pi\) | |||||||
\(632\) | 9.29404e8 | − | 5.36592e8i | 3.68174 | − | 2.12565i | ||||
\(633\) | −6.74088e7 | + | 1.16755e8i | −0.265770 | + | 0.460327i | ||||
\(634\) | − | 8.50266e7i | − | 0.333647i | ||||||
\(635\) | −1.49439e8 | − | 8.62789e7i | −0.583638 | − | 0.336964i | ||||
\(636\) | 6.12208e8 | − | 3.53459e8i | 2.37973 | − | 1.37394i | ||||
\(637\) | 1.08302e6 | 0.00419002 | ||||||||
\(638\) | −3.34963e7 | − | 5.80173e7i | −0.128984 | − | 0.223406i | ||||
\(639\) | −2.07462e8 | − | 1.19778e8i | −0.795125 | − | 0.459066i | ||||
\(640\) | 1.20425e8 | − | 2.08582e8i | 0.459385 | − | 0.795678i | ||||
\(641\) | 2.46684e8i | 0.936627i | 0.883562 | + | 0.468313i | \(0.155138\pi\) | ||||
−0.883562 | + | 0.468313i | \(0.844862\pi\) | |||||||
\(642\) | −1.05018e7 | + | 1.81896e7i | −0.0396878 | + | 0.0687413i | ||||
\(643\) | 1.95575e8 | 0.735665 | 0.367833 | − | 0.929892i | \(-0.380100\pi\) | ||||
0.367833 | + | 0.929892i | \(0.380100\pi\) | |||||||
\(644\) | 8.37741e8i | 3.13655i | ||||||||
\(645\) | 4.37780e7 | + | 9.45296e7i | 0.163146 | + | 0.352281i | ||||
\(646\) | −3.20483e8 | −1.18880 | ||||||||
\(647\) | 1.63445e8i | 0.603475i | 0.953391 | + | 0.301738i | \(0.0975667\pi\) | ||||
−0.953391 | + | 0.301738i | \(0.902433\pi\) | |||||||
\(648\) | −7.68244e7 | − | 4.43546e7i | −0.282341 | − | 0.163010i | ||||
\(649\) | −1.91314e8 | −0.699862 | ||||||||
\(650\) | 1.71357e8 | + | 9.89332e7i | 0.623968 | + | 0.360248i | ||||
\(651\) | 1.78274e8 | − | 3.08779e8i | 0.646167 | − | 1.11919i | ||||
\(652\) | −6.64198e8 | + | 3.83475e8i | −2.39638 | + | 1.38355i | ||||
\(653\) | 2.18471e8i | 0.784611i | 0.919835 | + | 0.392305i | \(0.128322\pi\) | ||||
−0.919835 | + | 0.392305i | \(0.871678\pi\) | |||||||
\(654\) | 1.39157e8 | + | 2.41026e8i | 0.497474 | + | 0.861650i | ||||
\(655\) | 8.83582e6 | − | 1.53041e7i | 0.0314429 | − | 0.0544608i | ||||
\(656\) | 3.42678e8 | 1.21388 | ||||||||
\(657\) | −3.97196e6 | − | 2.29321e6i | −0.0140058 | − | 0.00808626i | ||||
\(658\) | 5.17868e8 | + | 8.96974e8i | 1.81778 | + | 3.14849i | ||||
\(659\) | −1.22837e8 | − | 2.12759e8i | −0.429212 | − | 0.743417i | 0.567592 | − | 0.823310i | \(-0.307875\pi\) |
−0.996803 | + | 0.0798936i | \(0.974542\pi\) | |||||||
\(660\) | 1.27042e8 | + | 2.20044e8i | 0.441893 | + | 0.765381i | ||||
\(661\) | −3.08826e7 | −0.106933 | −0.0534663 | − | 0.998570i | \(-0.517027\pi\) | ||||
−0.0534663 | + | 0.998570i | \(0.517027\pi\) | |||||||
\(662\) | −6.69819e7 | − | 1.16016e8i | −0.230879 | − | 0.399893i | ||||
\(663\) | −6.26427e7 | + | 3.61668e7i | −0.214946 | + | 0.124099i | ||||
\(664\) | −2.52174e8 | − | 1.45593e8i | −0.861382 | − | 0.497319i | ||||
\(665\) | −1.46705e8 | − | 8.47004e7i | −0.498863 | − | 0.288019i | ||||
\(666\) | −1.63014e8 | −0.551824 | ||||||||
\(667\) | 5.54927e7i | 0.187007i | ||||||||
\(668\) | 6.36247e8 | − | 1.10201e9i | 2.13450 | − | 3.69706i | ||||
\(669\) | −1.54615e7 | + | 2.67802e7i | −0.0516386 | + | 0.0894407i | ||||
\(670\) | −1.62857e8 | − | 2.82077e8i | −0.541480 | − | 0.937871i | ||||
\(671\) | −3.11864e8 | + | 1.80055e8i | −1.03228 | + | 0.595988i | ||||
\(672\) | − | 5.74965e8i | − | 1.89467i | ||||||
\(673\) | 3.13802e8 | − | 1.81174e8i | 1.02946 | − | 0.594360i | 0.112632 | − | 0.993637i | \(-0.464072\pi\) |
0.916830 | + | 0.399277i | \(0.130739\pi\) | |||||||
\(674\) | 4.54060e8 | − | 2.62151e8i | 1.48297 | − | 0.856195i | ||||
\(675\) | −1.78597e8 | + | 1.03113e8i | −0.580713 | + | 0.335275i | ||||
\(676\) | −2.62990e8 | + | 4.55511e8i | −0.851331 | + | 1.47455i | ||||
\(677\) | − | 5.27995e7i | − | 0.170162i | −0.996374 | − | 0.0850812i | \(-0.972885\pi\) | ||
0.996374 | − | 0.0850812i | \(-0.0271150\pi\) | |||||||
\(678\) | −2.77988e8 | − | 1.60496e8i | −0.891943 | − | 0.514963i | ||||
\(679\) | −2.66953e8 | + | 1.54125e8i | −0.852757 | + | 0.492339i | ||||
\(680\) | 3.60834e8 | 1.14757 | ||||||||
\(681\) | 1.18767e7 | + | 2.05710e7i | 0.0376057 | + | 0.0651350i | ||||
\(682\) | 8.97522e8 | + | 5.18184e8i | 2.82938 | + | 1.63355i | ||||
\(683\) | 1.36124e8 | − | 2.35773e8i | 0.427239 | − | 0.740000i | −0.569387 | − | 0.822069i | \(-0.692819\pi\) |
0.996627 | + | 0.0820691i | \(0.0261528\pi\) | |||||||
\(684\) | 4.57002e8i | 1.42807i | ||||||||
\(685\) | −5.05796e7 | + | 8.76065e7i | −0.157363 | + | 0.272562i | ||||
\(686\) | 6.09176e8 | 1.88699 | ||||||||
\(687\) | − | 1.30105e8i | − | 0.401258i | ||||||
\(688\) | 1.00679e9 | + | 9.07470e7i | 3.09152 | + | 0.278655i | ||||
\(689\) | −3.09198e8 | −0.945320 | ||||||||
\(690\) | − | 2.91837e8i | − | 0.888368i | ||||||
\(691\) | 1.85895e8 | + | 1.07327e8i | 0.563423 | + | 0.325292i | 0.754518 | − | 0.656279i | \(-0.227871\pi\) |
−0.191095 | + | 0.981572i | \(0.561204\pi\) | |||||||
\(692\) | −4.54529e8 | −1.37165 | ||||||||
\(693\) | −1.44701e8 | − | 8.35433e7i | −0.434783 | − | 0.251022i | ||||
\(694\) | −1.93996e8 | + | 3.36011e8i | −0.580382 | + | 1.00525i | ||||
\(695\) | 7.28324e7 | − | 4.20498e7i | 0.216955 | − | 0.125259i | ||||
\(696\) | − | 1.03009e8i | − | 0.305527i | ||||||
\(697\) | 4.27885e7 | + | 7.41118e7i | 0.126365 | + | 0.218871i | ||||
\(698\) | −2.58640e8 | + | 4.47978e8i | −0.760554 | + | 1.31732i | ||||
\(699\) | −2.09944e8 | −0.614712 | ||||||||
\(700\) | −5.01819e8 | − | 2.89725e8i | −1.46303 | − | 0.844680i | ||||
\(701\) | 1.44259e7 | + | 2.49864e7i | 0.0418783 | + | 0.0725353i | 0.886205 | − | 0.463294i | \(-0.153332\pi\) |
−0.844327 | + | 0.535829i | \(0.819999\pi\) | |||||||
\(702\) | 1.97320e8 | + | 3.41769e8i | 0.570375 | + | 0.987919i | ||||
\(703\) | −8.64934e7 | − | 1.49811e8i | −0.248953 | − | 0.431199i | ||||
\(704\) | 7.18056e8 | 2.05798 | ||||||||
\(705\) | −1.30106e8 | − | 2.25350e8i | −0.371304 | − | 0.643118i | ||||
\(706\) | −5.70160e8 | + | 3.29182e8i | −1.62025 | + | 0.935453i | ||||
\(707\) | −2.96109e8 | − | 1.70959e8i | −0.837903 | − | 0.483763i | ||||
\(708\) | −4.15322e8 | − | 2.39786e8i | −1.17027 | − | 0.675654i | ||||
\(709\) | 3.56501e8 | 1.00028 | 0.500141 | − | 0.865944i | \(-0.333281\pi\) | ||||
0.500141 | + | 0.865944i | \(0.333281\pi\) | |||||||
\(710\) | 6.47007e8i | 1.80773i | ||||||||
\(711\) | 1.44525e8 | − | 2.50325e8i | 0.402100 | − | 0.696458i | ||||
\(712\) | 3.76281e8 | − | 6.51738e8i | 1.04249 | − | 1.80565i | ||||
\(713\) | −4.29233e8 | − | 7.43454e8i | −1.18420 | − | 2.05109i | ||||
\(714\) | 2.54371e8 | − | 1.46861e8i | 0.698832 | − | 0.403471i | ||||
\(715\) | − | 1.11134e8i | − | 0.304039i | ||||||
\(716\) | −1.51060e9 | + | 8.72145e8i | −4.11538 | + | 2.37602i | ||||
\(717\) | −3.38965e8 | + | 1.95701e8i | −0.919595 | + | 0.530929i | ||||
\(718\) | −4.91155e8 | + | 2.83568e8i | −1.32692 | + | 0.766098i | ||||
\(719\) | 9.40289e7 | − | 1.62863e8i | 0.252973 | − | 0.438163i | −0.711370 | − | 0.702818i | \(-0.751925\pi\) |
0.964343 | + | 0.264655i | \(0.0852582\pi\) | |||||||
\(720\) | − | 3.89167e8i | − | 1.04265i | ||||||
\(721\) | 3.70285e8 | + | 2.13784e8i | 0.987940 | + | 0.570388i | ||||
\(722\) | 3.49276e7 | − | 2.01655e7i | 0.0928020 | − | 0.0535792i | ||||
\(723\) | 9.80329e7 | 0.259392 | ||||||||
\(724\) | 9.52180e8 | + | 1.64922e9i | 2.50901 | + | 4.34574i | ||||
\(725\) | −3.32409e7 | − | 1.91917e7i | −0.0872287 | − | 0.0503615i | ||||
\(726\) | 5.36637e7 | − | 9.29483e7i | 0.140240 | − | 0.242902i | ||||
\(727\) | − | 3.34772e8i | − | 0.871257i | −0.900127 | − | 0.435629i | \(-0.856526\pi\) | ||
0.900127 | − | 0.435629i | \(-0.143474\pi\) | |||||||
\(728\) | −3.40085e8 | + | 5.89045e8i | −0.881442 | + | 1.52670i | ||||
\(729\) | −2.86141e8 | −0.738581 | ||||||||
\(730\) | 1.23873e7i | 0.0318425i | ||||||||
\(731\) | 1.06086e8 | + | 2.29071e8i | 0.271585 | + | 0.586432i | ||||
\(732\) | −9.02697e8 | −2.30149 | ||||||||
\(733\) | 1.99155e8i | 0.505685i | 0.967507 | + | 0.252843i | \(0.0813655\pi\) | ||||
−0.967507 | + | 0.252843i | \(0.918635\pi\) | |||||||
\(734\) | 7.36682e8 | + | 4.25323e8i | 1.86291 | + | 1.07555i | ||||
\(735\) | 1.10486e6 | 0.00278258 | ||||||||
\(736\) | −1.19889e9 | − | 6.92177e8i | −3.00708 | − | 1.73614i | ||||
\(737\) | 1.70460e8 | − | 2.95245e8i | 0.425814 | − | 0.737532i | ||||
\(738\) | 1.46539e8 | − | 8.46041e7i | 0.364572 | − | 0.210486i | ||||
\(739\) | − | 6.49415e8i | − | 1.60912i | −0.593870 | − | 0.804561i | \(-0.702400\pi\) | ||
0.593870 | − | 0.804561i | \(-0.297600\pi\) | |||||||
\(740\) | 1.58761e8 | + | 2.74982e8i | 0.391785 | + | 0.678592i | ||||
\(741\) | −7.58864e7 | + | 1.31439e8i | −0.186513 | + | 0.323050i | ||||
\(742\) | 1.25555e9 | 3.07341 | ||||||||
\(743\) | 2.54313e8 | + | 1.46828e8i | 0.620015 | + | 0.357966i | 0.776875 | − | 0.629655i | \(-0.216804\pi\) |
−0.156860 | + | 0.987621i | \(0.550137\pi\) | |||||||
\(744\) | 7.96771e8 | + | 1.38005e9i | 1.93471 | + | 3.35101i | ||||
\(745\) | −3.13413e7 | − | 5.42848e7i | −0.0757964 | − | 0.131283i | ||||
\(746\) | 1.64810e8 | + | 2.85459e8i | 0.396978 | + | 0.687586i | ||||
\(747\) | −7.84275e7 | −0.188151 | ||||||||
\(748\) | 3.07858e8 | + | 5.33226e8i | 0.735608 | + | 1.27411i | ||||
\(749\) | −2.32989e7 | + | 1.34516e7i | −0.0554485 | + | 0.0320132i | ||||
\(750\) | 4.43436e8 | + | 2.56018e8i | 1.05111 | + | 0.606857i | ||||
\(751\) | −2.88020e8 | − | 1.66289e8i | −0.679992 | − | 0.392593i | 0.119860 | − | 0.992791i | \(-0.461755\pi\) |
−0.799852 | + | 0.600197i | \(0.795089\pi\) | |||||||
\(752\) | −2.52499e9 | −5.93753 | ||||||||
\(753\) | 7.00741e7i | 0.164124i | ||||||||
\(754\) | −3.67259e7 | + | 6.36111e7i | −0.0856758 | + | 0.148395i | ||||
\(755\) | −1.45924e8 | + | 2.52748e8i | −0.339067 | + | 0.587281i | ||||
\(756\) | −5.77852e8 | − | 1.00087e9i | −1.33737 | − | 2.31639i | ||||
\(757\) | 4.26340e8 | − | 2.46148e8i | 0.982809 | − | 0.567425i | 0.0796917 | − | 0.996820i | \(-0.474606\pi\) |
0.903117 | + | 0.429395i | \(0.141273\pi\) | |||||||
\(758\) | − | 1.59053e8i | − | 0.365203i | ||||||
\(759\) | 2.64537e8 | − | 1.52730e8i | 0.605007 | − | 0.349301i | ||||
\(760\) | 6.55680e8 | − | 3.78557e8i | 1.49366 | − | 0.862364i | ||||
\(761\) | −2.12821e7 | + | 1.22872e7i | −0.0482903 | + | 0.0278804i | −0.523951 | − | 0.851749i | \(-0.675542\pi\) |
0.475660 | + | 0.879629i | \(0.342209\pi\) | |||||||
\(762\) | 3.13891e8 | − | 5.43676e8i | 0.709438 | − | 1.22878i | ||||
\(763\) | 3.56489e8i | 0.802550i | ||||||||
\(764\) | −1.65824e9 | − | 9.57388e8i | −3.71851 | − | 2.14688i | ||||
\(765\) | 8.41661e7 | − | 4.85933e7i | 0.187998 | − | 0.108541i | ||||
\(766\) | 9.21977e8 | 2.05132 | ||||||||
\(767\) | 1.04880e8 | + | 1.81657e8i | 0.232437 | + | 0.402593i | ||||
\(768\) | 1.56199e8 | + | 9.01817e7i | 0.344822 | + | 0.199083i | ||||
\(769\) | 3.91166e8 | − | 6.77519e8i | 0.860165 | − | 1.48985i | −0.0116044 | − | 0.999933i | \(-0.503694\pi\) |
0.871769 | − | 0.489917i | \(-0.162973\pi\) | |||||||
\(770\) | 4.51277e8i | 0.988487i | ||||||||
\(771\) | −6.71382e7 | + | 1.16287e8i | −0.146490 | + | 0.253727i | ||||
\(772\) | −5.97555e8 | −1.29875 | ||||||||
\(773\) | 7.59054e8i | 1.64337i | 0.569945 | + | 0.821683i | \(0.306965\pi\) | ||||
−0.569945 | + | 0.821683i | \(0.693035\pi\) | |||||||
\(774\) | 4.52934e8 | − | 2.09760e8i | 0.976814 | − | 0.452377i | ||||
\(775\) | 5.93786e8 | 1.27563 | ||||||||
\(776\) | − | 1.37768e9i | − | 2.94825i | ||||||
\(777\) | 1.37301e8 | + | 7.92710e7i | 0.292693 | + | 0.168986i | ||||
\(778\) | −9.86707e8 | −2.09532 | ||||||||
\(779\) | 1.55504e8 | + | 8.97802e7i | 0.328949 | + | 0.189919i | ||||
\(780\) | 1.39291e8 | − | 2.41260e8i | 0.293522 | − | 0.508395i | ||||
\(781\) | −5.86483e8 | + | 3.38606e8i | −1.23112 | + | 0.710790i | ||||
\(782\) | − | 7.07200e8i | − | 1.47884i | ||||||
\(783\) | −3.82775e7 | − | 6.62985e7i | −0.0797366 | − | 0.138108i | ||||
\(784\) | 5.36057e6 | − | 9.28478e6i | 0.0111240 | − | 0.0192674i | ||||
\(785\) | 5.77653e7 | 0.119415 | ||||||||
\(786\) | 5.56778e7 | + | 3.21456e7i | 0.114661 | + | 0.0661994i | ||||
\(787\) | 3.99704e8 | + | 6.92308e8i | 0.820001 | + | 1.42028i | 0.905681 | + | 0.423960i | \(0.139360\pi\) |
−0.0856801 | + | 0.996323i | \(0.527306\pi\) | |||||||
\(788\) | 9.46277e8 | + | 1.63900e9i | 1.93393 | + | 3.34966i | ||||
\(789\) | −8.30858e7 | − | 1.43909e8i | −0.169159 | − | 0.292993i | ||||
\(790\) | −7.80682e8 | −1.58341 | ||||||||
\(791\) | −2.05578e8 | − | 3.56072e8i | −0.415383 | − | 0.719464i | ||||
\(792\) | 6.46723e8 | − | 3.73386e8i | 1.30180 | − | 0.751592i | ||||
\(793\) | 3.41933e8 | + | 1.97415e8i | 0.685679 | + | 0.395877i | ||||
\(794\) | −7.15185e8 | − | 4.12912e8i | −1.42875 | − | 0.824891i | ||||
\(795\) | −3.15436e8 | −0.627783 | ||||||||
\(796\) | − | 9.29157e8i | − | 1.84226i | ||||||
\(797\) | 4.63571e7 | − | 8.02928e7i | 0.0915674 | − | 0.158599i | −0.816603 | − | 0.577199i | \(-0.804146\pi\) |
0.908171 | + | 0.418600i | \(0.137479\pi\) | |||||||
\(798\) | 3.08149e8 | − | 5.33729e8i | 0.606390 | − | 1.05030i | ||||
\(799\) | −3.15282e8 | − | 5.46085e8i | −0.618101 | − | 1.07058i | ||||
\(800\) | 8.29248e8 | − | 4.78767e8i | 1.61963 | − | 0.935091i | ||||
\(801\) | − | 2.02694e8i | − | 0.394406i | ||||||
\(802\) | −3.09987e8 | + | 1.78971e8i | −0.600924 | + | 0.346944i | ||||
\(803\) | −1.12285e7 | + | 6.48277e6i | −0.0216858 | + | 0.0125203i | ||||
\(804\) | 7.40100e8 | − | 4.27297e8i | 1.42404 | − | 0.822170i | ||||
\(805\) | 1.86906e8 | − | 3.23730e8i | 0.358290 | − | 0.620576i | ||||
\(806\) | − | 1.13629e9i | − | 2.17012i | ||||||
\(807\) | 4.61121e7 | + | 2.66228e7i | 0.0877392 | + | 0.0506563i | ||||
\(808\) | 1.32342e9 | − | 7.64077e8i | 2.50879 | − | 1.44845i | ||||
\(809\) | −5.63117e8 | −1.06354 | −0.531769 | − | 0.846889i | \(-0.678473\pi\) | ||||
−0.531769 | + | 0.846889i | \(0.678473\pi\) | |||||||
\(810\) | 3.22656e7 | + | 5.58856e7i | 0.0607133 | + | 0.105159i | ||||
\(811\) | 4.50617e8 | + | 2.60164e8i | 0.844783 | + | 0.487736i | 0.858887 | − | 0.512165i | \(-0.171156\pi\) |
−0.0141040 | + | 0.999901i | \(0.504490\pi\) | |||||||
\(812\) | 1.07552e8 | − | 1.86285e8i | 0.200886 | − | 0.347944i | ||||
\(813\) | − | 2.21609e7i | − | 0.0412396i | ||||||
\(814\) | −2.30415e8 | + | 3.99090e8i | −0.427206 | + | 0.739943i | ||||
\(815\) | 3.42223e8 | 0.632174 | ||||||||
\(816\) | 7.16055e8i | 1.31788i | ||||||||
\(817\) | 4.33094e8 | + | 3.04953e8i | 0.794174 | + | 0.559200i | ||||
\(818\) | 1.48151e9 | 2.70673 | ||||||||
\(819\) | 1.83196e8i | 0.333477i | ||||||||
\(820\) | −2.85431e8 | − | 1.64794e8i | −0.517678 | − | 0.298882i | ||||
\(821\) | 2.09796e8 | 0.379113 | 0.189556 | − | 0.981870i | \(-0.439295\pi\) | ||||
0.189556 | + | 0.981870i | \(0.439295\pi\) | |||||||
\(822\) | −3.18721e8 | − | 1.84014e8i | −0.573846 | − | 0.331310i | ||||
\(823\) | −1.75799e8 | + | 3.04493e8i | −0.315367 | + | 0.546232i | −0.979516 | − | 0.201369i | \(-0.935461\pi\) |
0.664148 | + | 0.747601i | \(0.268794\pi\) | |||||||
\(824\) | −1.65494e9 | + | 9.55480e8i | −2.95802 | + | 1.70781i | ||||
\(825\) | 2.11282e8i | 0.376271i | ||||||||
\(826\) | −4.25881e8 | − | 7.37648e8i | −0.755698 | − | 1.30891i | ||||
\(827\) | −2.95146e7 | + | 5.11208e7i | −0.0521820 | + | 0.0903819i | −0.890937 | − | 0.454128i | \(-0.849951\pi\) |
0.838755 | + | 0.544510i | \(0.183284\pi\) | |||||||
\(828\) | −1.00845e9 | −1.77649 | ||||||||
\(829\) | 8.47059e8 | + | 4.89050e8i | 1.48679 | + | 0.858399i | 0.999887 | − | 0.0150556i | \(-0.00479252\pi\) |
0.486905 | + | 0.873455i | \(0.338126\pi\) | |||||||
\(830\) | 1.05911e8 | + | 1.83443e8i | 0.185228 | + | 0.320824i | ||||
\(831\) | −2.98740e8 | − | 5.17432e8i | −0.520583 | − | 0.901675i | ||||
\(832\) | −3.93644e8 | − | 6.81812e8i | −0.683493 | − | 1.18384i | ||||
\(833\) | 2.67739e6 | 0.00463208 | ||||||||
\(834\) | 1.52981e8 | + | 2.64972e8i | 0.263718 | + | 0.456774i | ||||
\(835\) | −4.91732e8 | + | 2.83902e8i | −0.844635 | + | 0.487650i | ||||
\(836\) | 1.11883e9 | + | 6.45959e8i | 1.91490 | + | 1.10557i | ||||
\(837\) | 1.02563e9 | + | 5.92148e8i | 1.74910 | + | 1.00984i | ||||
\(838\) | −3.87845e8 | −0.659062 | ||||||||
\(839\) | − | 3.91723e8i | − | 0.663274i | −0.943407 | − | 0.331637i | \(-0.892399\pi\) | ||
0.943407 | − | 0.331637i | \(-0.107601\pi\) | |||||||
\(840\) | −3.46947e8 | + | 6.00929e8i | −0.585362 | + | 1.01388i | ||||
\(841\) | −2.90287e8 | + | 5.02792e8i | −0.488023 | + | 0.845280i | ||||
\(842\) | 3.96052e8 | + | 6.85983e8i | 0.663462 | + | 1.14915i | ||||
\(843\) | 3.85590e7 | − | 2.22621e7i | 0.0643641 | − | 0.0371606i | ||||
\(844\) | − | 1.25824e9i | − | 2.09284i | ||||||
\(845\) | 2.03255e8 | − | 1.17349e8i | 0.336877 | − | 0.194496i | ||||
\(846\) | −1.07975e9 | + | 6.23396e8i | −1.78326 | + | 1.02956i | ||||
\(847\) | 1.19057e8 | − | 6.87374e7i | 0.195931 | − | 0.113121i | ||||
\(848\) | −1.53043e9 | + | 2.65078e9i | −2.50972 | + | 4.34696i | ||||
\(849\) | − | 4.12872e8i | − | 0.674672i | ||||||
\(850\) | 4.23623e8 | + | 2.44579e8i | 0.689799 | + | 0.398256i | ||||
\(851\) | 3.30583e8 | − | 1.90862e8i | 0.536403 | − | 0.309693i | ||||
\(852\) | −1.69759e9 | −2.74482 | ||||||||
\(853\) | −8.11167e7 | − | 1.40498e8i | −0.130696 | − | 0.226373i | 0.793249 | − | 0.608898i | \(-0.208388\pi\) |
−0.923945 | + | 0.382525i | \(0.875055\pi\) | |||||||
\(854\) | −1.38847e9 | − | 8.01635e8i | −2.22927 | − | 1.28707i | ||||
\(855\) | 1.01960e8 | − | 1.76600e8i | 0.163129 | − | 0.282548i | ||||
\(856\) | − | 1.20240e8i | − | 0.191703i | ||||||
\(857\) | −1.99411e8 | + | 3.45390e8i | −0.316816 | + | 0.548741i | −0.979822 | − | 0.199873i | \(-0.935947\pi\) |
0.663006 | + | 0.748614i | \(0.269280\pi\) | |||||||
\(858\) | 4.04317e8 | 0.640118 | ||||||||
\(859\) | − | 4.01350e7i | − | 0.0633204i | −0.999499 | − | 0.0316602i | \(-0.989921\pi\) | ||
0.999499 | − | 0.0316602i | \(-0.0100794\pi\) | |||||||
\(860\) | −7.94954e8 | − | 5.59750e8i | −1.24982 | − | 0.880032i | ||||
\(861\) | −1.64567e8 | −0.257829 | ||||||||
\(862\) | 1.19764e9i | 1.86984i | ||||||||
\(863\) | −6.66112e8 | − | 3.84580e8i | −1.03637 | − | 0.598349i | −0.117567 | − | 0.993065i | \(-0.537510\pi\) |
−0.918803 | + | 0.394716i | \(0.870843\pi\) | |||||||
\(864\) | 1.90978e9 | 2.96103 | ||||||||
\(865\) | 1.75645e8 | + | 1.01408e8i | 0.271385 | + | 0.156684i | ||||
\(866\) | 8.49110e8 | − | 1.47070e9i | 1.30741 | − | 2.26449i | ||||
\(867\) | 2.15923e8 | − | 1.24663e8i | 0.331315 | − | 0.191285i | ||||
\(868\) | 3.32762e9i | 5.08832i | ||||||||
\(869\) | −4.08564e8 | − | 7.07653e8i | −0.622588 | − | 1.07835i | ||||
\(870\) | −3.74668e7 | + | 6.48945e7i | −0.0568970 | + | 0.0985485i | ||||
\(871\) | −3.73790e8 | −0.565683 | ||||||||
\(872\) | −1.37982e9 | − | 7.96640e8i | −2.08100 | − | 1.20147i | ||||
\(873\) | −1.85532e8 | − | 3.21351e8i | −0.278854 | − | 0.482988i | ||||
\(874\) | −7.41935e8 | − | 1.28507e9i | −1.11130 | − | 1.92483i | ||||
\(875\) | 3.27931e8 | + | 5.67993e8i | 0.489507 | + | 0.847850i | ||||
\(876\) | −3.25011e7 | −0.0483488 | ||||||||
\(877\) | 4.76846e8 | + | 8.25921e8i | 0.706934 | + | 1.22445i | 0.965989 | + | 0.258584i | \(0.0832557\pi\) |
−0.259055 | + | 0.965863i | \(0.583411\pi\) | |||||||
\(878\) | 1.21004e9 | − | 6.98616e8i | 1.78779 | − | 1.03218i | ||||
\(879\) | 2.73835e8 | + | 1.58099e8i | 0.403202 | + | 0.232789i | ||||
\(880\) | −9.52761e8 | − | 5.50077e8i | −1.39809 | − | 0.807189i | ||||
\(881\) | 5.98549e7 | 0.0875330 | 0.0437665 | − | 0.999042i | \(-0.486064\pi\) | ||||
0.0437665 | + | 0.999042i | \(0.486064\pi\) | |||||||
\(882\) | − | 5.29390e6i | − | 0.00771561i | ||||||
\(883\) | −2.09171e8 | + | 3.62295e8i | −0.303822 | + | 0.526235i | −0.976998 | − | 0.213247i | \(-0.931596\pi\) |
0.673176 | + | 0.739482i | \(0.264929\pi\) | |||||||
\(884\) | 3.37541e8 | − | 5.84638e8i | 0.488618 | − | 0.846311i | ||||
\(885\) | 1.06996e8 | + | 1.85322e8i | 0.154361 | + | 0.267361i | ||||
\(886\) | 1.84641e9 | − | 1.06603e9i | 2.65478 | − | 1.53274i | ||||
\(887\) | 1.03021e9i | 1.47624i | 0.674671 | + | 0.738118i | \(0.264285\pi\) | ||||
−0.674671 | + | 0.738118i | \(0.735715\pi\) | |||||||
\(888\) | −6.13650e8 | + | 3.54291e8i | −0.876358 | + | 0.505966i | ||||
\(889\) | 6.96390e8 | − | 4.02061e8i | 0.991167 | − | 0.572251i | ||||
\(890\) | −4.74104e8 | + | 2.73724e8i | −0.672517 | + | 0.388278i | ||||
\(891\) | −3.37718e7 | + | 5.84945e7i | −0.0477443 | + | 0.0826956i | ||||
\(892\) | − | 2.88602e8i | − | 0.406635i | ||||||
\(893\) | −1.14581e9 | − | 6.61536e8i | −1.60901 | − | 0.928964i | ||||
\(894\) | 1.97494e8 | − | 1.14023e8i | 0.276402 | − | 0.159580i | ||||
\(895\) | 7.78326e8 | 1.08566 | ||||||||
\(896\) | 5.61182e8 | + | 9.71996e8i | 0.780153 | + | 1.35127i | ||||
\(897\) | −2.90042e8 | − | 1.67456e8i | −0.401868 | − | 0.232019i | ||||
\(898\) | 4.50894e8 | − | 7.80972e8i | 0.622653 | − | 1.07847i | ||||
\(899\) | 2.20425e8i | 0.303376i | ||||||||
\(900\) | 3.48764e8 | − | 6.04077e8i | 0.478414 | − | 0.828637i | ||||
\(901\) | −7.64387e8 | −1.04505 | ||||||||
\(902\) | − | 4.78342e8i | − | 0.651806i | ||||||
\(903\) | −4.83495e8 | − | 4.35800e7i | −0.656643 | − | 0.0591867i | ||||
\(904\) | 1.83761e9 | 2.48742 | ||||||||
\(905\) | − | 8.49750e8i | − | 1.14643i | ||||||
\(906\) | −9.19521e8 | − | 5.30886e8i | −1.23645 | − | 0.713866i | ||||
\(907\) | −1.48221e9 | −1.98650 | −0.993252 | − | 0.115979i | \(-0.962999\pi\) | ||||
−0.993252 | + | 0.115979i | \(0.962999\pi\) | |||||||
\(908\) | −1.91987e8 | − | 1.10844e8i | −0.256457 | − | 0.148066i | ||||
\(909\) | 2.05796e8 | − | 3.56448e8i | 0.273996 | − | 0.474575i | ||||
\(910\) | 4.28498e8 | − | 2.47394e8i | 0.568624 | − | 0.328295i | ||||
\(911\) | − | 5.44712e7i | − | 0.0720463i | −0.999351 | − | 0.0360231i | \(-0.988531\pi\) | ||
0.999351 | − | 0.0360231i | \(-0.0114690\pi\) | |||||||
\(912\) | 7.51226e8 | + | 1.30116e9i | 0.990344 | + | 1.71533i | ||||
\(913\) | −1.10855e8 | + | 1.92007e8i | −0.145661 | + | 0.252292i | ||||
\(914\) | −5.09044e8 | −0.666679 | ||||||||
\(915\) | 3.48831e8 | + | 2.01398e8i | 0.455357 | + | 0.262900i | ||||
\(916\) | 6.07128e8 | + | 1.05158e9i | 0.789940 | + | 1.36822i | ||||
\(917\) | 4.11750e7 | + | 7.13173e7i | 0.0533981 | + | 0.0924883i | ||||
\(918\) | 4.87808e8 | + | 8.44908e8i | 0.630552 | + | 1.09215i | ||||
\(919\) | 5.98262e8 | 0.770805 | 0.385403 | − | 0.922749i | \(-0.374063\pi\) | ||||
0.385403 | + | 0.922749i | \(0.374063\pi\) | |||||||
\(920\) | 8.35350e8 | + | 1.44687e9i | 1.07277 | + | 1.85808i | ||||
\(921\) | −4.31921e8 | + | 2.49370e8i | −0.552874 | + | 0.319202i | ||||
\(922\) | 3.70304e8 | + | 2.13795e8i | 0.472460 | + | 0.272775i | ||||
\(923\) | 6.43029e8 | + | 3.71253e8i | 0.817759 | + | 0.472133i | ||||
\(924\) | −1.18404e9 | −1.50089 | ||||||||
\(925\) | 2.64032e8i | 0.333604i | ||||||||
\(926\) | −1.28400e9 | + | 2.22396e9i | −1.61709 | + | 2.80088i | ||||
\(927\) | −2.57348e8 | + | 4.45740e8i | −0.323059 | + | 0.559554i | ||||
\(928\) | 1.77727e8 | + | 3.07833e8i | 0.222388 | + | 0.385186i | ||||
\(929\) | 3.39213e8 | − | 1.95845e8i | 0.423083 | − | 0.244267i | −0.273312 | − | 0.961925i | \(-0.588119\pi\) |
0.696396 | + | 0.717658i | \(0.254786\pi\) | |||||||
\(930\) | − | 1.15922e9i | − | 1.44117i | ||||||
\(931\) | 4.86514e6 | − | 2.80889e6i | 0.00602902 | − | 0.00348086i | ||||
\(932\) | 1.69688e9 | − | 9.79693e8i | 2.09606 | − | 1.21016i | ||||
\(933\) | −6.99211e8 | + | 4.03690e8i | −0.860921 | + | 0.497053i | ||||
\(934\) | −7.37804e8 | + | 1.27791e9i | −0.905524 | + | 1.56841i | ||||
\(935\) | − | 2.74741e8i | − | 0.336116i | ||||||
\(936\) | −7.09077e8 | − | 4.09386e8i | −0.864701 | − | 0.499235i | ||||
\(937\) | −9.21333e8 | + | 5.31932e8i | −1.11995 | + | 0.646602i | −0.941388 | − | 0.337327i | \(-0.890477\pi\) |
−0.178560 | + | 0.983929i | \(0.557144\pi\) | |||||||
\(938\) | 1.51783e9 | 1.83914 | ||||||||
\(939\) | −2.64363e8 | − | 4.57890e8i | −0.319303 | − | 0.553050i | ||||
\(940\) | 2.10317e9 | + | 1.21427e9i | 2.53216 | + | 1.46194i | ||||
\(941\) | −6.36329e8 | + | 1.10215e9i | −0.763682 | + | 1.32274i | 0.177258 | + | 0.984164i | \(0.443277\pi\) |
−0.940940 | + | 0.338572i | \(0.890056\pi\) | |||||||
\(942\) | 2.10156e8i | 0.251414i | ||||||||
\(943\) | −1.98115e8 | + | 3.43145e8i | −0.236256 | + | 0.409207i | ||||
\(944\) | 2.07648e9 | 2.46838 | ||||||||
\(945\) | 5.15691e8i | 0.611074i | ||||||||
\(946\) | 1.26673e8 | − | 1.40536e9i | 0.149627 | − | 1.66003i | ||||
\(947\) | 3.08642e8 | 0.363417 | 0.181709 | − | 0.983352i | \(-0.441837\pi\) | ||||
0.181709 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(948\) | − | 2.04832e9i | − | 2.40421i | ||||||
\(949\) | 1.23111e7 | + | 7.10781e6i | 0.0144045 | + | 0.00831644i | ||||
\(950\) | 1.02637e9 | 1.19710 | ||||||||
\(951\) | −8.62086e7 | − | 4.97726e7i | −0.100233 | − | 0.0578694i | ||||
\(952\) | −8.40746e8 | + | 1.45621e9i | −0.974437 | + | 1.68778i | ||||
\(953\) | 8.04877e8 | − | 4.64696e8i | 0.929931 | − | 0.536896i | 0.0431414 | − | 0.999069i | \(-0.486263\pi\) |
0.886790 | + | 0.462173i | \(0.152930\pi\) | |||||||
\(954\) | 1.51139e9i | 1.74073i | ||||||||
\(955\) | 4.27199e8 | + | 7.39931e8i | 0.490479 | + | 0.849535i | ||||
\(956\) | 1.82646e9 | − | 3.16352e9i | 2.09043 | − | 3.62074i | ||||
\(957\) | −7.84319e7 | −0.0894863 | ||||||||
\(958\) | −2.50854e9 | − | 1.44830e9i | −2.85314 | − | 1.64726i | ||||
\(959\) | −2.35702e8 | − | 4.08247e8i | −0.267243 | − | 0.462879i | ||||
\(960\) | −4.01586e8 | − | 6.95567e8i | −0.453905 | − | 0.786186i | ||||
\(961\) | −1.26122e9 | − | 2.18450e9i | −1.42109 | − | 2.46140i | ||||
\(962\) | 5.05261e8 | 0.567532 | ||||||||
\(963\) | −1.61927e7 | − | 2.80466e7i | −0.0181318 | − | 0.0314052i | ||||
\(964\) | −7.92353e8 | + | 4.57465e8i | −0.884479 | + | 0.510654i | ||||
\(965\) | 2.30915e8 | + | 1.33319e8i | 0.256962 | + | 0.148357i | ||||
\(966\) | 1.17776e9 | + | 6.79982e8i | 1.30655 | + | 0.754338i | ||||
\(967\) | 4.67762e8 | 0.517303 | 0.258652 | − | 0.965971i | \(-0.416722\pi\) | ||||
0.258652 | + | 0.965971i | \(0.416722\pi\) | |||||||
\(968\) | 6.14425e8i | 0.677397i | ||||||||
\(969\) | −1.87603e8 | + | 3.24939e8i | −0.206191 | + | 0.357133i | ||||
\(970\) | −5.01095e8 | + | 8.67923e8i | −0.549042 | + | 0.950968i | ||||
\(971\) | 8.08546e8 | + | 1.40044e9i | 0.883176 | + | 1.52971i | 0.847791 | + | 0.530331i | \(0.177932\pi\) |
0.0353851 | + | 0.999374i | \(0.488734\pi\) | |||||||
\(972\) | 1.97300e9 | − | 1.13911e9i | 2.14846 | − | 1.24042i | ||||
\(973\) | 3.91905e8i | 0.425444i | ||||||||
\(974\) | −2.22125e9 | + | 1.28244e9i | −2.40393 | + | 1.38791i | ||||
\(975\) | 2.00617e8 | − | 1.15826e8i | 0.216448 | − | 0.124966i | ||||
\(976\) | 3.38491e9 | − | 1.95428e9i | 3.64081 | − | 2.10202i | ||||
\(977\) | 4.77227e8 | − | 8.26581e8i | 0.511730 | − | 0.886343i | −0.488177 | − | 0.872745i | \(-0.662338\pi\) |
0.999908 | − | 0.0135985i | \(-0.00432868\pi\) | |||||||
\(978\) | 1.24504e9i | 1.33097i | ||||||||
\(979\) | −4.96237e8 | − | 2.86502e8i | −0.528860 | − | 0.305338i | ||||
\(980\) | −8.93009e6 | + | 5.15579e6i | −0.00948807 | + | 0.00547794i | ||||
\(981\) | −4.29132e8 | −0.454552 | ||||||||
\(982\) | −1.24607e9 | − | 2.15826e9i | −1.31586 | − | 2.27913i | ||||
\(983\) | −1.15292e9 | − | 6.65636e8i | −1.21377 | − | 0.700771i | −0.250192 | − | 0.968196i | \(-0.580494\pi\) |
−0.963579 | + | 0.267425i | \(0.913827\pi\) | |||||||
\(984\) | 3.67754e8 | − | 6.36969e8i | 0.385987 | − | 0.668549i | ||||
\(985\) | − | 8.44483e8i | − | 0.883654i | ||||||
\(986\) | −9.07923e7 | + | 1.57257e8i | −0.0947149 | + | 0.164051i | ||||
\(987\) | 1.21259e9 | 1.26114 | ||||||||
\(988\) | − | 1.41648e9i | − | 1.46872i | ||||||
\(989\) | −6.72931e8 | + | 9.55693e8i | −0.695635 | + | 0.987938i | ||||
\(990\) | −5.43236e8 | −0.559864 | ||||||||
\(991\) | 6.88485e8i | 0.707414i | 0.935356 | + | 0.353707i | \(0.115079\pi\) | ||||
−0.935356 | + | 0.353707i | \(0.884921\pi\) | |||||||
\(992\) | −4.76214e9 | − | 2.74942e9i | −4.87828 | − | 2.81648i | ||||
\(993\) | −1.56839e8 | −0.160179 | ||||||||
\(994\) | −2.61112e9 | − | 1.50753e9i | −2.65869 | − | 1.53500i | ||||
\(995\) | −2.07301e8 | + | 3.59056e8i | −0.210442 | + | 0.364496i | ||||
\(996\) | −4.81308e8 | + | 2.77884e8i | −0.487131 | + | 0.281245i | ||||
\(997\) | − | 4.84420e8i | − | 0.488806i | −0.969674 | − | 0.244403i | \(-0.921408\pi\) | ||
0.969674 | − | 0.244403i | \(-0.0785920\pi\) | |||||||
\(998\) | −1.92968e7 | − | 3.34230e7i | −0.0194130 | − | 0.0336243i | ||||
\(999\) | −2.63303e8 | + | 4.56055e8i | −0.264095 | + | 0.457426i |
(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 | 43.7.d.a.37.21 | yes | 42 | |
43.7 | odd | 6 | inner | 43.7.d.a.7.1 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.d.a.7.1 | ✓ | 42 | 43.7 | odd | 6 | inner | |
43.7.d.a.37.21 | yes | 42 | 1.1 | even | 1 | trivial |